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All Textbook Solutions for College Physics
Integrated Concepts A short circuit in a 120-V appliance cord has a 0.500- resistance. Calculate the temperature rise of the 2.00 g of surrounding materials, assuming their specific heat capacity is 0.200 cal/g.°C and that it takes 0.0500 s for a circuit breaker to interrupt the current. Is this likely to be damaging?Construct Your Own Problem Consider a person working in an environment where electric currents might pass through her body. Construct a problem in which you calculate the resistance of insulation needed to protect the person from harm. Among the things to be considered are the voltage to which the person might be exposed, likely body resistance (dry, wet, ...), and acceptable currents (safe but sensed, safe and unfelt, ...).Integrated Concepts Use the ECG in Figure 20.34 to determine the heart rate in beats per minute assuming a constant time between beats. Figure 20.34 A lead II ECG with corresponding arterial blood pressure. The QRS complex is created by the depolarization and contraction of the ventricles and is followed shortly by the maximum or systolic blood pressure. See text for further description.Integrated Concepts (a) Referring to Figure 20.34, find the time systolic pressure lags behind the middle of the QRS complex, (b) Discuss the reasons for the lime lag. Figure 20.34 A lead II ECG with corresponding arterial blood pressure. The QRS complex is created by the depolarization and contraction of the ventricles and is followed shortly by the maximum or systolic blood pressure. See text for further description.A switch has a variable resistance that is nearly zero when closed and extremely large when open, and it is placed in series with the device it controls. Explain the effect the switch in Figure 21.43 has on current when open and when closed.What is the voltage across the open switch in Figure 21.43?There is a voltage across an open switch, such as in Figure 21.43. Why, then, is the power dissipated by the open switch small?Why is the power dissipated by a closed switch, such as in Figure 21.43, small?A student in a physics lab mistakenly wired a light bulb, battery, and switch as shown in Figure 21.44. Explain why the bulb is on when the switch is open, and off when the switch is closed. (Do not try this-it is hard on the battery!)Knowing that the severity of a shock depends on the magnitude of the current through your body, would you prefer to be in series or parallel with a resistance, such as the heating element of a toaster, if shocked by it? Explain.Would your headlights dim when you start your car's engine if the wires in your automobile were superconductors? (Do not neglect the battery’s internal resistance.) Explain.Some strings of holiday lights are wired in series to save wiring costs. An old version utilized bulbs that break the electrical connection, like an open switch, when they burn out. If one such bulb burns out, what happens to the others? If such a string operates on 120 V and has 40 identical bulbs, what is the normal operating voltage of each? Newer versions use bulbs that short circuit, like a closed switch, when they burn out. If one such bulb burns out, what happens to the others? If such a string operates on 120 V and has 39 remaining identical bulbs, what is then the operating voltage of each?If two household lightbulbs rated 60 W and 100 W are connected in series to household power, which will be brighter? Explain.Suppose you are doing a physics lab that asks you to put a resistor into a circuit, but all the resistors supplied have a larger resistance than the requested value. How would you connect the available resistances to attempt to get the smaller value asked for?Before World War II, some radios got power through a “resistance cord" that had a significant resistance. Such a resistance cord reduces the voltage to a desired level for the radio’s tubes and the like, and it saves the expense of a transformer. Explain why resistance cords become warm and waste energy when the radio is on.Some light bulbs have three power settings (not including zero), obtained from multiple filaments that are individually switched and wired in parallel. What is the minimum number of filaments needed for three power settings?Is every emf a potential difference? Is every potential difference an emf? Explain.Explain which battery is doing the charging and which is being charged in Figure 21.45.Given a battery, an assortment of resistors, and a variety of voltage and current measuring devices, describe how you would determine the internal resistance of the battery.Two different 12-V automobile batteries on a store shelf are rated at 600 and 850 “cold cranking amps." Which has the smallest internal resistance?What are the advantages and disadvantages of connecting batteries in series? In parallel?Semitractor trucks use four large 12-V batteries. The starter system requires 24 V, while normal operation of the truck’s other electrical components utilizes 12 V. How could the four batteries be connected to produce 24 V? To produce 12 V? Why is 24 V better than 12 V for starting the truck's engine (a very heavy load)?Call all of the currents going into the junction in Figure 21.46 be positive? Explain.Apply the junction rule to junction b in Figure 21.47. Is any new information gained by applying the junction rule at e? (In the figure, each emt is represented by script E.)(a) What is the potential difference going from point a to point b in Figure 21.47? (b) What is the potential difference going from c to b? (c) From e to g? (d) From e to d?Apply the loop rule to loop afedcba in Figure 21.47.Apply the loop rule to loops abgefa and cbgedc in Figure 21.47.Why should you not connect an ammeter directly across a voltage source as shown in Figure 21.48? (Note that script E in the figure stands for emf.)Suppose you are using a multimeter (one designed to measure a range of voltages, currents, and resistances) to measure current in a circuit and you inadvertently leave it in a voltmeter mode. What effect will the meter have on the circuit? What would happen if you were measuring voltage but accidentally put the meter in the ammeter mode?Specify the points to which you could connect a voltmeter to measure the following potential differences in Figure 21.49: (a) the potential difference of the voltage source; (b) the potential difference across R1; (c) across R2: (d) across ; (e) across R2and R3.Not that there may be more than one answer to each part.To measure currents in Figure 21.49, you would replace a wire between two points with an ammeter. Specify the points between which you would place an ammeter to measure the following: (a) the total current: (b) the current flowing through R1(c) through R2; (d) through R3. Note that there may be more than one answer to each part.Why can a null measurement be more accurate than one using standard voltmeters and ammeters? What factors limit the accuracy of null measurements?If a potentiometer is used to measure cell emfs on the order of a few volts, why is it most accurate for the standard emfs to be the same order of magnitude and the resistances to be in the range of a few ohms?Regarding the units involved in the relationship t = RC, verify that the units of resistance times capacitance are time, that is, . F = S.The RC time constant in heart defibrillation is crucial to limiting the time the current flows. If the capacitance in the defibrillation unit is fixed, how would you manipulate resistance in the circuit to adjust the RC constant t? Would an adjustment of the applied voltage also be needed to ensure that the current delivered has an appropriate value?When making an ECG measurement, it is important to measure voltage variations over small time intervals. The time is limited by the RC constant of the circuit-it is not possible to measure time variations shorter than RC. How would you manipulate R and C in the circuit to allow the necessary measurements?Draw two graphs of charge versus time on a capacitor. Draw one for charging an initially uncharged capacitor in series with a resistor, as in the circuit in Figure 21.38, starting from t = 0. Draw the other for discharging a capacitor through a resistor, as in the circuit in Figure 21.39, starting at t = 0, with an initial charge Q0. Show at least two intervals of t.When charging a capacitor, as discussed in conjunction with Figure 21.38, how long does it take for the voltage on the capacitor to reach emf? Is this a problem?When discharging a capacitor, as discussed in conjunction with Figure 21.39, how long does it take for the voltage on the capacitor to reach zero? Is this a problem?Referring to Figure 21.38, draw a graph of potential difference across the resistor versus time, showing at least two intervals of t. Also draw a graph of current versus time for this situation.A long, inexpensive extension cord is connected from inside the house to a refrigerator outside. The refrigerator doesn't run as it should. What might be the problem?In Figure 21.41. does the graph indicate the time constant is shorter for discharging than for charging? Would you expect ionized gas to have low resistance? How would you adjust R to get a longer time between flashes? Would adjusting R affect the discharge time?An electronic apparatus may have large capacitors at high voltage in the power supply section, presenting a shock hazard even when the apparatus is switched off. A “bleeder resistor" is therefore placed across such a capacitor, as shown schematically in Figure 21.50, to bleed the charge from it after the apparatus is off. Why must the bleeder resistance be much greater than the effective resistance of the rest of the circuit? How does this affect the time constant for discharging the capacitor?