A circular wire loop of radius r = 0.095 m and resistance R = 8.9 ohm. rotates a

Question

A circular wire loop of radius r = 0.095 m and resistance R = 8.9 ohm. rotates about a shaft through its diameter at a constant rate of f = 15 Hz in a uniform B = 0.26-1 magnetic field directed perpendicular to the rotation axis. The plane of the loop is perpendicular to the magnetic field at time t = 0. Select the correct expression for the time-dependent magnetic flux through the loop. Find the value of the magnetic flux through the loop, in webers, at time t = 3.4 s. Select the expression for the time-dependent emf induced in the loop based on the expression you entered in part (a)b. Calculate the induced emf in the loop, in volts, at time t = 3.4 s. Select the expression for the induced current in the loop based on the expression you entered in part (c). Find the induced current in the loop, in amperes, at time t = 3.4 s.

Explanation / Answer

a) Angle traversed by the loop, = (2f)t

Magnetic flux through the loop, = B.A = B(r2)cos = r2B cos(2ft)

b) At t = 3.4 s, = * 0.0952 * 0.26 * cos(2 * 15 * 3.4) = 7.37 * 10-3 Wb

c) emf, = -d/dt = 22r2Bf sin(2ft)

d) At t = 3.4 s, = 22 * 0.0952 * 0.26 * 15 * sin(2 * 15 * 3.4) = 0

e) I = /R = (22r2Bf/R) sin(2ft)

f) At t = 3.4 s, I = /R = 0

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