Question

(11%) Problem 8: A circular wire loop of radius r = 0.35 m and resistance R= 11 12 rotates about a shaft through its diameter at a constant rate of f= 5.5 Hz in a uniform B = 0.21-T magnetic field directed perpendicular to the rotation axis. The plane of the loop is perpendicular to the magnetic field at time t = 0. 4 17% Part (a) Select the correct expression for the time-dependent magnetic flux through the loop. 17% Part (b) Find the value of the magnetic flux through the loop, in webers, at time t = 0.121 s. A 17% Part (c) Select the expression for the time-dependent emf induced in the loop based on the expression you entered in part (a).B. A 17% Part (d) Calculate the induced emf in the loop, in volts, at time t = 0.121 s. 4 17% Part (0) Select the expression for the induced current in the loop based on the expression you entered in part (c). 17% Part (f) Find the induced current in the loop, in amperes, at time t= 0.121 s. nrode Summer

Answer 1

(a)

Integral (B.dA)

B.dA cos (wt)

B.cos wt integral (dA)

B cos 2$\pi$ft . $\pi$ $r^{2}$

so,

$\phi$ = B $\pi$ $r^{2}$ cos ((2$\pi$ft)

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(b)

at t = 0.121 s

$\phi$ = 0.21 * $\pi$ * 0.35^2 cos ( 2$\pi$ * 5.5 * 0.121)

$\phi$ = 0.081 Wb

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(c)

emf = d$\phi$ / dt

emf = 2$\pi ^{2}$ f B sin (2$\pi$ft)

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(d)

at t = 0.121 s

emf = 0.2 V

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(e)

I = emf / R

I = 2$\pi ^{2}$ f B sin (2$\pi$ft) / R

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(f)

I = 0.018 Amps