(a) What is the resistance often 275-O resistors connected in series? (b) In parallel?(a) What is the resistance of a 1.00 102-O, a 2.50-k O, and a 4.00-kresistor connected in series? (b) In parallel?What are the largest and smallest resistances you can obtain by connecting a 36.0-O, a 50.0-O, and a 700-O resistor together?An 1800-W toaster, a 1400-W electric frying pan, and a 75-W lamp are plugged into the same outlet in a 15-A, 120-V circuit. (The three devices are in parallel when plugged into the same socket.). (a) What current is drawn by each device? Will this combination blow the 15-A fuse?Your car’s 30.0-W headlight and 2.40-kW starter are ordinarily connected in parallel in a 12.0-V system. What power would one headlight and the starter consume if connected in series to a 12.0-V battery? (Neglect any other resistance in the circuit and any change in resistance in the two devices.)(a) Given a48.0-V battery and 24.0-O and 96.0-O resistors, find the current and power for each when connected in series, (b) Repeat when the resistances are in parallel.Referring to the example combining series and parallel circuits and Figure 21.6, calculate I3in the following two different ways: (a) from the known values of I and I2 ; (b) using Ohm’s law for R3. In both parts explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.Referring to Figure 21.6: (a) Calculate P3 and note how it this module. (b) Find the total power supplied by the source and compare it with the sum of the powers dissipated by the resistors.Refer to Figure 21.7 and the discussion of lights dimming when a heavy appliance comes on. (a) Given the voltage source is 120 V, the wire resistance is 0.400, and the bulb is nominally 75.0 W, what power will the bulb dissipate if a total of 15.0 A passes through the wires when the motor comes on? Assume negligible change in bulb resistance. (b) What power is consumed by the motor?A 240-kV power transmission line carrying 5.00x102. A is hung from grounded metal towers by ceramic insulators, each having a 1.00x 109- resistance. Figure 21.51. (a) What is the resistance to ground of 100 of these insulators? (b) Calculate the power dissipated by 100 of them, (c) What fraction of the power carried by the line is this? Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.Show that if two resistors R1and R2are combined and one is much greater than the other (R 1 >>R 2 ): (a) Their series resistance is very nearly equal to the greater resistance R 1. (b) Their parallel resistance is very nearly equal to smaller resistance R2.Unreasonable Results Two resistors, one having a resistance of 145 , are connected in parallel to produce a total resistance of 150 O. (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Unreasonable Results Two resistors, one having a resistance of 900 k, are connected in series to produce a total resistance of 0.500 ?O. (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Standard automobile batteries have six lead-acid cells in series, creating a total emf of 12.0 V. What is the emf of an individual lead-acid cell?Car bon-zinc dry cells (sometimes referred to as non- alkaline cells) have an emf of 1.54 V, and they are produced as single cells or in various combinations to form other voltages. (a) How many 1.54-V cells are needed to make the common 9-V battery used in many small electronic devices? (b)What is the actual emf of the approximately 9-V battery? (c) Discuss how internal resistance in the series connection of cells will affect the terminal voltage of this approximately 9-V battery.What is the output voltage of a 3.0000-V lithium cell in a digital wristwatch that draws 0.300 mA, if the cell s internal resistance is 2.00 ?(a) What is the terminal voltage of a large 1.54-V carbon-zinc dry cell used in a physics lab to supply 2.00 A to a circuit if the cell’s internal resistance is 0.100 ? (b) How much electrical power does the cell produce? (c) What power goes to its load?What is the internal resistance of an automobile battery that has an emf of 12.0 V and a terminal voltage of 15.0 V while a current of 8.00 A is charging it?(a) Find the terminal voltage of a 12.0-V motorcycle battery having a 0.600- internal resistance, if it is being charged by a current of 10.0 A. (b) What is the output voltage of the battery charger?A car battery with a 12-V emf and an internal resistance of 0.050 is being charged with a current of 60 A. Note that in this process the battery is being charged. (a) What is the potential difference across its terminals? (b) At what rate is thermal energy being dissipated in the battery? (c) At what rate is electric energy being converted to chemical energy? (d) What are the answers to (a) and (b) when the battery is used to supply 60 A to the starter motor?The hot resistance of a flashlight bulb is 2.30 , and it is run by a 1.58-V alkaline cell having a 0.100-O internal resistance. (a) What current flows? (b) Calculate the power supplied to the bulb using I2Rbulh? (c). power the same as calculated using V2Rbulb?The label or a portable radio recommends the use of rechargeable nickel-cadmium cells (nicads), although they have a 1.25-V emf while alkaline cells have a 1.58-V emf. The radio has a 3.20- resistance, (a) Draw a circuit diagram ot the radio and its batteries. Now, calculate the power delivered to the radio, (b) When using Nicad cells each having an internal resistance of 0.0400O. (c) When using alkaline cells each having an internal resistance of 0.200 . (d) Does this difference seem significant, considering that the radio s effective resistance is lowered when its volume is turned up?An automobile starter motor has an equivalent resistance of 0.0500 and is supplied by a 12.0-V battery with a 0.0100- internal resistance, (a) What is the current to the motor? (b) What voltage is applied to it? (c) What power is supplied to the motor? (d) Repeat these calculations for when the battery connections are corroded and add 0.0900 to the circuit. (Significant problems are caused by even small amounts of unwanted resistance in low-voltage, high-current applications.)A child’s electronic toy is supplied by three 1.58-V alkaline cells having internal resistances of 0.0200 in series with a 1.53-V carbon-zinc dry cell having a 0.100- internal resistance. The load resistance is 10.0 . (a) Draw a circuit diagram of the toy and its batteries, (b) What current flows? (c) How much power is supplied to the load? (d) What is the internal resistance of the dry cell if it goes bad, resulting in only 0.500 W being supplied to the load?(a) What is the internal resistance of a voltage source if its terminal voltage drops by 2.00 V when the current supplied increases by 5.00 A? (b) Can the emf of the voltage source be found with the information supplied?A person with body resistance between his hands of 1.00 k accidentally grasps the terminals of a 20.0-kV power supply. (Do NOT do this!) (a) Draw a circuit diagram to represent the situation. (b) If the internal resistance of the power supply is 2000 , what is the current through his body? (c) What is the power dissipated in his body? (d) If the power supply is to be made safe by increasing its internal resistance, what should the internal resistance be for the maximum current in this situation to be 1.00 mA or less? (e) Will this modification compromise the effectiveness of the power supply for driving low-re si stance devices? Explain your reasoning,Electric fish generate current with biological cells called electroplaques, which are physiological emf devices. The electroplaques in the South American eel are arranged in 140 rows, each row stretching horizontally along the body and each containing 5000 electroplaques. Each electroplaque has an emf of 0.15 V and internal resistance of 0.25 . If the water surrounding the fish has resistance of 800 , how much current can the eel produce in water from near its head to near its tail?Integrated Concepts A 12.0-V emf automobile battery has a terminal voltage of 16.0 V when being charged by a current of 10.0 A. (a) What is the battery’s internal resistance? (b) What power is dissipated inside the battery? (c) At what rate (in °C/min ) will its temperature increase if its mass is 20.0 kg and it has a specific heat of 0.300 kcal/kg. °C, assuming no heat escapes?Unreasonable Results A 1.58-V alkaline cell with a 0.200- internal resistance is supplying 8.50 A to a load, {a) What is its terminal voltage? (b) What is the value of the load resistance? (c) What is unreasonable about these results? (d) Which assumptions are unreasonable or inconsistent?Unreasonable Results (a) What is the internal resistance of a 1.54-V dry cell that supplies 1.00 W of power to a 15.0- bulb? