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Electric Charges And Fields

Question

Suppose the loop in Question No. 4 is stationary but the current feeding the electromagnet that produces the magnetic field is gradually reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 T s^–1. If the cut is joined and the loop has a resistance of 1.6 Ω, how much power is dissipated by the loop as heat? What is the source of this power?

Solution

Using formula, we get

Induced emf,
$|ε| = A \frac{dB}{dt} [E = \frac{dθ}{dt} (∵ θ = B . A .)]$

$|ε| = 8 \times 10^{- 2} \times 2 \times 10^{- 2} \times 0.02 V = 3.2 \times 10^{- 5} V$

Therefore,
$I n d u c e d c u r r e n t, I_{o} = \frac{|ε|}{R} = \frac{3.2 \times 10^{- 5}}{1.6} A = 2 \times 10^{- 5} A$

Power loss = $I_{0}^{2} R = {(2 \times 10^{- 5})}^{2} \times 1.6 W$