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All Textbook Solutions for College Physics

Suppose a parachutist lands on a high-voltage wire and grabs the wire as she prepares to be rescued. Will she be electrocuted? If the wire then breaks, should she continue to hold onto the wire as she falls to the ground?A ski resort consists of a few chairlifts and several interconnected downhill runs on the side of a mountain, with a lodge at the bottom. The lifts are analogous to batteries, and the runs are analogous to resistors. Describe how two runs can be in series. Describe how three runs can be in parallel. Sketch a junction of one lift and two runs. One of the skiers is carrying an altimeter. State Kirchhoffs junction rule and Kirchhoffs loop rule for ski resorts.Embodied in Kirchhoffs rules are two conservation laws. What are they?Why is it dangerous to turn on a light when you are in a bathtub?A battery haring an emf of 9.00 V delivers 117 mA when connected to a 72.0- load. Determine the internal resistance of the battery.2P A battery with an emf of 12.0 V has a terminal voltage of 11.5 V when the current is 3.00 A (a) Calculate the batterys internal resistance r. (b) Find the load resistance R.A battery with a 0.100- internal resistance supplies 15.0 W of total power with a 9.00 V terminal voltage. Determine (a) the current I and (b) the power delivered to the load resistor.Two resistors, R1 and R2 are connected in series. (a) If R1 = 2.00 and R2 = 4.00 , calculate the single resistance equivalent to the series combination. (b) Repeat the calculation for a parallel combination of R1 and R2.Three 9.0- resistors are connected in series with a 12-V battery. Find (a) the equivalent resistance of the circuit and (b) the current in each resistor. (c) Repeat for the case in which all three resistors are connected in parallel across the battery.(a) Find the equivalent resistance between points a and b in Figure P18.7. (b) Calculate the current in each resistor if a potential difference of 34.0 V is applied between points a and b. Figure P18.7 Consider the combination of resistors shown in Figure P18.8. (a) Find the equivalent resistance between point a and b. (b) If a voltage of 35.0 V is applied between points a and b, find the current in each resistor. Figure P18.8 9P Consider the circuit shown in Figure P18.10. (a) Calculate the equivalent resistance of the 10.0- and 5.00- resistors connected in parallel. (b) Using the result of part (a), calculate the combined resistance of the 10.0-, 5.00-, and 4.00- resistors. (c) Calculate the equivalent resistance of the combined resistance found in part (b) and the parallel 3.00- resistor. (d) Combine the equivalent resistance found in part (c) with the 2.00- resistor. (e) Calculate the total current in the circuit. (f) What is the voltage drop across the 2.00- resistor? (g) Subtracting the result of part (f) from the battery voltage, find the voltage across the 3.00- resistor. (h) Calculate the current in the 3.00- resistor. Figure P18.10 Consider the circuit shown in Figure P18.11. Find (a) the potential difference between points a and b and (b) the current in the 20.0- resistor. Figure P18.11 Four resistors are connected to a battery as shown in Figure P18.12. (a) Determine the potential difference across each resistor in terms of . (b) Determine the current in each resistor in terms of I. Figure P18.12 The resistance between terminals a and b in Figure P18.13 is 75 . If the resistors labeled R have the same value, determine R. Figure P18.13 A battery with = 6.00 V and no internal resistance supplies current to the circuit shown in Figure P18.14. When the double-throw switch S is open as shown in the figure, the current in the battery is 1.00 mA. When the switch is closed in position a, the current in the battery is 1.20 mA. When the switch is closed in position b, the current in the battery is 2.00 mA. Find the resistances (a) R1, (b) R2, and (c) R3. Figure P18.14 Find the current in the 12- resistor in Figure P18.15. Figure P18.15 (a) Is it possible to reduce the circuit shown in Figure P18.16 to a single equivalent resistor connected across the battery? Explain. (b) Find the current in the 2.00- resistor. (c) Calculate the power delivered by the battery to the circuit. Figure P18.16 (a) You need a 45- resistor, but the stockroom has only 20.- and 50.- resistors. How can the desired resistance be achieved under these circumstances? (b) What can you do if you need a 35- resistor?(a) Find the current in each resistor of Figure P18.18 by using the rules for resistors in series and parallel. (b) Write three independent equations for the three currents using Kirchhoffs laws: one with the node rule; a second using the loop rule through the battery, the 6.0- resistor, and the 24.0- resistor; and the third using the loop rule through the 12.0- and 24.0- resistors. Solve to check the answers found in part (a). Figure Pl8.18 Figure P18.19 shows a Wheatstone bridge, a circuit used to precisely measure an unknown resistance R by varying Rvar until the ammeter reads zero current and the bridge is said to be balanced. If the bridge is balanced with Rvar = 9.00 , find (a) the value of the unknown resistance Rand (b) the current in the 1.00 resistor. (Hint: With the bridge balanced, the wire through the ammeter can effectively be removed from the circuit, leaving two pairs of resistors in parallel.) Figure Pl8.19 For the circuit shown in Figure P18.20, calculate (a) the current in the 2.00- resistor and (b) the potential difference between points a and b, V= Vb Va. Figure P18.20 Taking R = 1.00 k and = 250 V in Figure P18.21, determine the direction and magnitude of the current in the horizontal wire between a and e. Figure P18.21 In the circuit of Figure P18.22, the current I1 is 3.0 A and the values of and R are unknown. What are the currents I2 and I3? Figure P18.22 In the circuit of Figure P18.23, determine (a) the current in each resistor, (b) the potential difference across the 2.00 102- resistor, and (c) the power delivered by each battery. Figure P18.23 Four resistors are connected to a battery with a terminal voltage of 12 V, as shown in Figure P18.24. (a) How would you reduce the circuit to an equivalent single resistor connected to the battery? Use this procedure to find the equivalent resistance of the circuit. (b) Find the current delivered by the battery to this equivalent resistance. (c) Determine the power delivered by the battery. (d) Determine the power delivered to the 50.0- resistor. Figure P18.24 Using Kirchhoffs rules (a) find the current in each resistor shown in Figure P18.25 and (b) find the potential difference between point c and f. Figure P18.25 Figure P18.26 shows a voltage divider, a circuit used to obtain a desired voltage Vout from a source voltage . Determine the required value of R2 if = 5.00 V, Vout = 1.50 V and R1 = 1.00 103 (Hint: Use Kirchhoff's loop rule, substituting Vout = IR2, to find the current. Then solve Ohms law for R2. Figure P18.26 (a) Can the circuit shown in Figure P18.27 be reduced to a single resistor connected to the batteries? Explain. (b) Calculate each of the unknown currents I1, I2, and I3 for the circuit. Figure P18.27 A dead battery is charged by connecting it to the live battery of another car with jumper cables (Fig. P18.28). Determine the current in (a) the starter and in (b) the dead battery. Figure P18.28 (a) Can the circuit shown in Figure P18.29 be reduced to a single resistor connected to the batteries? Explain. (b) Find the magnitude of the current and its direction in each resistor. Figure P18.29 For the circuit shown in Figure P18.30, use Kirchhoffs rules to obtain equations for (a) the upper loop, (b) the lower loop, and (c) the node on the left side. In Figure P18.29 each case suppresses units for clarity and simplify, combining like terms. (d) Solve the node equation for I36. (e) Using the equation found in (d), eliminate I36 from the equation found in part (b). (f) Solve the equations found in part (a) and part (e) simultaneously for the two unknowns for I18 and I12, respectively. (g) Substitute the answers found in part (f) into the node equation found in part (d), solving for I36. (h) What is the significance of the negative answer for I12? Figure P18.30 Find the potential difference across each resistor in Figure P18.31. Figure P18.31 Show that = RC has units of time.Consider the series RC circuit shown in Figure 18.17 for which R = 75.0 k, C = 25.0 F, and = 12.0 V. Find (a) the time constant of the circuit and (b) the charge on the capacitor one time constant after the switch is closed.An uncharged capacitor and a resistor are connected in series to a source of emf. If = 9.00 V, C = 20.0 F, and R = 1.00 102 , find (a) the time constant of the circuit, (b) the maximum charge on the capacitor, and (c) the charge on the capacitor after one time constant.Consider a series RC circuit as in Figure P18.35 for which R = 1.00 M, C = 5.00 F, and = 30.0 V. Find (a) the time constant of the circuit and (b) the maximum charge on the capacitor after the switch is thrown closed. (c) Find the current in the resistor 10.0 s after the switch is closed. Figure P18.35 Problem 35 and 38.The RC charging circuit in a camera flash unit has a voltage source of 275 V and a capacitance of 125 F. (a) Find its resistance R if the capacitor charges to 90.0% of its final value in 15.0 s. (b) Find the average current delivered to the flash bulb if the capacitor discharges 90.0% of its full charge in 1.00 ms.Figure P18.37 shows a simplified model of a cardiac defibrillator, a device used to patients in ventricular fibrillation. When the switch S is toggled to the left, the capacitor C charges through the resistor R .When the switch is toggled to the right, the capacitor discharges current through the patients torso, modeled as the resistor Rtorso, allowing