First slide

Faraday's law of Electromagnetic induction

Question

A rectangular loop of sides 8 cm and 2 cm having resistance of 1.6 $Ω$ is placed in a magnetic field of 0.3 T directed normal to the loop. The magnetic field is gradually reduced at the rate of 0.02 T/s. How much power is dissipated by the loop as heat ?

Moderate

A

1.6 x 10^-4 W
B

3.2 x 10^-8 W
C

6.4 x 10^-10 W
D

12.8 x 10^-8 W

Solution

We know that induced e.m.f. (e) is equal to the product of rate of change of magnetic field and area. Hence
$e = (0 \cdot 02) \times (8 \times 2 \times 10^{- 4}) = 3 \cdot 2 \times 10^{- 5} V Now i = \frac{e}{R} = \frac{3 \cdot 2 \times 10^{- 5}}{1 \cdot 6} = 2 \cdot 0 \times 10^{- 5} amp ∴ power loss = i^{2} R = {(2 \cdot 0 \times 10^{- 5})}^{2} \times 1 \cdot 6 = 6 \cdot 4 \times 10^{- 10} W$

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