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Apply the loop rule to loop abcdefgha in Figure 21.25Apply the loop rule to loop aedcba in Figure 21.25.Verify the second equation in Example 21.5 by substituting the values found for the currents I1 and I2.Verify the third equation in Example 21.5 by substituting the values found for the currents I1 and I3.Apply the junction rule at point a in Figure 21.52.Apply the loop rule to loop abcdefghija in Figure 21.52.Apply the loop rule to loop akledcba in Figure 21.52.Find the currents flowing in the circuit in Figure 21.52. Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.Solve Example 21.5, but use loop abcdefgha instead of loop akledcba. Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.Find the currents flowing in the circuit in Figure 21.47.Unreasonable Results Consider the circuit in Figure 21.53, and suppose that the emfs are unknown and the currents are given to be I1 = 5.00 A. I2= 3.0 A, and I3 = 2.00 A. (a) Could you find the emfs? (b) What is wrong with the assumptions?What is the sensitivity of the galvanometer (that is, what current gives a full-scale deflection) inside a voltmeter that has a 1,00-M resistance or its 30.0-V scale?What is the sensitivity of the galvanometer (that is, what current gives a full-scale deflection) inside a voltmeter that has a 25.0-k resistance on its 10G-V scale?Find the resistance that must be placed in series with a 25.0-galvanometer having a 50.0-A sensitivity (the same as the one discussed in the text) to allow it to be used as a voltmeter with a 0.100-v full-scale reading.Find the resistance that must be placed in series with a 25.0- galvanometer having a 50.0-A sensitivity (the same as the one discussed in the text) to allow it to he used as a voltmeter with a 0.300-V full-scale reading. Include a circuit diagram with your solution.Find the resistance that must be placed in series with a 25.0- galvanometer having a 50.0-A sensitivity (the same as the one discussed in the text) to allow it to be used as an ammeter with a 10.0-A full-scale reading. Include a circuit diagram with your solution.Find the resistance that must be placed in paralled with a 25.0- galvanometer having a 50.0A sensitivity (the same as the one discussed in the text) to allow it to be used as an ammeter with a 300-mA full-scale reading.Find the resistance that must be placed in series with a 10.0- galvanometer having a 100A sensitivity to allow it to be used as a voltmeter with: (a) 300-V full-scale reading, and (b) a 300-V full scale reading.Find the resistance that must be placed in parallel with a 10.0 galvanometer having a 100A sensitivity to allow it to be used as an ammeter with” (a) 2 20.0-A full-scale reading, and (b) a 100-mA full scale reading.Suppose you measure the terminal voltage of a 1.585-V alkaline cell having an internal resistance of 0.100 by placing a 1.00-k voltmeter across its terminals. (See Figure 21.54.) (a) What current flows? (b) Find the terminal voltage, (c) To see how close the measured terminal voltage is to the emf; calculate their ratio.Suppose you measure the terminal voltage of a 3.2G0-V lithium cell having an internal resistance of 5.00 by placing a 1.00-k voltmeter across its terminals, (a) What current flows? (b) Find the terminal voltage, (c) To see how close the measured terminal voltage is to the emf, calculate their ratio.A certain ammeter has a resistance of 5.00X10-5 an its 3.00-A scale and contains a 10.0- galvanometer. What is the sensitivity of the galvanometer?A 1,00-?O voltmeter is placed in parallel with a 75.0kresistor in a circuit, (a) Draw a circuit diagram of the connection, (b) What is the resistance of the combination? If the voltage across the combination is kept the same as it was across the 75.0-kresistor alone, what is the percent increase in current? (d) If the current through the combination is kept the same as it was through the 75.0-kresistor alone, what is the percentage decrease in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.A 0.0200- ammeter is placed in series with a 10.00- resistor in a circuit, (a) Draw a circuit diagram of the connection, (b) Calculate the resistance of the combination, (c) If the voltage is kept the same across the combination as it was through the 10.00- resistor alone, what is the percent decrease in current? (d) If the current is kept the same through the combination as it was through the 10.00-resistor alone, what is the percent increase in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.Unreasonable Results Suppose you have a 40.0- galvanometer with a 25.0-A sensitivity, (a) What resistance would you put in series with it to allow it to be used as a voltmeter that has a full-scale deflection for 0.500 mV? (b) What is unreasonable about this result? (c) Which assumptions are responsible?Unreasonable Results (a) What resistance would you put in parallel with a 40.0- galvanometer having a 25.0-A sensitivity to allow it to be used as an ammeter that has a full-scale deflection for 10.0? (b) What is unreasonable about this result? (c) Which assumptions are responsible?What is the emf x of a cell being measured in a potentiometer if the standard cell’s emf is 12.0 V and the potentiometer balances for Rx= 5,000 and Rs= 2.500 ?Calculate the emfx of a dry cell for which a potentiometer is balanced when Rx= 1,200 , while an alkaline standard cell with an emf of 1.600 V requires Rs= 1.247 to balance the potentiometer.When an unknown resistance Rxis placed in a Wheatstone bridge, it is possible to balance the bridge by adjusting to be 2500 . What is Rxif R2R1 = 0.625?To what value must you adjust R3to balance a Wheatstone bridge, if the unknown resistance Rxis 100 , R1is 50.0 , and R2is 175 ?(a) What is the unknown emfx in a potentiometer that balances when Rxis 10.0 O, and balances when Rsis 15.0for a standard 3.000-V emf? (b) The same emfx is placed in the same potentiometer, which now balances when Rsis 15.0for a standard emf of 3.100 V. At what resistance Rxwill the potentiometer balance?Suppose you want to measure resistances in the range from 10,0 to 10.0 k using a Wheatstone bridge that has R2R1 = 2.000. Over what range should R3be adjustable?The timing device in an automobile’s intermittent wiper system is based on an RC time constant and utilizes 0.5.00F capacitor and available resistor. Over what range must R be made to vary to achieve time constants from 2.00 to 15.0 s?A heart pacemaker fires 72 times a minute, each time a 25.0 nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance?The duration of a photographic flash is related to an RC time constant, which is 0.100 s for a certain camera, (a) If the resistance of the flash lamp is 0.0400 during discharge, what is the size of the capacitor supplying its energy? (b) What is the time constant for charging the capacitor, if the charging resistance is 800k ?A 2.00- and a 7.50-F capacitor can be connected in series or parallel, as can a 25.0- and a 100k resistor. Calculate the four RC time constants possible from connecting the resulting capacitance and resistance in series.After two time constants, what percentage of the final voltage, emf, is on an initially uncharged capacitor C, charged through a resistance R ?A 500- resistor, an uncharged 1.50-F capacitor and a 6.16-V emf are connected in series, (a) What is the initial current? (b) What is the RC time constant? (c) What is the current after one time constant? (d) What is the voltage on the capacitor after one time constant?A heart defibrillator being used on a patient has an RC time constant of 10.0 ms due to the resistance of the patient and the capacitance of the defibrillator. (a) If the defibrillator has an 8.00F capacitance, what is the resistance of the path through the patient? (You may neglect the capacitance of the patient and the resistance of the defibrillator.) (b) If the initial voltage is 12.0 kV, how long does it take to decline to 6.00x102 V?An ECG monitor must have an RC time constant less than 1.00 102 to be able to measure variations in voltage over small time intervals, (a) If the resistance of the circuit (due mostly to that of the patient’s chest) is1.00k , what is the maximum capacitance of the circuit? (b) Would it be difficult in practice to limit the capacitance to less than the value found in (a)?Figure 21.55 shows how a bleeder resistor is used to discharge a capacitor after an electronic device is shut off allowing a person to work on the electronics with less risk of shock, (a) What is the time constant? (b) How long will it take to reduce the voltage on the capacitor to 0.250% (5% of 5%) of its full value once discharge begins? (c) If the capacitor is charged to a voltage V0through a 100-O resistance, calculate the time it takes to rise to 0.865V0(This is about two time constants.)Using