the hearts normal rhythm to be reestablished. (a) If the capacitor is initially uncharged with C = 8.00 F and = 1250 V, find the value of R required to charge the capacitor to a voltage of 775 V in 1.50 s. (b) If the capacitor is then discharged across the patients torso with, Rtorso = 1250 , calculate the voltage across the capacitor after 5.00 ms. Figure P18.37 The capacitor in Figure P18.35 is uncharged for t 0. If = 9.00 V, R = 55.0 , and C = 2.00 F, use Kirchhoffs loop rule to find the current through the resistor at the times: (a) t = 0, when the switch is closed, and (b) t = , one time constant after the switch is closed.What minimum number of 75-W light bulbs must be connected in parallel to a single 120-V household circuit to trip a 30.0-A circuit breaker?A 1 150-W toaster and an 825-W microwave oven are connected in parallel to the same 20.0-A, 120-V circuit. (a) Find the toasters resistance R. (b) If the microwave fails and is replaced, what maximum power rating can be used without tripping the 20.0-A circuit breaker?41P 42P Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed pulse duration = 50.0 m/s 2.0 103 s = 0.10 m). In the resting state, the outer surface of the axon wall is charged positively with K+ ions and the inner wall has an equal and opposite charge of negative organic ions, as shown in Figure P18.43. Model the axon as a parallel-plate capacitor and take C = 0A/d and Q = C V to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.0 108 m, axon radius r = 1.0 101 m, and cell-wall dielectric constant = 3.0. (a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 102 V? Is this a large charge per unit area? Hint: Calculate the charge per unit area in terms of electronic charge e per squared (2). An atom has a cross section of about 1 2 (1 = 1010 m). (b) How much positive charge must flow through the cell membrane to reach the excited state of + 3.0 102 V from the resting state of 7.0 102 V? How many sodium ions (Na+) is this? (c) If it takes 2.0 ms for the Na+ ions to enter the axon, what is the average current in the axon wall in this process? (d) How much energy does it take to raise the potential of the inner axon wall to + 3.0 102 V, starting from the resting potential of 7.0 102 V? Figure P18.43 Problem 43 and 44.Consider the model of the axon as a capacitor from Problem 43 and Figure P18.43. (a) How much energy does it take to restore the inner wall of the axon to 7.0 102 V, starting from +3.0 102 V? (b) Find the average current in the axon wall during this process.45P How many different resistance values can be constructed from a 2.0-, a 4.0-, and a 6.0- resistor? Show how you would get each resistance value either individually or by combining them.(a) Calculate the potential difference between points a and b in Figure P18.47 and (b) identify which point is at the higher potential. Figure P18.47 For the circuit shown in Figure P18.48, the voltmeter reads 6.0 V and the ammeter reads 3.0 m.A. Find (a) the value of R,(b) the emf of the battery and (c) the voltage across the 3.0-k resistor.(d) What assumptions did you have to make to solve this problem?Figure P18.49 shows separate series and parallel circuits. (a) What is the ratio Vseries/Vparallel? (b) What is the ratio of the power dissipated by the resistors in the series to the parallel circuit, Pseries/Pparallel? Figure P18.49 Three 60.0-W, 120-V lightbulbs are connected across a 120-V power source, as shown in Figure P18.50. Find (a) the total power delivered to the three bulbs and (b) the potential difference across each. Assume the resistance of each bulb is constant (even though, in reality, the resistance increases markedly with current). Figure P18.50 When two unknown resistors are connected in series with a battery, the battery delivers 225 W and carries a total current of 5.00 A. For the same total current, 50.0 W is delivered when the resistors are connected in parallel. Determine the value of each resistor.The circuit in Figure P18.52a consists of three resistors and one battery with no internal resistance. (a) Find the current in the 5.00- resistor. (b) Find the power delivered to the 5.00- resistor. (c) In each of the cir circuits in Figures P18.52b, P18.52c, and P18.52d, an additional 15.0-V battery has been inserted into the circuit. Which diagram or diagrams represent a circuit that requires the use of Kirchhoffs rules to find the currents? Explain why. (d) In which of these three new circuits is the smallest amount of power delivered to the 10.0- resistor? (You need not calculate the power in each circuit if you explain your answer.) Figure P18.52 A circuit consists of three identical lamps, each of resistance R, connected to a battery as in Figure P18.53. (a) Calculate an expression for the equivalent resistance of the circuit when the switch is open. Repeat the calculation when the switch is closed. (b) Write an expression for the power supplied by the battery when the switch is open. Repeat the calculation when the switch is closed. (c) Using the results already obtained, explain what happens to the brightness of the lamps when the switch is closed. Figure P18.53 The resistance between points a and b in Figure P18.54 drops to one-half its original value when switch S is closed. Determine the value of R. Figure P18.54 The circuit in Figure P18.55 has been connected for several seconds. Find the current (a) in the 4.00-V battery,(b) in the 3.00- resistor,(c)in the 8.00-V battery, and (d)in the 3.00-V battery.(e)Find the charge on the capacitor.56AP The student engineer of a campus radio station wishes to verify the effectiveness of the lightning rod on the antenna mast (fig. P18.57). the unknown resistance Rx is between points C and E. point E is a true ground but is inaccessible for direct measurement because the stratum in which it is located is several meters below Earths Surface.Two identical rods are driven into the ground at A and B, introducing an unknown resistance Ry The procedure for the unknown resistance Rx is as follows. Measure resistsnce R1 between points A and B Then Connect A and B with a heavy conducting wire and measure resistance R2 between points A and C. (a) Derive a formula For Rx in terms of the observable resistances R1 and R2 (b) A satisfactory ground resistance would be Rx2.0 Is the grounding of the sation adequate if measurements give R1=13andR2=6.0?The resistor R in Figure P18.58 dissipates 20 W of power. Determine the value of R. Figure P18.58 A voltage V is applied to a series configuration of n resistors, each of resistance R. The circuit components are reconnected in a parallel configuration, and voltage V is again applied. Show that the power consumed by the series configuration is 1/n2 times the power consumed by the parallel configuration.For the network in Figure P18.60, show that the resistance between points a and b is Rab=2717. (Hint: Connect a battery with emf across points a and b and determine /I, where I is the current in the battery.) Figure P18.60 A battery with an internal resistance of 10.0 produces an open circuit voltage of 12.0 V. A variable load resistance with a range from 0 to 30.0 is connected across the battery. (Note: A battery has a resistance that depends on the condition of its chemicals and that increases as the battery ages. This internal resistance can be represented in a simple circuit diagram as a resistor in series with the battery.) (a) Graph the power dissipated in the load resistor as a function of the load resistance. (b) With your graph, demonstrate the following important theorem: The power delivered to a load is a maximum if the load resistance equals the internal resistance of the source.The circuit in Figure P18.62 contains two resistors, R1 = 2.0 k and R2 = 3.0 k, and two capacitors, C1 = 2.0 F and C2 = 3.0 F, connected to a battery with emf = 120 V. If there are no charges on the capacitors before switch S is dosed, determine the charges q1 and q2 on capacitors C1 and C2, respectively, as functions of time, after the switch is closed. Hint: First reconstruct the circuit so that it becomes a simple RC circuit containing a single resistor and single capacitor in series, connected to the battery, and then determine the total charge q stored in the circuit. Figure P18.62 An electric eel generates electric currents through its highly specialized Hunters organ, in which thousands of disk-shaped cells called electrocytes are lined up in series, very much in the same way batteries are lined up inside a flashlight. When activated, each electrocyte can maintain a potential difference of about 150 mV at a current of 1.0 A for about 2.0 ms. Suppose a grown electric eel has 4.0 103 electrocytes and can deliver up to 3.00 102 shocks in rapid series over about 1.0 s. (a) What maximum electrical power can an electric eel generate? (b) Approximately how much energy does it release in one shock? (c) How high would a mass of 1.0 kg have to be lifted so that its gravitational potential energy equals the energy released in 3.00 102 such shocks?In Figure P18.64, R1 = 0.100 , R2 = 1.00 , and R3 = 10.0 . Find the equivalent resistance of the circuit and the current in each resistor when a 5.00-V power supply is connected between (a) points A and B, (b) points A and C, and (c) points A and D. Figure P18.64 What are the expected readings of the ammeter and voltmeter for the circuit in Figure P18.65? Figure P18.65 Consider the two arrangements of batteries and bulbs shown in Figure P18.66. The two bulbs are identical and have resistance R, and the two batteries are identical with output voltage V. (a) In case 1, with the two bulbs in series, compare the brightness of each bulb, the current in each bulb, and the power delivered to each bulb. (b) In case 2, with the two bulbs in parallel, compare the brightness of each bulb, the current in each bulb, and the power supplied to each