(a)
The maximum induced emf in the coil.
(a)
Answer to Problem 31.71AP
The maximum induced emf in the coil is
Explanation of Solution
Given Info: The number of turns in the rectangular coil is
The area of the rectangular coil is,
Here,
Substitute
Thus, the area of the coil is
The angle between the normal area component and the magnetic field is,
Here,
The flux induced in the coil is,
Here,
The emf induced in the coil is,
Substitute
Substitute
The induced emf is maximum for the maximum value of
Substitute
Substitute
Conclusion:
Therefore, the maximum induced emf in the coil is
(b)
The maximum rate of change of magnetic flux.
(b)
Answer to Problem 31.71AP
The maximum rate of change of magnetic flux is
Explanation of Solution
Given Info: The number of turns in the rectangular coil is
The induced flux is,
Substitute
Differentiate the above equation with respect to time with respect to time for the rate of change of flux.
For the maximum rate of change of flux the value of
Substitute
Substitute
Conclusion:
Therefore, the maximum rate of change of magnetic flux is
(c)
The induced emf at
(c)
Answer to Problem 31.71AP
The induced emf at
Explanation of Solution
Given Info: The number of turns in the rectangular coil is
The expression for the induced emf is,
Substitute
Conclusion:
Therefore, the induced emf at
(d)
The torque exerted by magnetic field on the coil for maximum emf.
(d)
Answer to Problem 31.71AP
The torque exerted by magnetic field on the coil is
Explanation of Solution
Given Info: The number of turns in the rectangular coil is
The formula to calculate the induced current in the coil is,
Here,
Substitute
Thus, the current in the coil is
The formula to calculate the magnetic moment of the coil is,
The formula to calculate the torque experienced by the coil is,
The maximum value of
Substitute
Substitute
Substitute
Conclusion:
Therefore, the torque exerted by magnetic field on the coil is
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Chapter 31 Solutions
Physics For Scientists And Engineers, Volume 2
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- When the current in a toroidal solenoid changes at a rate of0.025 A/s, the magnitude of the induced emf is 12.0 mV. When thecurrent equals 1.50 A, the average flux through each turn of the solenoidis 0.003 Wb. How many turns does the solenoid have?arrow_forwardA 550-turn solenoid, 28 cmcm long, has a diameter of 2.3 cmcm . A 18-turn coil is wound tightly around the center of the solenoid. If the current in the solenoid increases uniformly from 0 to 6.1 AA in 0.65 ss , what will be the induced emf in the short coil during this time?arrow_forwardA single circular loop of wire with radius 2.40 cm lies in the xy-plane. There is a uniform magnetic field that changes at a steady rate from 0.140 T in the +z-direction at to 0.110 T in the -z-direction at 2 s. Take the area vector for the loop to be in the +z-direction. Find (a) the magnetic flux through the loop at t = 0 and t=2 s, and (b) the magnitude of the induced emf in the loop while the field is changing.A. a) Flux(t=0) = 2.53 * 10^{-4} Wb and Flux(t=2) = -1.99 * 10^{-4} Wb b) emf = 0.226 mV B. a) Flux(t=0) = 1.44 * 10^{-4} Wb and Flux(t=2) = -4.32 * 10^{-4} Wb b) emf = 0.477 mVC. a) Flux(t=0) = -2.53 * 10^{-4} Wb and Flux(t=2) = 2.53 * 10^{-4} Wb b) emf = 1 mV D.a) Flux(t=0) = 4.32 * 10^{-4} Wb and Flux(t=2) = 1.02 * 10^{-4} Wb b) emf = 1.34 mVarrow_forward
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