Question

Problem 4. The generator coil shown in the figure below is rotated through one-fourth of a revolution (from 0 = 00 to 0 = 90°) in 15.0 ms. The 200-turn circular coil has a 5.00 cm radius and is in a uniform 1.25 T magnetic field. What is the average emf induced? Carbon brush Carbon brush N Path of motion 2 Coil rotated by mechanical means 90

Answer 1

Induced EMF is given by:

emf = -N*d(phi)/dt

phi = magnetic flux = B.A = B*A*cos theta

emf = -N*d(B*A*cos$\theta$)/dt = -N*B*A*d(cos$\theta$)/dt

for given loop, A = pi*r^2

r = radius of circle = 5.00 cm = 0.05 m

B = magnetic field = 1.25 T

N = number of turns = 200

dt = time interval = 15.0 ms = 0.015 s

d(cos$\theta$) = cos$\theta$f - cos$\theta$i

$\theta$i = initial angle = 0 deg

$\theta$f = final angle = 90 deg

then, d(cos$\theta$) = cos 90 deg - cos 0 deg = -1

So,

emf = -200*1.25*(pi*0.05^2)*(-1)/(0.015) = 130.899 volts

emf = 131 Volts

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