the exact exponential treatment, find how much time is required to discharge a 250-? capacitor through a 500- resistor down to 1.00% of its original voltage.Using the exact exponential treatment, find how much time is required to charge an initially uncharged 100-pF capacitor through a 75.0-M resistor to 90.0% of its final voltage.Integrated Concepts If you wish to take a picture of a bullet traveling at 500 m/s, then a very brief flash of light produced by an RC discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one RC constant is acceptable, and given that the flash is driven by a 600F capacitor, what is the resistance in the flash tube?Integrated Concepts A flashing lamp in a Christmas earring is based on an RC discharge of a capacitor through its resistance. The effective duration of the flash is 0.250 s, during which it produces in average 0.500 W from an average 3.00 V. (a) What energy does it dissipate? (b) How much charge moves through the lamp? (c) Find the capacitance. (d) What is the resistance of the lamp?Integrated Concepts A 160F capacitor charged to 450 V is discharged through a 31.2-k resistor. (a) Find the time constant. (b) Calculate the temperature increase of the resistor, given that its mass is 2.50 g and its specific heat is 1.67kJkgC' noting that most of the thermal energy is retained in the short time of the discharge, (c) Calculate the new resistance, assuming it is pure carbon, (d) Does this change in resistance seem significant?Unreasonable Results (a) Calculate the capacitance needed to get an RC time constant of 1,00x103 s with a 0.100- resistor, (b) What is unreasonable about this result? (c) Which assumptions are responsible?Construct Your Own Problem Consider a camera's flash unit. Construct a problem in which you calculate the size of the capacitor that stores energy for the flash lamp. Among the things to be considered are th voltage applied to the capacitor, the energy needed in the flash and the associated charge needed on the capacitor, the resistance of the flash lamp during discharge, and the desired RC time constant.Construe! Your Own Problem Consider a rechargeable lithium cell that is to be used to power a camcorder. Construct a problem in which you calculate the internal resistance of the cell during normal operation. Also, calculate the minimum voltage output of a battery charger to be used to recharge your lithium cell. Among the things to be considered are the emf and useful terminal voltage of a lithium cell and the current it should be able to supply to a camcorder.Volcanic and other such activity at the mid-Athletic ridge extrudes material to fill the gap between separating tectonic plates associated with continental drift. The magnetization of rocks is found to reverse in a coordinated manner with distance from the ridge. What does this imply about the Earth's magnetic field and how could the knowledge of the spreading rate he used to give its historical record?Explain why the magnetic field would not be unique (that is, not have a single value) at a point in space where magnetic field lines might cross. (Consider the direction of the field at such a point.)List the ways in which magnetic field lines and electric field lines the similar. For example, the field direction is tangent to the line at any point in space. Also list the ways in which they differ. For example, electric force is parallel to electric field lines, whereas magnetic force on moving charges is perpendicular to magnetic field lines.Noting that the magnetic field lines of a bar magnet resemble the electric field lines of a pair of equal and opposite charges, do you expect the magnetic field to rapidly decrease in strength with distance from the magnet? Is this consistent with your experience with magnets?Is the Earth's magnetic field parallel to the ground at all locations? If not, where is it parallel to the surface? Is its strength the same at all locations? If not, where is it greatest?If a charged particle moves in a straight line through some region of space, can you say that the magnetic field in that region is necessarily zero?How can the motion of a charged particle be used to distinguish between a magnetic and an electric field?High-velocity charged particles can damage biological cells and are a component of radiation exposure in a variety of locations ranging from research facilities to natural background. Describe how you could use a magnetic field to shield yourself.If a cosmic ray proton approaches the Earth from outer space along a line toward the center of the Earth that lies in the plane of the equator, in what direction will it be deflected by the Earth’s magnetic field? What about an electron? A neutron?What are the signs of the charges on the particles in Figure 22.46?Which of the particles in Figure 22.47 has the greatest velocity, assuming they have identical charges and masses?Which of the particles in Figure 22.47 has the greatest mass, assuming all have identical charges and velocities?While operating, a high-precision TV monitor is placed on its side during maintenance. The image on the monitor changes color and blurs slightly. Discuss the possible relation of these effects to the Earth’s magnetic field.Discuss how the Hall effect could be used to obtain information on free charge density in a conductor. (Hint: Consider how drift velocity and current are related.)Draw a sketch of the situation in Figure 22.30 showing the direction of electrons carrying the current, and use RHR-l to verify the direction of the force on the wire.Verify than the direction of the line force in an MHD drive, such as that in Figure 22.32, does not depend on the sign of the charges carrying the current across the fluid.Why would a magnetohydrodynamic drive work better in ocean water than in fresh water? Also, why would superconducting magnets be desirable?Which is more likely to interfere with compass readings. AC current in your refrigerator or DC current when you start your car? Explain.Draw a diagram and use RHR-l to show that the forces on the top and bottom segments of the motor’s current loop in Figure 22.34 are vertical and produce no torque about the axis of rotation.Make a drawing and use RHR—2 to find the direction of the magnetic field of a current loop in a motor (such as in Figure 22.34). Then show that the direction of the torque on the loop is the same as produced by like poles repelling and unlike poles attracting.Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?It you have three parallel wires in the same plane, as in Figure 22.48, with currents in the outer two running in opposite directions, is it possible for the middle wire to be repelled by both? Attracted by both? Explain.Suppose two long straight wires run perpendicular to one another without touching. Does one exert a net force on the other? If so, what is its direction? Does one exert a net torque on the other? If so, what is its direction? Justify your responses by using the right hand rules.Use the right hand rules to show that the force between the two loops in Figure 22.49 is attractive it the currents are in the same direction and repulsive it they are in opposite directions. Is this consistent with like poles of the loops repelling and unlike poles of the loops attracting? Draw sketches to justify your answers.If one of the loops in Figure 22.49 is titled slightly relative to the other and then currents are in the same direction, what are the directions of the torques they exert on each other? Does this imply that the poles of the bar magnet—like fields they create will line up with each other if the loops are allowed to rotate?Electric field lines can be shielded by me Faraday cage effect. Can we have magnetic shielding? Can we have gravitational shielding?Measurements at the weak and ?uctuating magnetic fields associated with brain activity are called magnetoencephalograms (MEGS). Do the brain’s magnetic fields imply coordinated or uncoordinated nerve impulses? Explain.Discuss the possibility that a Hall voltage would be generated on the moving heart of a patient during MRI imaging. Also discuss the same effect on the wires of a pacemaker. (The fact that patients with pacemakers are not given MRIs is significant)A patient in an MRI unit turns his head quickly to one side and experiences momentary dizziness and a strange taste in his mouth. Discuss the possible causes.You are told that in a certain region there is either a uniform electric or magnetic field. What measurement or observation could you make to determine the type? (Ignore the Earth’s magnetic field.)An example of magnetohydrodynamics (MHD) comes from the flow of a river (salty water). This fluid interacts with the Earth’s magnetic field to produce a potential difference between the two river banks. How would you go about calculating the potential difference?Draw gravitational field lines between 2 masses, electric field lines between a positive and negative charge, electric field lines between 2 positive charges and magnetic field ?nes around a magnet. Qualitatively describe the differences between the fields and the entities responsible for the field lines.What is the direction of the magnetic force on a positive charge that moves as shown in each of the six cases shown in Figure 22.59?Repeal Exercise 22.1 for a negative charge.What is the direction of the velocity of a negative charge that experiences the magnetic force shown in each of the three cases in Figure 22.51, assuming it moves perpendicular to B?Repeal Exercise 22.3 for a positive charge.What is the direction of the magnetic field that produces the magnetic force on a positive charge as shown in each of the three cases in the figure below, assuming B is perpendicular to V?Repeal Exercise 22.5 for a negative charge.What is the maximum force on an aluminum rod with a 0.100C charge that you pass between the poles of a 1.50T permanent magnet at a speed of 5.00 m/s? In what direction is the force?