1) A wire loop of radius 0.40 m lies so that an external magnetic field of magni

Question

1) A wire loop of radius 0.40 m lies so that an external magnetic field of magnitude 0.30 T is perpendicular to the loop. The field reverses its direction, and its magnitude changes to 0.20 T in 1.5 s. Find the magnitude of the average induced emf in the loop during this time.

2) In a model AC generator, a 499 turn rectangular coil 6.0 cm by 22 cm rotates at 116 rev/min in a uniform magnetic field of 0.55 T.

(a) What is the maximum emf induced in the coil?

(b) What is the instantaneous value of the emf in the coil at t = (?/40) s? Assume that the emf is zero at t = 0

(c) What is the smallest value of t for which the emf will have its maximum value?

Explanation / Answer

1) induced emf is given by

E = d(BA)/dt = A(B2-B1)t

E = pi r2(0.2 - (-0.3))/1.5

E = 0.17V

2) a) maximum emf

E = NBAw

N= 499

B - 0.55 T

A = 6 x22= 132 cm2

w = 12.1 rad/s

E = 43.9 V

b) at t = T/40s

E = NBAw sin 2 pi/40 = 0.12 V

c) for E to be maximum

wt = pi/2

t = pi/2w = 0.13s

c) wt = pi/2

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