bulb. (c) Which bulbs are brighter, those in case 1 or those in case 2? (d) In each case, if one bulb fails, will the other go out as well? If the other bulb doesnt fail, will it get brighter or stay the same? (Problem 66 is courtesy of E. F. Redish. For other problems of this type, visit http://www.physics.umd.edu/perg/.) Figure P18.66 The given pair of capacitors in Figure P18.67 is fully charged by a 12.0-V battery. The battery is disconnected and the circuit closed. After 1.00 ms, how much charge remains on (a) the 3.00-F capacitor? (b) The 2.00-F capacitor? (c) What is the current in the resistor? Figure P18.67 2.00-nF capacitor with an initial charge of 5.10 C is discharged through a 1.30-k resistor. (a) Calculate the magnitude of the current in the resistor 9.00 s after the resistor is connected across the terminals of the capacitor. (b) What charge remains on the capacitor after 8.00 s? (c) What is the maximum current in the resistor?A charged particle moves in a straight line through a region of space. Which of the following answers must be true? (Assume any other fields are negligible.) The magnetic field (a) has a magnitude of zero (b) has a zero component perpendicular to the particles velocity (c) hits a zero component parallel to the particles velocity in that region.The north-pole end of a bar magnet is held near a stationary positively charged piece of plastic. Is the plastic (a) attracted, (b) repelled, or (c) unaffected by the magnet?As a charged particle moves freely in a circular path in the presence of a constant magnetic field applied perpendicular to the particles velocity, the particles kinetic energy (a) remains constant, (b) increases, or (c) decreases.A square and a circular loop with the same area lie in the xy-plane, where there is a uniform magnetic field B pointing at some angle with respect to the positive z-direction. Each loop carries the same current, in the same direction. Which magnetic torque is larger? (a) the torque on the square loop (b) the torque on the circular loop (c) the torques are the same (d) more information is needed Which of the following actions would double the magnitude of the magnetic force per unit length between two parallel current-carrying wires? Choose all correct answers. (a) Double one of the currents. (b) Double the distance between them. (c) Reduce the distance between them by half. (d) Double both currents.19.6QQ 1CQ 2CQ How can the motion of a charged particle be used to distinguish between a magnetic field and an electric field in a certain region? Give a specific example to justify your answer.4CQ The following statements are related to the force of a magnetic field on a current-carrying wire. Indicate whether each statement is true (T) or false (F). (a) The magnetic force on the wire is independent of the direction of the current. (b) The force on the wire is directed perpendicular to both the wire and the magnetic field. (c) The force takes its largest value when the magnetic field is parallel to the wire.Will a nail be attracted to either pole of a magnet? Explain what is happening inside the nail when it is placed near the magnet.Figure CQ19.7 shows a coaxial cable carrying current I in its inner conductor and a return current of the same magnitude in the opposite direction in the outer conductor. The magnetic field strength at r = r0 is Find the ratio B/B0, at (a) r = 2r0 and (b) r = 4r0. Figure CQ19.7 A magnet attracts a piece of iron. The iron can then attract another piece of iron. On the basis of domain alignment, explain what happens in each piece of iron.Figure CQ19.9 shows four positive charges, A, B, C, and D, moving in the xy-plane in the presence of a constant magnetic field. Rank the charges by the magnitude of the magnetic force exerted on them, from largest to smallest. (a) C, D, B, A (b) D, C, B, A (c) A, B, C, D (d) C, B, A, D Figure CQ19.9 Is the magnetic field created by a current loop uniform? Explain.Suppose you move along a wire at the same speed as the drift speed of the electrons in the wire. Do you now measure a magnetic field of zero?Why do charged particles from outer space, called cosmic rays, strike Earth more frequently at the poles than at the equator?A hanging Slinky toy is attached to a powerful battery and a switch. When the switch is closed so that the toy now carries current, does the Slinky compress or expand?How can a current loop he used to determine the presence of a magnetic field in a given region of space?15CQ Figure CQ19.16 shows four permanent magnets, each having a hole through its center. Notice that the blue and yellow magnets are levitated above the red ones. (a) How does this levitation occur? (b) What purpose do the rods serve? (c) What can you say about the poles of the magnets from this observation? (d) If the upper magnet were inverted, what do you suppose would happen? Figure CQ19.16 Two charged particles are projected in the same direction into a magnetic field perpendicular to their velocities. If the two particles are deflected in opposite directions, what can you say about them?18CQ A magnetic field exerts a torque on each of the current-carrying single loops of wire shown in Figure CQ19.19. The loops lie in the xy-plane, each carrying the same magnitude current, and the uniform magnetic field points in the positive x-direction. Rank the coils by the magnitude of the torque exerted on them by the field, from largest to smallest. (a) A, B, C (b) A, C, B (c) B, A, C (d) B, C, A (e) C, A, B Figure CQ19.19 Consider an electron near the Earths equator. In which direction does it tend to deflect if its velocity is (a) directed downward? (b) Directed northward? (c) Directed westward? (d) Directed southeastward?(a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields in Figure P19.2, as shown. (b) Repeat part (a), assuming the moving particle is an electron. Figure P19.2 Problems 2 and 22.Find the direction of the magnetic field acting on the positively charged particle moving in the various situations shown in Figure P19.3 if the direction of the magnetic force acting on it is as indicated. Figure P19.3 (Problems 3 and 25) For Problem 25, replace the velocity vector with a current in that direction.4P A laboratory electromagnet produces a magnetic field of magnitude 1.50 T. A proton moves through this field with a speed of 6.00 106 m/s. (a) Find the magnitude of the maximum magnetic force that could be exerted on the proton. (b) What is the magnitude of the maximum acceleration of the proton? (c) Would the field exert the same magnetic force on an electron moving through the field with the same speed? (d) Would the electron undergo the same acceleration? Explain.6P Electrons and protons travel from the Sun to the Earth at a typical velocity of 4.00 105 m/s in the positive x-direction. Thousands of miles from Earth, they interact with Earths magnetic field of magnitude 3.00 108 T in the positive z-direction. Find the (a) magnitude and (b) direction of the magnetic force on a proton. Find the (c) magnitude and (d) direction of the magnetic force on an electron.An oxygen ion (O+) moves in the xy-plane with a speed of 2.50 103 m/s. If a constant magnetic field is directed along the z-axis with a magnitude of 2.00 105 T, find (a) the magnitude of the magnetic force acting on the ion and (b) the magnitude of the ions acceleration.A proton moving at 4.00 106 m/s through a magnetic field of magnitude 1.70 T experiences a magnetic force of magnitude 8.20 1013 N. What is the angle between the protons velocity and the field?Sodium ions (Na+) move at 0.851 m/s through a blood-stream in the arm of a person standing near a large magnet. The magnetic field has a strength of 0.254 T and makes an angle of 51.0 with the motion of the sodium ions. The arm contains 100 cm3 of blood with a concentration of 3.00 1020 Na+ ions per cubic centimeter. If no other ions were present in the arm, what would be the magnetic force on the arm?At the equator, near the surface of Earth, the magnetic field is approximately 50.0 T northward, and the electric field is about 100. N/C downward in fair weather. Find the gravitational, electric, and magnetic forces on an electron with an instantaneous velocity of 6.00 106 m/s directed to the east in this environment.A proton travels with a speed of 5.02 106 m/s at an angle of 60 with the direction of a magnetic field of magnitude 0.180 T in the positive x-direction. What are (a) the magnitude of the magnetic force on the proton and (b) the protons acceleration?An electron moves in a circular path perpendicular to a magnetic field of magnitude 0.235 T. If the kinetic energy of the electron is 3.30 1019 J, find (a) the speed of the electron and (b) the radius of the circular path.Figure P19.14a is a diagram of a device called a velocity selector, in which particles of a specific velocity pass through undeflected while those with greater or lesser velocities are deflected either upwards or downwards. An electric field is directed perpendicular to a magnetic field, producing an electric force and a magnetic force on the charged particle that can be equal in magnitude and opposite in direction (Fig. P19.14b) and hence cancel. Show that particles with a speed of v = E/B will pass through the velocity selector undeflected. Figure P19.14 15P A mass spectrometer is used to examine the isotopes of uranium. Ions in the beam emerge from the velocity selector at a speed of 3.00 105 m/s and enter a uniform magnetic field of 0.600 T directed perpendicularly to the velocity of the ions. What is the distance between the impact points formed on the photographic plate by singly charged ions of 235U and 238U?Jupiters magnetic field occupies a volume of space larger than the Sun and contains ionized particles ejected from sources including volcanoes on Io, one of Jupiters moons. A sulfur ion (S+) in Jupiters magnetic