(a) Aircraft sometimes acquire small static charges. Suppose a supersonic jet has a 0.500C charge and ?ies due west at a speed of 660 m/s ever the Earth’s south magnetic pole, where the 8.00105T magnetic field points straight up. What are the direction and the magnitude of the magnetic force on the plane? (b) Discuss whether the value obtained in part (a) implies this is a significant or negligible effect.(a) A cosmic ray proton moving toward the Earth at 5.00107m/s experiences a magnetic force of 1.701016N. What is the strength of the magnetic field it there is a 45° angle between it and the proton’s velocity? (b) Is the value obtained in part (a) consistent with the known strength of the Earth’s magnetic field on its surface? Discuss.An electron moving at 4.00103m/s in a 1.25T magnetic field experiences a magnetic force of 1.401016N. What angle does the velocity at the electron make with the magnetic field? There are two answers.(a) A physicist performing a sensitive measurement wants to limit the magnetic force on a moving charge in her equipment to less than 1.001012N. What is the greatest the charge can be if it moves at a maximum speed of 30.0 m/s in the Earth’s field? (b) Discuss whether it would be difficult to limit the charge to less than the value found in (a) by competing it with typical static electricity and noting that static is often absent.A cosmic ray electron moves at 7.50106m/s perpendicular to the Earth's magnetic field at an altitude where field strength is 1.00105T. What is the radius of the circular pain the electron follows?A proton moves at 7.50107m/s perpendicular to a magnetic field. The field causes the proton to travel in a circular path of radius 0.800 m. What is the field strength?(a) Viewers of Star Trek hear of an antimatter drive on the Starship Enterprise. One possibility for such a futuristic energy source is to store antimatter charged particles in a vacuum chamber, circulating in a magnetic field, and then extract them as needed. Antimatter annihilates with normal matter, producing pure energy. What strength magnetic field is needed to hold antiprotons, moving at 5.00107m/s in a circular path 2.00 m in radius? Antiprotons have the same mass as protons but the opposite (negative) charge. (b) Is this field strength obtainable with today’s technology or is it a futuristic possibility?(a) An oxygen16 ion with a mass at 2.661026kg travels at 5.00106m/s perpendicular to a 1.20T magnetic field, which makes it move in a circular arc with a 0.231-m radius. What positive charge is on the ion? (b) What is the radio of this charge to the charge of an electron? (c) Discuss why the radio found in (b) should be an integer.What radius circular path does an electron travel if it moves at the same speed and in the same magnetic field as the proton in Exercise 22.13?A velocity selector in a mass spectrometer uses a 0.100T magnetic field. (a) What electric field strength is needed to select a speed of 4.00106m/s ? (b) What is the voltage between the plates if they are separated by 1.00 cm?An electron in a TV CRT moves with a speed at 6.00107m/s, in a direction perpendicular to the Earth’s field, which has a strength of 5.00105T. (a) What strength electric field must be applied perpendicular to the Earth’s field to make the election moves in a straight line? (b) If this is done between plates separated by 1.00 cm, what is the voltage applied? (Note that TVs are usually surrounded by a ferromagnetic material to shield against external magnetic fields and avoid the need for such a correction.)(a) At what speed will a proton move in a circular path of the same radius as the electron in Exercise 22.12? (b) What would the radius of the path be it the proton had the same speed as the electron? (c) What would the radius be if the proton had the same kinetic energy as the electron? (d) The same momentum?A mass spectrometer is being used to separate common oxygen16 from the much rarer oxygen18, taken from a sample of old glacial ice. (The relative abundance of these oxygen isotopes is related to climatic temperature at the time the ice was deposited.) The ratio of the masses of these two ions is 16 to 18, the mass of oxygen-16 is 2.661026kg, and they are singly charged and travel at 5.00106m/s in a 1.20T magnetic field. What is the separation between their paths when they hit a target after traversing a semicircle?(a) Triply charged uranium-235 and uranium-238 ions are being separated in a mass spectrometer. (The much rarer uranium-235 is used as reactor fuel.) The masses of the ions are 3.901025kg kg and 3.951025kg, respectively, and 1hey travel at 3.00105m/s in a 0.250T field. What is the separation between their paths when they hit a target after traversing a semicircle? (b) Discuss whether this distance between their pains seems to be big enough to be practical in the separation of uranium-235 from uranium-238.A large water main is 2.50 m in diameter and the average water velocity is 6.00 m/s. Find the Hall voltage produced if the pipe runs perpendicular to the Earth's 5.00105T field.What Hall voltage is produced by a 0.200T field applied across a 2.60-cm-diameter aorta when blood velocity is 60.0 cm/s?(a) What is the speed of a supersonic aircraft with a 17.0-m wingspan, if it experiences a 1.60V Hall voltage between its wing lips when in level flight over the north magnetic pole, where the Earth's field strength is 8.00105T ? (b) Explain why very little current flows as a result of this Hall voltage.A nonmechanical water meter could utilize the Hall effect by applying a magnetic field across a metal pipe and measuring the Hall voltage produced. What is the average fluid velocity in a 3.00-cm-diameter pipe, if a 0.500-T field across it creates a 60.0-mV Hall voltage?Calculate the Hall voltage induced on a patient’s heart while being scanned by an MRI unit. Approximate the conducting pain on the heart wall by a wire 7.50 cm long that moves at 10.0 cm/s perpendicular to a 1.50T magnetic field.A Hall probe calibrated to read 1.00V when placed in a 2.00T field is placed in a 0.150T field. What is its output voltage?Using information in Example 20.6, what would the Hall voltage be if a 2.00T field is applied across a 10-gauge copper wire (2.588 mm in diameter) carrying a 20.0-A current?Show that the Hall voltage across wires made of the same material, carrying identical currents, and subjected to the same magnetic field is inversely proportional to their diameters. (Hint Consider how drift velocity depends on wire diameter.)A patient with a pacemaker is mistakenly being scanned for an MRI image. A 10. 0-cm-long section of pacemaker wire moves at a speed of 10.0 cm/s perpendicular to the MRI unit’s magnetic field and a 20.0-mV Hall voltage is induced. What is the magnetic field strength?What is the direction of the magnetic force on the current in earth of the six cases in Figure 22.53?What is the direction of a current that experiences the magnetic force shown in each of the three cases in Figure 22.54, assuming the current runs perpendicular to B?What is the direction of the magnetic field that produces the magnetic force shown on the currents in each of the three cases in Figure 22.55, assuming B is perpendicular to I?(a) What is the force per meter on a lightning bolt at the equator that carries 20,000 A perpendicular to the Earth's 3.00105-T field? (b) What is the direction of the force it the current is straight up and the Earth’s field direction is due north, parallel to the ground?(a) A DC power line for a light-rail system carries 1000 A at an angle of 30.0° to the Earth’s 5.00105-T field. What is the force on a 100-m section of this line? (b) Discuss practical concerns this presents, if any.What force is exerted on the water in an MHD drive utilizing a 25.0-cm-diameter tube, it 100-A current is passed across the tube that is perpendicular to a 2.00T magnetic field? (The relatively small size of this force indicates the need for very large currents and magnetic fields to make practical MHD drives.)A wire carrying a 30.0-A current passes between the poles of a strong magnet that is perpendicular to its field and experiences a 2.16-N force on the 4.00 cm of wire in the field. What is the average field strength?