A circular wire loop of radius r = 0.095 m and resistance R = 9.9 Ohm rotates ab

Question

A circular wire loop of radius r = 0.095 m and resistance R = 9.9 Ohm rotates about a shaft through its diameter at a constant rate of f = 11.4 Hz in a uniform B = 0.24-T magnetic field directed perpendicular to the rotation axis. The plane of the loop is perpendicular to the magnetic field at time t = 0. Randomized Variables: r = 0.095 m R = 9.1 Ohm. f = 11.4 Hz B = 0.24 T t = 4.1 s 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 = 4.1 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 = 4.1 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 = 4.1 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 = 4.1 s, = * 0.0952 * 0.24 * cos(2 * 11.4 * 4.1) = -4.27 * 10-4 Wb

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

d) At t = 4.1 s, = 22 * 0.0952 * 0.24 * 11.4 * sin(2 * 11.4 * 4.1) = -0.486 V

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

f) At t = 4.1 s, I = /R = -0.486/9.1 = -0.053 A

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