field has mass 5.32 1026 kg and kinetic energy 75.0 eV. (a) Find the maximum magnetic force on the ion from Jupiters magnetic field of magnitude 4.28 104 T. (b) Find the radius of the sulfur ions circular path, assuming its velocity is perpendicular to Jupiters magnetic field.Electrons in Earths upper atmosphere have typical speeds near 6.00 105 m/s. (a) Calculate the magnitude of Earths magnetic field if an electrons velocity is perpendicular to the magnetic field and its circular path has a radius of 7.00 102 m. (b) Calculate the number of times per second that an electron circles around a magnetic field line.19P A proton (charge +e, mass mp), a deuteron (charge +e, mass 2mp), and an alpha particle (charge +2e, mass 4mp) are accelerated from rest through a common potential difference V. Each of the particles enters a uniform magnetic field B, with its velocity in a direction perpendicular to B. The proton moves in a circular path of radius p. In terms of p, determine (a) the radius rd of the circular orbit for the deuteron and (b) the radius r for the alpha particle.A particle passes through a mass spectrometer as illustrated in Figure P19.15. The electric field between the plates of the velocity selector has a magnitude of 8 250 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.093 1 T. In the deflection chamber the particle strikes a photographic plate 39.6 cm removed from its exit point alter traveling in a semicircle. (a) What is the mass-to-charge ratio of the particle? (b) What is the mass of the particle if it is doubly ionized? (c) What is its identity, assuming its an element?In Figure P19.2, assume in each case the velocity vector shown is replaced with a wire carrying a current in the direction of the velocity vector. For each case, find the direction of the magnetic force acting on the wire.A current I = 15 A is directed along the positive x-axis and perpendicular to a magnetic field. A magnetic force per unit length of 0.12 N/m acts on the conductor in the negative y-direction. Calculate the magnitude and direction of the magnetic field in the region through which the current passes.A straight wire carrying a 3.0-A current is placed in a uniform magnetic field of magnitude 0.28 T directed perpendicular to the wire. (a) Find the magnitude of the magnetic force on a section of the wire having a length of 14 cm. (b) Explain why you cant determine the direction of the magnetic force from the information given in the problem.In Figure P19.3, assume in each case the velocity vector shown is replaced with a wire carrying a current in the direction of the velocity vector. For each case, find the direction of the magnetic Field that will produce the magnetic force shown.A wire having a mass per unit length of 0.500 g/cm carries a 2.00-A current horizontally to the south. What are the direction and magnitude of the minimum magnetic field needed to lift this wire vertically upward?A wire carries a current of 10.0 A in a direction that makes an angle of 30.0 with the direction of a magnetic field of strength 0.300 T. Find the magnetic force on a 5.00-m length of the wire.At a certain location, Earth has a magnetic field of 0.60 104 T, pointing 75 below the horizontal in a north-south plane. A 10.0-m-long straight wire carries a 15-A current, (a) If the current is directed horizontally toward the east, what are the magnitude and direction of the magnetic force on tile wire? (b) What are the magnitude and direction of the force if the current is directed vertically upward?A wire with a mass of 1.00 g/cm is placed on a horizontal surface with a coefficient of friction of 0.200. The wire carries a current of 1.50 A eastward and moves horizontally to the north. What are the magnitude and the direction of the smallest vertical magnetic field that enables the wire to move in this fashion?Mass m = 1.00 kg is suspended vertically at rest by an insulating string connected to a circuit partially immersed in a magnetic field as in Figure P19.30. The magnetic field has magnitude Bin = 2.00 T and the length = 0.500 m. (a) Find the current I. (b) If = 115 V, find the required resistance R. Figure P19.30 Consider the system pictured in Figure P19.31. A 15-cm length of conductor of mass 15 g, free to move vertically, is placed between two thin, vertical conductors, and a uniform magnetic field acts perpendicular to the page. When a 5.0-A current is directed as shown in the figure, the horizontal wire moves upward at constant velocity in the presence of gravity. (a) What forces act on the horizontal wire, and under what condition is the wire able to move upward at constant velocity? (b) Find the magnitude and direction of the minimum magnetic field required to move the wire at constant speed. (c) What happens if the magnetic field exceeds this minimum value? (The wire slides without friction on the two vertical conductors.) Figure P19.31 A metal rod of mass m carrying a current I glides on two horizontal rails a distance d apart. If the coefficient of kinetic friction between the rod and rails is k, what vertical magnetic field is required to keep the rod moving at a constant speed?In Figure P19.33, the cube is 40.0 cm on each edge. Four straight segments of wireab, bc, cd, and daform a closed loop that carries a current I = 5.00 A in the direction shown. A uniform magnetic field of magnitude B = 0.020 0 T is in the positive y-direction. Determine the magnitude and direction of the magnetic force on each segment. Figure P19.33 A horizontal power line of length 58 m carries a current of 2.2 kA as shown in Figure P19.34. Earths magnetic field at this location has a magnitude equal to 5.0 105. T and makes an angle of 65 with the power line. Find the magnitude and direction of the magnetic force on the power line. Figure P19.34 A wire is formed into a circle having a diameter of 10.0 cm and is placed in a uniform magnetic field of 3.00 mT. The wire carries a current of 5.00 A. Find the maximum torque on the wire.A current of 17.0 mA is maintained in a single circular loop with a circumference of 2.00 m. A magnetic field of 0.800 T is directed parallel to the plane of the loop. What is the magnitude of the torque exerted by the magnetic field on the loop?An eight-turn coil encloses an elliptical area having a major axis of 40.0 cm and a minor axis of 30.0 cm (Fig. P19.37). The coil lies in the plane of the page and carries a clockwise current of 6.00 A. If the coil is in a uniform magnetic field of 2.00 104 T directed toward the left of the page, what is the magnitude of the torque on the coil? Hint: The area of an ellipse is A = ab, where a and b are, respectively, the semimajor and semiminor axes of the ellipse. Figure P19.37 A current-carrying rectangular wire loop with width a = 0.120 m and length b = 0.200 m is in the xy-plane, supported by a non-conducting, frictionless axle of negligible weight A current of I = 3.00 A travels counterclockwise in the circuit (Fig. P19.38). Calculate the magnitude and direction of the force exerted on the (a) left and (b) right segments of wire by a uniform magnetic field of 0.250 T that points in the positive x- direction. Find the magnetic force exerted on the (c) top and (d) bottom segments. (e) Find the magnitude of the net torque on the loop about the axle. Figure P19.38 A 6.00-turn circular coil of wire is centered on the origin in the xy-plane. The coil has radius r = 0.200 m and carries a counterclockwise current I = 1.60 A (Fig. P19.39). (a) Calculate tile magnitude of the coils magnetic moment. (b) Find the magnitude of the magnetic torque on the coil due to a 0.200-T magnetic field that is directed at an angle = 60.0from the positive z-direction and has components only in the xz-plane. Figure P19.39 The orientation of small satellites is often controlled using torque from current-carrying coils in Earths magnetic field. Suppose a multiturn coil has a cross-sectional area of 6.36 104 m2, dissipates 0.200 W of electrical power from a 5.00-V power supply, and provides a magnetic moment of magnitude 0.020 0 A m2. (a) Find the coil current I. (b) Calculate the number of turns in the coil. (c) Calculate the maximum magnitude of torque if Earths magnetic field has magnitude 3.75 105 T at the satellites location.Along piece of wire with a mass of 0.100 kg and a total length of 4.00 m is used to make a square coil with a side of 0.100 m. The coil is hinged along a horizontal side, carries a 3.40-A current, and is placed in a vertical magnetic field with a magnitude of 0.010 0 T. (a) Determine the angle that the plane of the coil makes with the vertical when the coil is in equilibrium. (b) Find the torque acting on the coil due to the magnetic force at equilibrium.A rectangular loop has dimensions 0.500 m by 0.300 m. The loop is hinged along the x-axis and lies in the xy-plane (Fig. P19.42). A uniform magnetic field of 1.50 T is directed at an angle of 40.0 with respect to the positive y-axis and lies parallel everywhere to the yz-plane. The loop carries a current of 0.900 A in the direction shown. (Ignore gravitation.) (a) In what direction is magnetic force exerted on wire segment ab? What is the direction of the magnetic torque associated with this force, as computed with respect to the x-axis? (b) What is the direction of the magnetic force exerted on segment cd? What is the direction of the magnetic torque associated with this force, again computed with respect to the x-axis? (c) Can the forces examined in parts (a) and (b) combine to cause the loop to rotate around the x-axis? Can they affect the motion of the loop in any way? Explain. (d) What is the direction (in the yz-plane) of the magnetic force exerted on segment bc? Measuring torques with respect to the x-axis, what is the direction of the torque exerted by the force on segment bc? (e) Looking toward the origin along the positive x-axis. Will