(a) A 0.750-m-long section of cable carrying current to a car starter motor makes an angle at 60° with the Earth’s 5.00105-T field. What is the current when the wire experiences a force of 7.00103N ? (b) If you run the wire between the poles of a strong horseshoe magnet, subjecting 5.00 cm of it to a 1.75T field, what force is exerted on this segment of wire?(a) What is the angle between a wire carrying an 8.00-A current and the 1.20-T field it is in if 50.0 cm of the wire experiences a magnetic force of 2.40 N? (b) What is the force on the wire if it is rotated to make an angle of 90° with the field?The force on the rectangular loop of wire in the magnetic field in Figure 22.56 can be used to measure field strength. The field is uniform, and the plane of the loop is perpendicular to the field. (a) What is the direction of the magnetic force on the loop? Justify the claim that the forces on the sides of the loop are equal and opposite, independent at how much of the loop is in the field and do not affect the net force on the loop. (b) If a current of 5.00 A is used, what is the force per tesla on the 20.0-cm-wide loop? Figure 22.56 A rectangular loop of wire carrying a current is perpendicular to a magnetic field. The field is uniform in the region shown and is zero outside that region.(a) By how many percent is the torque of a motor decreased if its permanent magnets lose 5.0% of their strength? (b) How many percent would the current need to be increased to return the torque to original values?(a) What is me maximum torque on a 150Turn square loop of wire 18.0 cm on a side that carries a 50.0-A current in a 1.60T field? (b) What is the torque when (is 10.9°?Find the current through a loop needed to create a maximum torque of 9.00 N (m. The loop has 50 square turns that are 15.0 cm on a side and is in a uniform 0.800T magnetic field.Calculate the magnetic field strength needed on a 200-1urn square loop 20.0 cm on a side to create a maximum torque of 300 N (m it me loop is carrying 25.0 A.Since the equation for torque on a current-carrying loop is =NIABsin, the units of N (m must equal units of A (m2 T. Verify this.(a) At what angle (is the torque on a current loop 90.0% of maximum? (b) 50.0% of maximum? (c) 10.0% of maximum?A proton has a magnetic field due to its spin on its axis. The field is similar to that created by a circular current loop 0.6501015m in radius with a current of 1.05104A (no kidding). Find the maximum torque on a proton in a 2.50T field. (This is a significant torque on a small particle.)(a) A 200Turn circular loop of radius 50.0 cm is vertical, with its axis on an east-west line. A current of 100 A circulates clockwise in the loop when viewed from the east. The Earth’s field here is due norm, parallel to me ground, with a strength of 3.00105T. What are 1he direction and magnitude of the torque on the loop? (b) Does this device have any practical applications as a motor?Repeat Exercise 22.41, but with the loop lying flat on the ground with its current circulating counterclockwise (when viewed from above) in a location where the Earth’s field is north, but at an angle 45.0° below the horizontal and with a strength at 6.00105T.(a) The hot and neutral wires supplying DC power to a light-rail commuter train carry 800 A and are separated by 7.50 cm. What is the magnitude and direction of the force between 50.0 m of these wires? (b) Discuss the practical consequences of this force, if any.The force per meter between the two wires of a jumper cable being used to start a stalled car is 0.225 N/m. (a) What is the current in the wires, given they are separated by 2.00 cm? (b) Is the force attractive or repulsive?A 2.50m segment of wire supplying current to the motor of a submerged submarine carries 1000 A and feels a 4.00-N repulsive force from a parallel wire 5.00 cm away. What is the direction and magnitude of the current in the other wire?The wire carrying 400 A to The motor of a commuter train feels an attractive force of 4.00103N/m due to a parallel wire carrying 5.00 A to a headlight. (a) How far apart are the wires? (b) Are the currents in the same direction?An AC appliance cord has its hot and neutral wires separated by 3.00 mm and carries a 5.00-A current. (a) What is the average force per meter between the wires in the cord? (b) What is the maximum force per meter between the wires? (c) Are the forces attractive or repulsive? (d) Do appliance cords need any special design features to compensate for these forces?Figure 22.57 shows a long straight wire near a rectangular current loop. What is the direction and magnitude of the total force on the loop?Find the direction and magnitude of the force that each wire experiences in Figure 22.58(a) by, using vector addition.Find the direction and magnitude of the force that each wire experiences in Figure 22.58(b), using vector addition.Indicate whether the magnetic field created in each of the three situations shown in Figure 22.59 is into or out of the page on the left and right of the current.What are the directions of the fields in the center of the loop and coils shown in Figure 22.60?What are the directions of the currents in the loop and coils shown in Figure 22.61?To see why an MRI utilizes iron to increase the magnetic field created by a coil, calculate the current needed in a 400-looppermeter circular coil 0.660 m in radius to create a 1.20T field (typical of an MRI instrument) at its center with no iron present. The magnetic field of a proton is approximately like that of a circular current loop 0.6501015m in radius carrying 1.05104A. What is the field at the center of such a loop?Inside a motor, 30.0 A passes through a 250-turn circular loop that is 10.0 cm in radius. What i5 the magnetic field strength created at its center?Nonnuclear submarines use batteries for power when submerged. (a) Find the magnetic field 50.0 cm from a straight wire carrying 1200 A from me batteries to the drive mechanism of a submarine. (b) What is the field if the wires to and from the drive mechanism are side by side? (c) Discuss the effects this could have for a compass on the submarine that is not shielded.How strong is the magnetic field inside a solenoid with 10,000 turns per meter that carries 20.0 A?What current is needed in the solenoid described in Exercise 22.58 to produce a magnetic field 104 times the Earth’s magnetic field of 5.00105T ?How far from the starter cable of a car, carrying 150 A, must you be to experience a field less than the Earth's (5.00105T) ? Assume a long straight wire carries the current. (In practice, the body of your car shields the dashboard compass.)Measurements affect the system being measured, such as the current loop in Figure 22.56. (a) Estimate file field the loop creates by calculating the field at the center of a circular loop 20.0 cm in diameter carrying 5.00 A. (b) What is the smallest field strength this loop can be used to measure, if its field must alter the measured field by less than 0.0100%?Figure 22.62 shows a long straight wire just touching a loop carrying a current I1. Beth lie in the same plane. (a) What direction must the current I2 in the straight wire have to create a field at the center of the loop in the direction opposite to that created by the loop? (b) What is the ratio at I1/I2 that gives zero field strength at the center at the loop? (c) What is the direction of the field directly above the loop under this circumstance?Find the magnitude and direction of the magnetic field at the point equidistant from the wires in Figure 22.58(a), using the rules of vector addition to sum the contributions from each wire.Find the magnitude and direction of the magnetic field at the point equidistant from the wires in Figure 22.58(b), using the rules of vector addition to sum the contributions from each wire.What current is needed in the top wire in Figure 22.58(a) to produce a field of zero at the point equidistant from the wires, if the currents in the bottom two wires are both 10.0 A into the page?Calculate the size of the magnetic field 20 m below a high voltage power line. The line carries 450 MW at a voltage of 300,000 V.Integrated Concepts A pendulum is set up so that its bob (a thin copper disk) swings between the poles of a permanent magnet as shown in Figure 22.63. What is the magnitude and direction of the magnetic force on the bub at the lowest point in its path, if it has a positive 0.250C charge and is released from a height of 30.0 cm above its lowest point? The magnetic field strength is 1.50 T. (b) What is the acceleration of the bob at the bottom of its swing it its mass is 30.0 grams and it is hung from a fiexible string? Be certain to include a free-body diagram as pan of your analysis.Integrated Concepts (a) What voltage will accelerate electrons to a speed of 6.00107m/s ? (b) Find the radius of curvature of the path of a proton accelerated through this potential in a 0.500-T field and compare this with the radius of curvature of an electron accelerated through the same potential.Integrated Concepts Find the radius of curvature of the path of a 25.0-Mev proton moving perpendicularly to the 1.20T field