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Question
A rectangular loop of sides 10 cm and 5 cm with a cut, is stationary between the pole pieces of an electromagnet. The magnetic field of the magnet is normal to the loop. The current feeding the electromagnet is reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 Ts−1. If the cut is joined and the loop has a resistance of 2.0 Ω, the power dissipated by the loop as heat is
A rectangular loop of sides 10 cm and 5 cm with a cut, is stationary between the pole pieces of an electromagnet. The magnetic field of the magnet is normal to the loop. The current feeding the electromagnet is reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 Ts−1. If the cut is joined and the loop has a resistance of 2.0 Ω, the power dissipated by the loop as heat is
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Solution
The correct option is A 5 nW
From Faraday's law,
EMF, E=−dϕdt(1)
Since Flux, ϕ=B.A
where B=magnetic field, A=area of rectangular loop
Equation (1) becomes,
E=−d(B.A)dt=−Ad(B)dt(2)
Since A=10×5=50 cm2=50×10−4 m2
Also dBdt=−0.02
Substituting these values in (2) E=−Ad(B)dt=−50×10−4×(−0.02)
E=10−4 V
Power, P=E2R=10−4×10−42
⇒P=0.5×10−8 W=5 nW
From Faraday's law,
EMF, E=−dϕdt(1)
Since Flux, ϕ=B.A
where B=magnetic field, A=area of rectangular loop
Equation (1) becomes,
E=−d(B.A)dt=−Ad(B)dt(2)
Since A=10×5=50 cm2=50×10−4 m2
Also dBdt=−0.02
Substituting these values in (2) E=−Ad(B)dt=−50×10−4×(−0.02)
E=10−4 V
Power, P=E2R=10−4×10−42
⇒P=0.5×10−8 W=5 nW
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