the loop rotate clockwise or counterclockwise? (f) Compute the magnitude of the magnetic moment of the loop. (g) What is the angle between the magnetic moment vector and the magnetic field? (h) Compute the torque on the loop using the values found for the magnetic moment and magnetic field. Figure P19.42 A lightning bolt may carry a current of 1.00 104 A for a short time. What is the resulting magnetic field 1.00 102 m from the bolt? Suppose the bolt extends far above and below the point of observation.A long, straight wire going through the origin is carrying a current of 3.00 A in the positive z-direction (Fig. P19.44). At a point a distance r = 1.20 m from the origin on the positive x-axis, find the (a) magnitude and (b) direction of the magnetic field. At a point the same distance from the origin on the negative y-axis, find the (c) magnitude and (d) direction of the magnetic field. Figure P19.44 Neurons in our bodies carry weak currents that produce detectable magnetic fields. A technique called magnetoencephalography, or MEG, is used to study electrical activity in the brain using this concept This technique is capable of detecting magnetic fields as weak as 1.0 1015 T. Model the neuron as a long wire carrying a current and find the current it must carry to produce a field of this magnitude at a distance of 4.0 cm from the neuron.In 1962 measurements of the magnetic field of a large tornado were made at the Geophysical Observatory in Tulsa, Oklahoma. If tile magnitude of the tornados field was B = 1.50 108 T pointing north when the tornado was 9.00 km east of the observatory, what current was carried up or down the funnel of the tornado? Model the vortex as a long, straight wire carrying a current.A cardiac pacemaker can be affected by a static magnetic field as small as 1.7 mT. How close can a pacemaker wearer come to a long, straight wire carrying 20 A?The two wires shown in Figure P19.48 are separated by d = 10.0 cm and carry currents of I = 5.00 A in opposite directions. Find the magnitude and direction of the net magnetic field (a) at a point midway between the wires; (b) at point P1, 10.0 cm to the right of the wire on the right; and (c) at point P2, 2d = 20.0 cm to the left of the wire on the left. Figure P19.48 49P Two long, parallel wires carry currents of I1 = 3.00 A and I2 = 5.00 A in the direction indicated in Figure P19.50. (a) Find the magnitude and direction of the magnetic field at a point midway between the wires (d = 20.0 cm). (b) Find the magnitude and direction of the magnetic field at point P, located d = 20.0 cm above the wire carrying the 5.00-A current. Figure P19.50 Two long, parallel wires carry currents of I1 = 3.00 A and I2 = 5.00 A in the direction indicated in Figure P19.50. (a) Find the magnitude and direction of the magnetic field at a point midway between the wires (d = 20.0 cm). (b) Find the magnitude and direction of the magnetic field at point P, located d = 20.0 cm above the wire carrying the 5.00-A current. Figure P19.50 52P The magnetic field 40.0 cm away from a long, straight wire carrying current 2.00 A is 1.00 T. (a) At what distance is it 0.100 T? (b) At one instant, the two conductors in a long household extension cord carry equal 2.00-A currents in opposite directions. The two wires are 3.00 mm apart. Find the magnetic field 40.0 cm away from the middle of the straight cord, in the plane of the two wires. (c) At what distance is it one-tenth as large? (d) The center wire in a coaxial cable carries current 2.00 A in one direction, and the sheath around it carries current 2.00 A in the opposite direction. What magnetic field does the cable create at points outside?54P 55P 56P A wire with a weight per unit length of 0.080 N/m is suspended directly above a second wire. The top wire carries a current of 30.0 A, and the bottom wire carries a current of 60.0 A. Find the distance of separation between the wires so that the top wire will be held in place by magnetic repulsion.In Figure P19.58 the current in the long, straight wire is I1 = 5.00 A, and the wire lies in the plane of the rectangular loop, which carries 10.0 A. The dimensions shown are c = 0.100 m, a = 0.150 m, and = 0.450 m. Find the magnitude and direction of the net force exerted by the magnetic field due to the straight wire on the loop. Figure P19.58 A long solenoid that has 1.00 103 turns uniformly distributed over a length of 0.400 m produces a magnetic field of magnitude 1.00 104 T at its center. What current is required in the windings for that to occur?60P It is desired to construct a solenoid that will have a resistance of 5.00 (at 20C) and produce a magnetic field of 4.00 102 T at its center when it carries a current of 4.00 A. The solenoid is to be constructed from copper wire having a diameter of 0.500 mm. If the radius of the solenoid is to be 1.00 cm, determine (a) the number of turns of wire needed and (b) the length the solenoid should have.Certain experiments must be performed in the absence of any magnetic fields. Suppose such an experiment is located at the center of a large solenoid oriented so that a current of I = 1.00 A produces a magnetic field that exactly cancels Earths 3.50 105 T magnetic field. Find the solenoids number of turns per meter.Ail electron is moving at a speed of 1.0 104 in/s in a circular path of radius 2.0 cm inside a solenoid. The magnetic field of the solenoid is perpendicular to the plane of the electrons path. Find (a) the strength of the magnetic field inside the solenoid and (b) the current in the solenoid if it has 25 turns per centimeter.Figure P19.64 is a setup that can be used to measure magnetic fields. A rectangular coil of wire contains N turns and has a width w. The coil is attached to one arm of a balance and is suspended between the poles of a magnet. The field is uniform and perpendicular to the plane of the coil. The system is first balanced when the current in the coil is zero. When the switch is closed and the coil carries a current I, a mass m must be added to the right side to balance the system. (a) Find an expression for the magnitude of the magnetic field and determine its direction. (b) Why is the result independent of the vertical dimension of the coil? (c) Suppose the coil has 50 turns and width of 5.0 cm. When the switch is closed, the coil carries a current of 0.30 A, and a mass of 20.0 g must be added to the right side to balance the system. What is the magnitude of the magnetic field? Figure P19.64 Two coplanar and concentric circular loops of wire carry currents of I1 = 5.00 A and I2 = 3.00 A in opposite directions as in Figure P19.65. (a) If r1, = 12.0 cm and r2 = 9.00 cm, what are (a) the magnitude and (b) the direction of the net magnetic field at the center of the two loops? (c) Let r1, remain fixed at 12.0 cm and let r2 be a variable. Determine the value of r2 such that the net field at the center of the loop is zero. Figure P19.65 An electron moves in a circular path perpendicular to a constant magnetic field of magnitude 1.00 mT. The angular momentum of the electron about the center of the circle is 4.00 1025 kg m2/s. Determine (a) the radius of the circular path and (b) the speed of the electron.67AP A 0.200-kg metal rod carrying a current of 10.0 A glides on two horizontal rails 0.500 m apart. What vertical magnetic field is required to keep the rod moving at a constant speed if the coefficient of kinetic friction between the rod and rails is 0.100?Using an electromagnetic flowmeter (Fig. P19.69), a heart surgeon monitors the flow rate of blood through an artery. Electrodes A and B make contact with the outer surface of the blood vessel, which has interior diameter 3.00 mm. (a) For a magnetic field magnitude of 0.040 0 T, a potential difference of 160 V appears between the electrodes. Calculate the speed of the blood. (b) Verify that electrode A is positive, as shown. Does the sign of the emf depend on whether the mobile ions in the blood are predominantly positively or negatively charged? Explain. Figure P19.69 A uniform horizontal wire with a linear mass density of 0.50 g/m carries a 2.0-A current. It is placed in a constant magnetic field with a strength of 4.0 103 T. The field is horizontal and perpendicular to the wire. As the wire moves upward starting from rest, (a) what is its acceleration and (b) how long does it take to rise 0.50 m? Neglect the magnetic field of Earth.71AP Two long, parallel wires, each with a mass per unit length of 0.040 kg/m, are supported in a horizontal plane by 6.0-cm-long strings, as shown in Figure P19.72. Each wire carries the same current I, causing the wires to repel each other so that the angle between the supporting strings is 16. (a) Are the currents in the same or opposite directions? (b) Determine the magnitude of each current.Protons having a kinetic energy of 5.00 MeV are moving in the positive x-direction and enter a magnetic field of 0.050 0 T in the z-direction, out of the plane of the page, and extending from x = 0 to x = 1.00 m as in Figure P19.73. (a) Calculate the y-component of the protons momentum as they leave the magnetic field. (b) Find the angle a between the initial velocity vector of the proton beam and the velocity vector after the beam emerges from the field. Hint: Neglect t relativistic effects and note that 1 eV = 1.60 1019J. Figure P19.73 A straight wire of mass 10.0 g and length 5.0 cm is suspended from two identical springs that, in turn, form a closed circuit (Fig. P19.74). The springs stretch a distance of 0.50 cm under the weight of the wire. The circuit has a total resistance of 12 . When a magnetic field directed out of the page (indicated by the dots in the Figure) is turned on, the springs are observed to stretch an additional 0.30 cm. What is the strength of the magnetic field? (The upper portion of the circuit is fixed.) Figure P19.74 A 1.00-kg ball having net charge Q = 5.00 C is thrown out of a window horizontally at a speed v = 20.0 m/s. The window is at a height h = 20.0 m above the ground. A uniform horizontal magnetic field of magnitude B = 0.010 0 T is perpendicular to the plane of the balls trajectory. Find the magnitude of the magnetic force acting on the ball just before it hits the ground. Hint: Ignore magnetic forces in finding the balls final velocity.Two long, parallel conductors separated by 10.0 cm carry currents in the same direction. The first wire carries a current I1 = 5.00 A, and the second carries I2 = 8.00 A. (a) What is the magnitude of the magnetic field created by I1, at the location of I2? (b) What is the force per unit length exerted by I1, on I2? (c) What is the magnitude of the magnetic field created by I2 at the location of I1? (d) What is the force per length exerted by I2 on I1?20.1QQ A bar magnet is falling toward the center of a loop of wire, with the north pole oriented downward. Viewed from the same side of the loop as the magnet, as the north pole approaches the loop, what is the direction of the induced current? (a) clockwise (b) zero (c) counterclockwise (d) along the length of the magnet Two circular loops are side by side and lie in the xy-plane. A switch is closed, starting a counterclockwise current in the left-hand loop, as viewed from a point on the positive z-axis passing through the center of the loop. Which of the following statements is true of the right-hand loop? (a) The current remains zero. (b) An induced current moves counterclockwise. (c) An induced current moves clockwise.A horizontal metal bar oriented east-west drops straight down in a location where Earth's magnetic field is due north. As a result, an emf develops between the ends. Which end is positively charged? (a) the east end (b) the west end (c) neither end carries a charge You intend to move a rectangular loop of wire into a region of uniform magnetic field at a given speed so as to induce an emf in the loop. The plane of the loop must remain perpendicular to the magnetic field lines. In which orientation should you hold the loop while you move it into the region with the magnetic field to generate the largest emf? (a) with the long dimension of the loop parallel to the velocity vector (b) with the short dimension of the loop parallel to the velocity vector (c) either way because the emf is the same regardless of orientation 20.6QQ A bar magnet is held stationary while a circular loop of wire is moved toward the magnet at constant velocity at position A as in Figure CQ20.1. The loop passes over the magnets center at position B and moves away from the magnet at position C. Viewing the loop from the left as indicated in the figure, find the direction of the induced current in the loop (a) at position A and (b) at position C. (c) What is the induced current in the loop at position B? Indicate the directions as either CW (for clockwise) or CCW (for counterclockwise). Figure CQ20.1 Does dropping a magnet down a copper tube produce a current in the tube? Explain.Figure CQ20.3 shows three views of a circular loop in a magnetic field. In each view, the illustrated change results in an induced current. Indicate the direction of this induced current as either CW (for clockwise) or CCW (for counter clockwise) if: (a) the loop (viewed edge-on) is rotated away from perpendicular to the magnetic field, (b) the loop area increases, and (c) the magnetic field weakens. Figure CQ20.3 A loop of wire is placed in a uniform magnetic field. (a) For what orientation of the loop is the magnetic flux a maximum? (b) For what orientation is the flux zero?As the conducting bar in Figure CQ20.5 moves to the right, an electric field directed downward is set up. If the bar were moving to the left, explain why the electric field would be upward.How is electrical energy produced in dams? (That is, how is the energy of motion of the water converted to AC electricity?)Figure CQ20.7 shows a slidewire generator with motional cmf 0 when the wire at A slides across the top and bottom rails at constant velocity v0. (a) When the wire reaches B so that the area enclosed by the circuit is doubled, determine the ratio of the new cmf to the original cmf, /0. (b) If the wire's speed is doubled so that v = 2v0 determine the ratio /0. Figure CQ20.7 As the bar in Figure CQ20.5 moves perpendicular to the field, is an external force required to keep it moving with constant speed? Figure CQ20.5 Conceptual Questions 5 and 8.Eddy current are induced currents set up in a piece of metal when it moves through a nonuniform magnetic field. For example, consider the flat metal plate swinging at the end of a bar as a pendulum, as shown in Figure CQ20.9. (a) At position 1, the pendulum is moving from a region where there is no magnetic field into a region where the field B is directed into the paper. Show that at position 1 the direction of the eddy current is counterclockwise. (b) At position 2, the pendulum is moving out of the field into a region of zero field. Show that the direction of the eddy current is clockwise in this case. (c) Use right-hand rule number 2 to show that these eddy currents lead to a magnetic force on the plate directed at shown in the figure. Because the induced eddy current always produces a retarding force when the plate enters or leaves the field, the swinging plate quickly comes to rest. Figure CQ20.9 The switch S in Figure 20.27 is closed at t = 0 and the current at a reference time tref 0 is Iref. If the circuit is changed as, described below and the switch is again dosed at t = 0, determine whether the current I at the same time would be greater than, less than, or equal to the original value of Iref. Indicate your answers wilt G. L. or E, respectively. (a) Both the battery voltage and the resistance R are doubled. (b) The inductance L b doubled. (c) The battery voltage . the resistance R, and the inductance L are each doubled. Figure 20.27 A series RL circuit. As the current increases toward its maximum value, the inductor produces an emf that opposes the increasing current.A piece of aluminum is dropped vertically downward between the poles of an electromagnet. Does the magnetic field affect the velocity of the aluminum? Hint: See Conceptual Question 9.When the switch in Figure CQ20.12a is closed, a current is set up in the coil and the metal ring springs upward (Fig. CQ20.12b). Explain this behavior. Figure CQ20.12 Conceptual Questions 12 and 13 13CQ A magneto is used to cause the spark in a spark plug in many lawn mowers today. A magneto consists of a permanent magnet mounted on a flywheel so that it spins past a fixed coil. Explain how this arrangement generates a large enough potential difference to cause the spark.A uniform magnetic field of magnitude 0.50 T is directed perpendicular to the plane of a rectangular loop having dimensions 8.0 cm by 12 cm. Find the magnetic flux through the loop.Find the flux of Earths magnetic field of magnitude 5.00 105 T through a square loop of area 20.0 cm2 (a) when the field is perpendicular to the plane of the loop, (b) when the field makes a 30.0 angle with the normal to the plane of the loop, and (c) when the field makes a 90.0 angle with the normal to the plane.3P A long, straight wire carrying a current of 2.00 A is placed along the axis of a cylinder of radius 0.500 m and a length of 3.00 m. Determine the total magnetic flux through the cylinder.5P A magnetic field of magnitude 0.300 T is oriented perpendicular to the plane of a circular loop. (a) Calculate the loop radius if the magnetic flux through the loop is 2.70Wb. (b) Calculate the new magnetic flux if the loop radius is doubled.A cube of edge length = 2.5 cm is positioned as shown in Figure P20.7. There is a uniform magnetic field throughout the region with components Bx = +5.0 T, By = +4.0 T, and Bz = +3.0 T. (a) Calculate the flux through the shaded face of the cube. (b) What is the total flux emerging from the volume enclosed by the cube (i.e., the total flux through all six faces)? Figure P20.7 Transcranial magnetic stimulation (TMS) is a noninvasive technique used to stimulate regions of the human brain. A small coil is placed on the scalp, and a brief burst of current in the coil produces a rapidly changing magnetic field inside the brain. The induced emf can be sufficient to stimulate neuronal activity. One such device generates a magnetic field within the brain that rises from zero to 1.5 T in 120 ms. Determine the induced emf within a circle of tissue of radius 1.6 mm and that is perpendicular to the direction of the field.Three loops of wire move near a long straight wire carrying a current as in Figure P20.9. What is the direction of the induced current, if any, in (a) loop A, (b) loop B, and (c) loop C. Figure P20.9 The flexible loop in Figure P20.10 has a radius of 12 cm and is in a magnetic field of strength 0.15 T. The loop is grasped at points A and B and stretched until us area is nearly zero. If it takes 0.20 s to close the loop, what is the magnitude of the average induced cmf in it during this time? Figure P20.10 Problems 10, 12 and 22.Inductive charging is used to wirelessly charge electronic devices ranging front toothbrushes to cell phones. Suppose the base unit of an inductive charger produces a 1.00 103-T magnetic Held. Varying this magnetic Held magnitude changes the flux through a 15.0-turn circular loop in the device, creating an emf that charges its battery. Suppose the loop area is 3.00 104 m2 and the induced emf has an average magnitude of 5.00 V. Calculate the time required for the magnetic field to decrease to zero from its maximum value.Medical devices implanted inside the body are often powered using transcutaneous energy transfer (TET), a type of wireless charging using a pair of closely spaced coils. An emf is generated around a coil inside the body by varying the