of a cyclotron.Integrated Concepts To construct a nonmechanical water meter, a 0.500T magnetic field is placed across the supply water pipe to a home and the Hall voltage is recorded. (a) Find the flow rate in liters per second through a 3.00-cm-diameter pipe if the Hall voltage is 60.0 mV. (b) What would the Hall voltage be for the same flow rate through a 10.0-cm-diameter pipe with the same field applied?Integrated Concepts (a) Using the values given for an MHD drive in Exercise 22.59, and assuming the force is uniformly applied to the fluid, calculate the pressure created in N/m2. (b) Is 1his a signi?cant fraction of an atmosphere?Integrated Concepts (a) Calculate the maximum torque on a 50Turn, 1.50 cm radius circular current loop carrying 50A in a 0.500T field. (b) If this coil is to be used in a galvanometer that reads 50A full scale, what force constant spring must be used, if it is attached 1.00 cm from the axis of rotation and is stretched by the 60° are moved?Integrated Concepts A current balance used to define the ampere is designed so that the current through it is constant, as is the distance between wires. Even so, if the wires change length with temperature, the force between them will change. What percent change in force per degree will occur if the wires are copper?Integrated Concepts (a) Show that the period of the circular orbit of a charged particle moving perpendicularly to a uniform magnetic field is T = 2(m/(qB). (b) What is the frequency f? (c) What is the angular velocity ( Note that these results are independent of the velocity and radius of the orbit and, hence, of the energy of the particle. (Figure 22.64.] Figure 22.6-4 Cyclotrons accelerate charged particles orbiting in a magnetic field by placing an AC voltage on the metal Dees, between which the particles move, so that energy is added twice each orbit. The frequency is constant, since it is independent of the particle energyThe radius of the orbit simply increases with energy until the particles approach the edge and are extracted for various experiments and applications.Integrated Concepts A cyclotron accelerates charged particles as shown in Figure 22.64. Using the results of the previous problem, calculate the frequency of the accelerating voltage needed for a proton in a 1.20-T field.Integrated Concepts (a) A 0.140-kg baseball, pitched at 40.0 m/s horizontally and perpendicular to the Earth's horizontal 5.00105T field, has a 100-nC charge on it. What distance is it deflected from its path by the magnetic force, after traveling 30.0 m horizontally? (b) Would you suggest this as a secret technique for a pitcher to throw curve balls?Integrated Concepts (a) What is the direction of the force on a wire carrying a current due east in a location where the Earth’s field is due north? Both are parallel to the ground. (b) Calculate the force per meter if the wire carries 20.0 A and the field strength is 3.00105T. (c) What diameter copper wire would have its weight supported by this force? (d) Calculate the resistance per meter and the voltage per meter needed.Integrated Concepts One long straight wire is to be held directly above another by repulsion between 1heir currents. The lower wire carries 100 A and the wire 7.50 cm above it is 10gauge (2.588 mm diameter) copper wire. (a) What current must flow in the upper wire, neglecting the Earth’s field? (b) What is the smallest current if the Earth’s 3.00105T field is parallel to the ground and is not neglected? (c) Is the supported wire in a stable or unstable equilibrium if displaced vertically? If displaced horizontally?Unreasonable Results (a) Find the charge on a baseball, thrown at 35.0 m/s perpendicular to the Earth’s 5.00105T field, that experiences a 1.00-N magnetic force. (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?Unreasonable Results A charged particle having mass 6.641027kg (that of a helium atom) moving at 8.70105m/s perpendicular to a 1.50T magnetic field travels in a circular path of radius 16.0 mm. (a) What is the charge of the particle? (b) What is unreasonable about this result? (c) Which assumptions are responsible?Unreasonable Results An inventor wants to generate 120V power by moving a 1.00mlong wire perpendicular to the Earth’s 5.00105T field. (a) Find the speed with which the wire must move. (b) What is unreasonable about this result? (c) Which assumption is responsible?Unreasonable Results Frustrated by the small Hall voltage obtained in blood flow measurements, a medical physicist decides to increase the applied magnetic field strength to get a 0.500V output for blood moving at 30.0 cm/s in a 1.50cmdiameter vessel. (a) What magnetic field strength is needed? (b) What is unreasonable about this result? (c) Which premise is responsible?Unreasonable Results A surveyor 100 m from a long straight 200-kV DC power line suspects that its magnetic field may equal that of the Earth and affect compass readings. (a) Calculate the current in the wire needed to create a 5.00105T field at this distance. (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?Construct Your Own Problem Consider a mass separator that applies a magnetic field perpendicular to the velocity of ions and separates the ions based on the radius of curvature of their paths in the field. Construct a problem in which you calculate the magnetic field strength needed to separate two ions that differ in mass, but not charge, and have the same initial velocity. Among the things to consider are the types of ions, the velocities they can be given before entering the magnetic field, and a reasonable value for the radius of curvature of the paths they follow. In addition, calculate the separation distance between the ions at the point where they are detected.Construct Your Own Problem Consider using the torque on a current-carrying coil in a magnetic field to detect relatively small magnetic fields (less than the field of the Earth, for example). Construct a problem in which you calculate the maximum torque on a current- carrying loop in a magnetic field. Among the things to be considered are the size of the coil, the number of loops it has, the current you pass through the coil, and the size of the field you wish to detect. Discuss whether the torque produced is large enough to be effectively measured. Your instructor may also wish for you to consider the effects, if any, of the field produced by the coil on the surroundings that could affect detection of the small field.How do the multiple-loop coils and iron ring in the version of Faraday's apparatus shown in Figure 23.3 enhance the observation of induced emf?When a magnet is thrust into a coil as in Figure 23.4(a), what is the direction of the louse exerted by the coil on the magnet? Draw a diagram showing the direction of the current induced in the coil and the magnetic field it produces, to justify your response. How does the magnitude of the force depend on the resistance of the galvanometer?Explain how magnetic flux can be zero when the magnetic field is not zero.Is an emf induced in the coil in Figure 23.54 when it is stretched? If so, state why and give the direction of the induced current. Figure 23.54 A circular coil of wire is snatched in a magnetic field.A person who works with large magnets sometimes places her head inside a strong field. She reports feeling dizzy as she quickly turns her head. How might this be associated with induction?A particle accelerator sends highvelocity charged particles down an evacuated pipe. Explain how a coil of wire wrapped around the pipe could detect the passage of individual panicles. Sketch a graph of the voltage output of the coil as a single particle passes through it.Why must pan of the circuit be moving relative to other parts, to have usable motional emf? Consider, for example, that the rails in Figure 23.11 are stationary relative to the magnetic field, while the rod moves.A powerful induction cannon can be made by placing a metal cylinder inside a solenoid coil. The cylinder is forcefully expelled when solenoid current is turned on rapidly. Use Faraday’s and Lenz’s laws to explain how this works. Why might the cylinder get live/hot when the cannon is tired?An induction slave heats a pot with a coil carrying an alternating current located beneath the pot (and without a hot surface). Can me stove surface be a conductor? Why won’t a coil carrying a direct current work?Explain how you could thaw out a frozen water pipe by wrapping a coil carrying an alternating current mound it. Does it matter whether or not the pipe is a conductor? Explain.Explain why magnetic damping might not be effective on an object made of several thin conducting layers separated by insulation.Explain how electromagnetic induction can be used to detect metals? This technique is particularly important in detecting buried landmines for disposal, geophysical prospecting and at airports.Using RHR-l, show that the emfs in the sides of the generator loop in Figure 23.23 are in the same sense and thus add.The source of a generator’s electrical energy output is the work done to turn its coils. How is the work needed to turn the generator related to Lenz's law?Suppose you find that the belt drive connecting a powerful motor to an air conditioning unit is broken and the motel is running freely. Should you be worried that the motor is consuming a great deal at energy for no useful purpose? Explain why or why not.Explain what causes physical vibrations in transformers at twice the frequency of the AC power involved.Does plastic insulation on live/hot wires prevent shock hazards, thermal hazards, or both?Why are ordinary circuit breakers and fuses ineffective in preventing shocks?A GFI may trip just because the live/hot and neutral wires connected to it are significantly different in length. Explain why.How would you place two identical flat coils in contact so that they had the greatest mutual inductance? The least?How would you shape a given length of wire to give it the greatest self-inductance? The least?