Each of the three situations in Figure P32.68 shows a resistor in a circuit in which currents are induced. Using Lenz’s law, determine whether the current in each situation is from a to b or from b to a. a. If the current I in the wire in Figure P32.68A is increased from zero to I, what is the direction of the current induced across the resistor R? b. The switch in Figure P32.68B is initially closed and is thrown open at t = 0. What is the direction of the current induced across the resistor R immediately afterward? c. A bar magnet is brought close to the circuit shown in Figure P32.68C. What is the direction of the current induced across the resistor R?
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Chapter 32 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- When a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude Imax of the current without disconnecting the wire to shunt the current through a meter. The Rogowski coil, shown in Figure P23.8, simply clips around the wire. It consists of a toroidal conductor wrapped around a circular return cord. Let n represent the number of turns in the toroid per unit distance along it. Let A represent the cross-sectional area of the toroid. Let I(t) = Imax sin t represent the current to be measured. (a) Show that the amplitude of the emf induced in the Rogowski coil is Emax=0nAImax. (b) Explain why the wire carrying the unknown current need not be at the center of the Rogowski coil and why the coil will not respond to nearby currents that it does not enclose. Figure P23.8arrow_forwardThe switch in the circuit shown in the figure has been open for a long time. The resistors in the circuit each have a value of 60 Ω, the inductors each have a value of 60 mH, and V = 10 V. (a) What is the total equivalent inductance of the circuit between points A and B? (b) What is the current through R1 the instant after the switch is closed? (c) What is the current through R1 long after the switch has been closed?arrow_forwardThe magnetic field through a square loop of wire with sides of length 3.00 cm changes with time as shown in Figure P32.8, where the sign indicates the direction of the field relative to the axis of the loop. Plot the emf induced in the loop versus time. FIGURE P32.8arrow_forward
- In Figure P30.26, a semicircular conductor of radius R = 0.250 m is rotated about the axis AC at a constant rate of 120 rev/min. A uniform magnetic field of magnitude 1.30 T fills the entire region below the axis and is directed out of the page. (a) Calculate the maximum value of the emf induced between the ends of the conductor. (b) What is the value of the average induced emf for each complete rotation? (c) What If? How would your answers to parts (a) and (b) change if the magnetic field were allowed to extend a distance R above the axis of rotation? Sketch the emf versus time (d) when the field is as drawn in Figure P30.26 and (e) when the field is extended as described in part (c). Figure P30.26arrow_forwardTwo coaxial cables of length with radii a and b are carrying currents in opposite directions as shown in Figure P33.78. Determine the inductance of the system. Hint: Use Ampres law to write an expression for the magnetic field in the region between the cables, a distance r from the axis of the cables. Then calculate the magnetic flux through a narrow rectangular region between the cables such that the Field is perpendicular to the area everywhere. FIGURE P33.78arrow_forwardA Figure P32.74 shows an N-turn rectangular coil of length a and width b entering a region of uniform magnetic field of magnitude Bout directed out of the page. The velocity of the coil is constant and is upward in the figure. The total resistance of the coil is R. What are the magnitude and direction of the magnetic force on the coil a. when only a portion of the coil has entered the region with the field, b. when the coil is completely embedded in the field, and c. as the coil begins to exit the region with the field?arrow_forward
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