current through a nearby coil outside the body, producing a changing magnetic flux. Calculate the average induced emf if each 10-turn coil has a radius of 1.50 cm and the current in the external coil varies from its maximum value of 10.0 A to zero in 6.25 106 s. (Hint: Recall from Topic 19 that the magnetic field at the center of the current-carrying external coil is B=N0I2R. Assume this magnetic field is constant and oriented perpendicular to the internal coil.)A technician wearing a circular metal band on his wrist moves his hand into a uniform magnetic field of magnitude 2.5 T in a lime of 0.18 s. If the diameter of the band is 6.5 cm and the field is at an angle of 45 with the plane of the metal hand while the hand is in the field, find the magnitude of the average emf induced in the band.In Figure P20.14, what is the direction of the current induced in the resistor at the instant the switch is closed? Figure P20.14 15P Find the direction of the current in the resistor shown in Figure P20.16 (a) at the instant the switch is closed, (b) after the switch has been closed for several minutes, and (c) at the instant the switch is opened. Figure P20.16 A circular loop of wire lies below a long wire carrying a current that is increasing as in Figure P20.17a. (a) What is the direction of the induced current in the loop, if any? (b) Now suppose the loop is next to the same wire as in Figure P20.17b. What is the direction of the induced current in the loop, if any? Explain your answers. Figure P20.17 A square, single-turn wire loop = 1.00 cm on a side is placed inside a solenoid that has a circular cross section of radius r = 3.00 cm, as shown in the end view of Figure P20.18. The solenoid is 20.0 cm long and wound with 100 turns of wire. (a) If the current in the solenoid is 3.00 A, what is the flux through the square loop? (b) If the current in the solenoid is reduced to zero in 3.00 s, what is the induced emf in the square loop? Figure P20.18 19P A circular coil enclosing an area of 100 cm2 is made of 200 turns of copper wire. The wire making up the coil has resistance of 5.0 , and the ends of the wire are connected to form a closed circuit. Initially, a 1.1-T uniform magnetic field points perpendicularly upward through the plane of the coil. The direction of the field then reverses so that the final magnetic field has a magnitude of 1.1 T and points downward through the coil. If the time required for the field to reverse directions is 0.10 s, what is the average current in the coil during that time?To monitor the breathing of a hospital patient, a thin belt is girded around the patients chest as in Figure P20.21. The belt is a 200-turn coil. When the patient inhales, the area encircled by the coil increases by 39.0 cm2. The magnitude of Earths magnetic field is 50.0 T and makes an angle of 28.0 with the plane of the coil. Assuming a patient takes 1.80 s to inhale, find the magnitude of the average induced emf in the coil during that time. Figure P20.21 An N-turn circular wire coil of radius r lies in the xy-plane (the plane of the page), as in Figure P20.10. A uniform magnetic field is turned on, increasing steadily from 0 to B0 in the positive z-direction in t seconds. (a) Find a symbolic expression for the emf, , induced in the coil in terms of the variables given. (b) looking down on at the xy-plane from the positive z-axis, is the direction of the induced current clockwise or counterclockwise? (c) If each loop has resistance R, find an expression for the magnitude of the induced current, I.A truck is carrying a steel beam of length 15.0 m on a free-way. An accident causes the beam to be dumped off the truck and slide horizontally along the ground at a speed of 25.0 m/s. The velocity of the center of mass of the beam is north-ward while the length of the beam maintains an east-west orientation. The vertical component of the Earths magnetic field at this location has a magnitude of 35.0 T. What is the magnitude of the induced emf between the ends of the beam?24P 25P In one of NASAs space tether experiments, a 20.0-km-long conducting wire was deployed by the space shuttle as it orbited at 7.86 103 m/s around Earth and across Earths magnetic field lines. The resulting motional emf was used as power source. If the component of Earths magnetic field perpendicular to the tether was 1.50 105 T, determine the maximum possible potential difference between the two ends of the tether.27P An astronaut is connected to her spacecraft by a 25-m-long tether cord as she and the spacecraft orbit Earth in a circular path at a speed of 3.0 105 m/s. At one instant, the voltage measured between the ends of a wire embedded in the cord is measured to be 0.45 V. Assume the long dimension of the cord is perpendicular to the vertical component of Earths magnetic field at that instant. (a) What is the magnitude of the vertical component of Earths field at this location? (b) Does the measured voltage change as the system moves from one location to another? Explain.29P 30P 31P 32P Considerable scientific work is currently under way to determine whether weak oscillating magnetic fields such as those found near outdoor electric power lines can affect human health. One study indicated that a magnetic field of magnitude 1.0 103 T, oscillating at 60. Hz, might stimulate red blood cells to become cancerous. If the diameter of a red blood cell is 8.0 m, determine the maximum emf that can be generated around the perimeter of the cell.A flat coil enclosing an area of 0.10 m2 is rotating at 60 rev/s, with its axis of rotation perpendicular to a 0.20-T magnetic field. (a) If there are 1 000 turns on the coil, what is the maximum voltage induced in the coil? (b) When the maximum induced voltage occurs, what is the orientation of the coil with respect to the magnetic field?A generator connected to the wheel or hub of a bicycle can be used to power lights or small electronic devices. A typical bicycle generator supplies 6.00 V when the wheels rotate at = 20.0 rad/s. (a) If the generator's magnetic field has magnitude B = 0.600 T with N = 100 turns, find the loop area A. (b) Find the time interval between the maximum emf of +6.00 V and the minimum emf of 6.00 V.A motor has coils with a resistance of 30.0 and operates from a voltage of 240 V. When the motor is operating at its maximum speed, the back emf is 145 V. Find the current in the coils (a) when the motor is first turned on and (b) when the motor has reached maximum speed. (c) If the current in the motor is 6.0 A at some instant, what is the back emf at that time?A coil of 10.0 turns is in the shape of an eclipse having a major axis of 10.0 cm and a minor axis of 4.00 cm. The coil rotates at 1 00. rpm in a region in which the magnitude of Earths magnetic field is 55.0 T. What is the maximum voltage induced in the coil if the axis of rotation of the coil is along its major axis and is aligned (a) perpendicular to Earths magnetic field and (b) parallel to Earth's magnetic field? Note: The area of an ellipse is given by A = ab, where a is the length of the semi major axis and b is the length of the semi minor axis.38P 39P 40P 41P An emf of 24.0 mV is induced in a 500-turn coil when the current is changing at a rate of 10.0 A/s. What is the magnetic flux through each turn of the coil at an instant when the current is 4.00 A?43P 44P 45P 46P 47P 48P 49P 50P 51P 52P Additional Problems Two circular loop of wire surround an insulating rod as in Figure P20.53. Loop I carries a current I in the clockwise direction when viewed from the left end. If loop I moves toward loop 2, which remains stationary, what is the direction of the induced current in loop 2 when slewed from the left end? Figure P20.53 54AP 55AP 56AP An 820-turn wire coil of resistance 24.0 is placed on lop of a 12 500-turn, 7.00-cm-long solenoid, as in Figure P20.57. Both coil and solenoid have cross-sectional area of 1.00 104 m2. (a) How long does it take the solenoid current to reach 0.632 times its maximum value? (b) Determine the average back emf caused by the self-inductance of the solenoid during this interval. The magnetic field produced by the solenoid at the location of the coil is one-half as strong as the field at the center of the solenoid. (c) Determine the average rate of change in magnetic flux through each turn of the coil during the stated interval. (d) Find the magnitude of the average induced current in the coil. Figure P20.57 A spacecraft is in 4 circular orbit of radius equal to 3.0 104 km around a 2.0 1030 kg pulsar. The magnetic field of the pulsar at that radial distance is 1.0 102 T directed perpendicular to the velocity of the spacecraft. The spacecraft is 0.20 km long with a radius of 0.040 km and moves counter-clockwise in the xy-plane around the pulsar. (a) What is the speed of the spacecraft? (b) If the magnetic field points in the positive z-direction, is the emf induced from the back to the front of the spacecraft or from side to side? (c) Compute the induced emf. (d) Describe the hazards for astronauts inside any spacecraft moving in the vicinity of a pulsar.59AP 60AP 61AP 62AP The magnetic field shown in Figure P20.63 has a uniform magnitude of 25.0 mT directed into the paper The initial diameter of the kink it 2.00 cm. (a) The wire is quickly pulled taut, and the kink shrinks to a diameter of zero in 50.0 ms. Determine the average voltage induced between endpoints A and B. Include the polarity. (b) Suppose the kink is undisturbed, but the magnetic field increases to 100 mT in 4.00 103 s. Determine the average voltage across terminals A and B including polarity, during this period. Figure P20.63 64AP In Figure P20.65 the rolling axle of length 1.50 m is pushed along horizontal rails at a constant speed v = 3.00 m/s. A resist or R = 0.400 is connected to the rails at points a and b, directly opposite each other. (The wheels make good