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NCERT Class XII Chapter
Electromagnetic Induction
Questions With Solutions

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Question : 11 of 17
Marks: +1, -0
Suppose the loop shown in figure is stationary but the current feeding the electromagnet that produces the magnetic field is gradually reduced so that field decreases from its initial value of 0.3 T at the rate of 0.02 T s−1s^{-1}. If the cut is joined and the loop has a resistance of 1.6 W, how much power is dissipated by the loop as heat? What is the source of this power?
Solution:  
Here area is constant but the magnetic field is reducing at a constant rate
dBdt\frac{dB}{dt} = - (0.02) T s−1s^{-1}
Area of the loop, A = l × b = 8 × 2 cm2\mathrm{cm}^2 = 16 cm2\mathrm{cm}^2 = 16 × 10−4 m210^{-4}\,\mathrm{m}^2
Induced emf in the loop
ε = - dϕdt\frac{d\phi}{dt} = - A dBdt\frac{dB}{dt}
ε = - 16 × 10−410^{-4} [- 0.02] = 32 × 10−610^{-6} V
Induced current in the closed loop
I = ε/R = 32×10−61.6\frac{32 \times 10^{-6}}{1.6} = 20 µA
Power loop as heat P = I2I^2 R
P = (20×10−6)2(20 \times 10^{-6})^2 × 1.6 = 6.4 × 10−1010^{-10} W
Source of the power is work done in changing magnetic field.
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