A magnetic field is passing through a loop of wire whose area is 0.020 m2. The d

Question

A magnetic field is passing through a loop of wire whose area is 0.020 m2. The direction of the magnetic field is parallel to the normal to the loop, and the magnitude of the field is increasing at the rate of 0.19 T/s.
(a) Determine the magnitude of the emf induced in the loop. (V)

(b) Suppose that the area of the loop can be enlarged or shrunk. If the magnetic field is increasing as in part (a), at what rate (in m2/s) should the area be changed at the instant when B = 1.6 T if the induced emf is to be zero? (Give the magnitude of the rate of change of the area.) (m2/s)
Explain whether the area is to be enlarged or shrunk. (b) Suppose that the area of the loop can be enlarged or shrunk. If the magnetic field is increasing as in part (a), at what rate (in m2/s) should the area be changed at the instant when B = 1.6 T if the induced emf is to be zero? (Give the magnitude of the rate of change of the area.) (m2/s) Explain whether the area is to be enlarged or shrunk.

Explanation / Answer

A magnetic field is passing through a loop of wire whose area is 0.020 m2. The direction of the magnetic field is parallel to the normal to the loop, and the magnitude of the field is increasing at the rate of 0.19 T/s.
(a) Determine the magnitude of the emf induced in the loop. (V)

(b) Suppose that the area of the loop can be enlarged or shrunk. If the magnetic field is increasing as in part (a), at what rate (in m2/s) should the area be changed at the instant when B = 1.6 T if the induced emf is to be zero? (Give the magnitude of the rate of change of the area.) (m2/s) a) The magnitude of the emf induced in the loop is                    V= A(dB/dt)                      = (0.020 m^2)(0.19 T/s)                      = 0.0038 V b) The induced emf is                  V = B (dA/dt) + A(dB/dt)                  0 = (1.60 T)(dA/dt) + (0.020 m2)(0.19 T/s)            dA/dt = - 0.002375 m2/s So the magnitude of the induced emf is                 dA/dt = 0.002375 m2/s (b) Suppose that the area of the loop can be enlarged or shrunk. If the magnetic field is increasing as in part (a), at what rate (in m2/s) should the area be changed at the instant when B = 1.6 T if the induced emf is to be zero? (Give the magnitude of the rate of change of the area.) (m2/s) a) The magnitude of the emf induced in the loop is                    V= A(dB/dt)                      = (0.020 m^2)(0.19 T/s)                      = 0.0038 V b) The induced emf is                  V = B (dA/dt) + A(dB/dt)                  0 = (1.60 T)(dA/dt) + (0.020 m2)(0.19 T/s)            dA/dt = - 0.002375 m2/s So the magnitude of the induced emf is                 dA/dt = 0.002375 m2/s

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