€22. Verify, as was concluded without proof in Example 23.7, that units ofPresbycusis is a hearing loss due to age that progressively affects higher frequencies. A hearing aid amplifier is designed to amplify all frequencies equally. To adjust its output for presbycusis, would you put a capacitor in series or parallel with the hearing aid's speaker? Explain.Would you use a large inductance or a large capacitance in series with a system to filter out low frequencies, such as the 100 Hz hum in a sound system? Explain.High-frequency noise in AC power can damage computers. Does the plug-in unit designed to prevent this damage use a large inductance or a large capacitance (in series with the computer) to filter out such high frequencies? Explain.Does inductance depend on current, frequency, or both? What about inductive reactance?Explain why the capacitor in Figure 23.55(a) acts as a low-frequency filter between the two circuits, whereas that in Figure 23.55(b) acts as a high frequency filter. Figure 23.55 Capacitors and inductors. Capacitor with high frequency and low frequency.If the capacitors in Figure 23.55 are replaced by inductors, which acts as a low-frequency fitter and which as a high-frequency fitter?Does the resonant frequency of an AC circuit depend on the peak voltage of the AC source? Explain why or why not.Suppose you have a motor with a power factor significantly less than 1. Explain why it would be better to improve the power factor as a method at improving the motor's output, rather than to increase the voltage input.What is the value of the magnetic flux at coil 2 in Figure 23.56 due to coil 1? Figure 23.56 (a) The planes of the two coils are perpendicular. (b) The wire is perpendicular to the plane of the coil.What is the value of the magnetic flux through the coil in Figure 23.56 (b) due to the wire?Referring to Figure 23.5?(a), what is the direction of the current induced in coil 2: (a) If the current in coil 1 increases? (b) If the current in coil 1 decreases? (c) If the current in coil 1 is constant? Explicitly show how you follow the steps in the Problem-Solving Strategy for Lenz' 5 Law. Figure 23.57 (a) The coils lie in the same plane. (b) The wire is in the plane at the coilReferring to Figure 23.57(b), what is the direction of the current induced in the coil: (a) If the current in the wire increases? (b) If the current in fine wire decreases? (c) If the current in the wire suddenly changes direction? Explicitly show how you follow the steps in the Problem-Solving Strategy for Lenz’s Law.Referring to Figure 23.58, what are the directions of the currents in coils 1, 2, and 3 (assume that the coils are lying in the plane of the circuit): (a) When the switch is first closed? (b) When the switch has been closed for a long time? (c) Just after the switch is opened?Repeat the previous problem with the battery reversed.Verify that the units /t are volts. That is, show that 1 T (m2/s = 1 V.Suppose a 50-turn coil lies in the plane of the page in a uniform magnetic field that is directed into the page. The coil originally has an area of 0.250 m2. It is stretched to have no area in 0.100 s. What is the direction and magnitude of the induced emf if the uniform magnetic field has a strength of 1.50 T?(a) An MRI technician moves his hand from a region of very low magnetic field strength into an MRI scanner's 2.00 T field with his fingers pointing in the direction of the field. Find the average emf induced in his wedding ling, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field. (b) Discuss whether this current would significantly change the temperature of the ring.Integrated Concepts Referring to the situation in the previous problem: (a) What current is induced in the ring if its resistance is 0.0100 ? (b) What average power is dissipated? (c) What magnetic field is induced at the center of the ring? (d) What is the direction of the induced magnetic field relative to the MRI'S field?An emf is induced by rotating a 1000-turn, 20.0 cm diameter coil in the Earth’s 5.00105T magnetic field. What average emf is induced, given the plane of the coil is originally perpendicular to me Earth’s field and is rotated to be parallel to the field in 10.0 ms?A 0.250 m radius, 500-turn coil is rotated one-fourth of a revolution in 4.17 ms, originally having its plane perpendicular to a uniform magnetic field. (This is 60 rev/s.) Find the magnetic field strength needed to induce an average emf of 10,000 V.Integrated Concepts Approximately how does the emf induced in the loop in Figure 23.57(b) depend on the distance of the center of the loop from the wire?Integrated Concepts A lightning bolt produces a rapidly varying magnetic field. It the belt strikes the earth vertically and acts like a current in a long straight wire, it will induce a voltage in a loop aligned like that in Figure 23.57 (b). What voltage is induced in a 1.00 m diameter loop 50.0 m from a 2.00106A lightning strike, if the current falls to zero in 25.0s ? (b) Discuss circumstances under which such a voltage would produce noticeable consequences.Use Faraday’s law, Lenz’s law, and RHR—l to show that the magnetic force on the current in the moving rod in Figure 23.11 is in the opposite direction of its velocity.If a current flows in the Satellite Tether shown in Figure 23.12, use Faraday’s law, Lenz'S law, and RHRl to show that there is a magnetic force on the rather in the direction opposite to its velocity.(a) A jet airplane with a 75.0 m wingspan is flying at 280 m/s. What emf is induced between wing tips if the vertical component 01 the Earth’s field is 3.00105T ? (b) Is an emf of this magnitude likely to have any consequences? Explain.(a) A nonferrous screwdriver is being used in a 2.00 T magnetic field. What maximum emf can be induced along its 12.0 cm length when it moves at 6.00 m/s? (b) Is it likely that this emf will have any consequences or even be noticed?At what speed must the sliding rod in Figure 23.11 move to produce an emf of 1.00 V in a 1.50 T field, given the rod’s length is 30.0 cm?The 12.0 cm long rod in Figure 23.11 moves at 4.00 m/s. What is the strength of the magnetic field if a 95.0 V emf is induced?Prove that when B, l, and v are not mutually perpendicular, motional emf is given by emf=Blvsin. If v is perpendicular to B, then (is the angle between l and B. If l is perpendicular to B, then (is the angle between v and B.In the August 1992 space shuttle flight, only 250 m of the conducting tether considered in Example 23.2 could be let out. A 40.0 V motional emf was generated in me Earth’s 5.00105T field, while moving at 7.80103m/s. What was the angle between the shuttle’s velocity and the Earth’s field, assuming the conductor was perpendicular to the field?Integrated Concepts Derive an expression for the current in a system like that in Figure 23.11, under the following conditions. The resistance between the rails is R, the rails and the moving red are identical in cross section A and have the same resistivity . The distance between the rails is l, and the rod moves at constant speed v perpendicular to the uniform field B. At time zero, the moving red is next to the resistance R.Integrated Concepts The Tethered Satellite in Figure 23.12 has a mass at 525 kg and is at the end of a 20.0 km long, 2.50 mm diameter cable with the tensile strength of steel. (a) How much does the cable stretch if a 100 N force is exerted to pull the satellite in? (Assume the satellite and shuttle are at the same altitude above the Earth.) (b) What is the effective force constant of the cable? (c) How much energy is stored in it when Stretched by the 100 N force?Integrated Concepts The Tethered Satellite discussed in this module is producing 5.00 kV, and a current of 10.0 A flows. (a) What magnetic drag force does this produce if the system is moving at 7.80 km/s? (b) How much kinetic energy is removed from the system in 1.00 h, neglecting any change in attitude or velocity during that time? (c) What is the change in velocity if the mass of the system is 100,000 kg? (d) Discuss the long term consequences (say, a week-long mission) on the space shuttle’s orbit, noting what effect a decrease in velocity has and assessing the magnitude of the effect.