electrical contact with the rails, so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R.) A uniform magnetic field B = 0.800 T is directed vertically downward. (a) Find the induced current I in the resistor. (b) What horizontal force F is required to keep the axle rolling at constant speed? (c) Which end of the resistor, a or b. is at the higher electric potential? (d) Alter the axle rolls past the resistor, does the current in R reverse direction? Explain your answer. Figure P20.65 An N-turn square coil with side and resistance R is pulled to the right at constant speed v in the positive x-direction in the presence of a uniform magnetic field B acting perpendicular to the coil, as shown in Figure P20.66. At t = 0, the right side of the coil is at the edge of the field. After a time t has elapsed, the entire coil is in the region where B = 0. In terms of the quantities N, B, , v, and R, find symbolic expressions for (a) the magnitude of the induced emf in the loop during the time interval t, (b) the magnitude of the induced current in the coil, (c) the power delivered to the coil, and (d) the force required to remove the coil from the field. (e) What is the direction of the induced current in the loop? (f) What is the direction of the magnetic force on the loop while it is being pulled out of the field? Figure P20.66 A conducting rectangular loop of mass M, resistance R, and dimensions w by falls from rest into a magnetic field B, as shown in Figure P20.67. During the time interval before the top edge of the loop reaches the field, the loop approaches a terminal speed vT. (a) Show that vT=MgRB2w2 (b) Why is VT proportional to R? (c) Why is it inversely proportional to B2? Figure P20.67 Which of the following statements can be true for a resistor connected in a simple series circuit to an operating AC generator? (a) Pav = 0 and iav = 0 (b) Pav = 0 and iav 0 (c) Pav 0 and iav = 0 (d) Pav 0 and iav 0 For the circuit in Figure 21.8, is the instantaneous voltage of the source equal to (a) the sum of the maximum voltages across the elements, (b) the sum of the instantaneous voltages across the elements, or (c) the sum of the rms voltages across the elements? Figure 21.8 A series circuit consisting of a resistor, an inductor, and a capacitor connected to an AC generator.21.3QQ Suppose XL XC in Figure 21.12. If switch A is closed, what happens phase angle? (a) It increases. (b) It decreases. (c) It doesnt change. Figure 21.12 (Quick Quizzes 21.3-21.6)Suppose XL Xc in Figure 21.12. If switch A is left open and switch B is closed, what happens to the phase angle? (a) It increases. (b) It decreases. (c) It doesnt change. Figure 21.12 (Quick Quizzes 21.3-21.6)21.6QQ In an apparatus such as the one in Figure 21.22. suppose the black disk is replaced by one with half the radius. Which of the following are different after the disk is replaced? (a) radiation pressure on the disk (b) radiation force on the disk (c) radiation momentum delivered to the disk in a given time interval Figure 21.22 An .apparatus for measuring the radiation pressure of light. In practice, the system is contained in a high vacuum.Which of the following statements are true about light waves? (a) The higher the frequency, the longer the wavelength. (b) The lower the frequency, the longer the wavelength. (c) Higher-frequency light travels faster than lower-frequency light. (d) The shorter the wavelength, the higher the frequency. (e) The lower the frequency, the shorter the wavelength.An RLC circuit connected across an AC voltage source at frequency f has resistance R, capacitive reactance XG and inductive reactance XL. If the frequency is doubled so that fnew = 2f, find the ratios (a) Rnew/R, (b) XC,new/XC, and (c) XL,new/XL.(a) Does the phase angle in an RLC series circuit depend on frequency? (b) What is the phase angle for the circuit when the inductive reactance equals the capacitive reactance?3CQ Receiving radio antennas can be in the form of conducting lines or loops. What should the orientation of each of these antennas be relative to a broadcasting antenna that is vertical?The following statements are related to an RLC circuit connected across an AC power source. Choose the words that make each statement true. (i) The voltage across the [(a) capacitor; (b) inductor] leads the current by 90. (ii) The voltage across the [(c) capacitor; (d) resistor] is in phase with the current. (iii) At resonance, the phase angle between the current and the voltage [(e) is 0; (f) depends on frequency f]. (iv) The maximum and rms voltages from the power source are related by [(g) Vmax = 2 Vrms,; (h) Vmax = Vrms/2].6CQ In space sailing, which is a proposed alternative for transport to the planets, a spacecraft carries a very large sail. Sunlight striking the sail exerts a force, accelerating the spacecraft. Should the sail be absorptive or reflective to be most effective?8CQ A resistor, capacitor, and inductor are connected in series across an AC generator. Which one of the following statements is true? (a) All the power is lost in the inductor. (b) All the power is lost in the capacitor. (c) All the power is lost in the resistor. (d) Power is lost in all three elements.10CQ Why should an infrared photograph of a person look different from a photograph taken using visible light?If a high-frequency current is passed through a solenoid containing a metallic core, the core becomes warm due to induction. Explain why the temperature of the material rises in this situation.13CQ Why is the sum of the maximum voltages across each of the elements in a series RLC circuit usually greater than the maximum applied voltage? Doesnt this violate Kirchhoffs loop rule?If the resistance in an RLC circuit remains the same, but the capacitance and inductance are each doubled, how will the resonance frequency change?An inductor and a resistor are connected in series across an AC generator, as shown in Figure CQ21.16. Immediately after the switch is closed, which of the following statements is true? (a) The current is V/R. (b) The voltage across the inductor is zero. (c) The current in the circuit is zero. (d) The voltage across the resistor is V. (e) The voltage across the inductor is half its maximum value. Figure CQ21.16 A capacitor and a resistor are connected in series across an AC generator, as shown in Figure CQ21.17. After the switch is closed, which of the following statements is true? (a) The voltage across the capacitor lags the current by 90. (b) The voltage across the resistor is out of phase with the current. (c) The voltage across the capacitor leads the current by 90. (d) The current decreases as the frequency of the generator is increased, but its peak voltage remains the same. (e) None of these Figure CQ21.17 18CQ Which of the following statements is true regarding electromagnetic waves traveling through a vacuum? More than one statement may be correct. (a) All waves have the same wavelength. (b) All waves have the same frequency. (c) All waves travel at 3.00 108 m/s. (d) The electric and magnetic fields associated with the waves are perpendicular to each other and to the direction of wave propagation. (e) The speed of the waves depends on their frequency.(a) What is the resistance of a light bulb that uses an average power of 75.0 W when connected to a 60.0-Hz power source having a maximum voltage of 170. V? (b) What is the resistance of a 100.-W lightbulb?2P A 1.5-k resistor is connected to an AC voltage source with an rms voltage of 120 V. (a) What is the maximum voltage across the resistor? (b) What is the maximum current through the resistor? (c) What is the rms current through the resistor? (d) What is the average power dissipated by the resistor?Figure P21.4 show three lamp connected to a 120.-V AC (rms) household supply voltage. Lamps 1 and 2 have 150-W bulbs; lamp 3 has a 100.-W bulb. For each bulb, find (a) the rms current and (b) the resistance. Figure P21.4 A 24.0-k resistor connected to an AC voltage source dissipates an average power of 0.600 W. (a) Calculate the rms current in the resistor. (b) Calculate the rms voltage of the AC source.The output voltage of an AC generator is given by v = (170 V) sin (60t). The generator is connected across a 20.0- resistor. By inspection, what are the (a) maximum voltage and (b) frequency? Find the (c) rms voltage across the resistor, (d) rms current in the resistor, (e) maximum current in the resistor, (f) power delivered to the resistor, and (g) current when t = 0.005 0 s. (h) Should the argument of the sine function be in degrees or radians?(a) For what frequencies does a 22.0-F capacitor have a reactance below 175 ? (b) What is the reactance of a 44.0-F capacitor over this same frequency range?North American outlets supply AC electricity with a frequency of f = 60.0 Hz while the European standard is f = 50.0 Hz. What value of capacitance provides a capacitive reactance of 1.00 k (a) in North America and (b) in Europe?When a 4.0-F capacitor is connected to a generator whose rms output is 30. V, the current in the circuit is observed to be 0.30 A. What is the frequency of the source?An AC generator with an output rms voltage of 36.0 V at a frequency of 60.0 Hz is connected across a 12.0-F capacitor. Find the (a) capacitive reactance, (b) rms current, and (c) maximum current in the circuit. (d) Does the capacitor have its maximum charge when the current takes its maximum value? Explain.What maximum current is delivered by an AC source with Vmax, = 48.0 V and f = 90.0 Hz when connected across a 3.70 F capacitor?A generator delivers an AC voltage of the form v = (98.0 V) sin (80t) to a capacitor. The maximum current in the circuit is 0.500 A. Find the (a) rms voltage of the generator, (b) frequency of the generator, (c) rms current, (d) reactance, and (e) value of the capacitance.13P

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