Question

Suppose the loop in Exercise 6.4 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 W, how much power is dissipated by the loop as heat? What is the source of this power?

Answer 1

magnetic field is gradually reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 Ts-¹ .

here, area is constant but the magnetic field is reducing at a constant rate.

i.e., $\frac{dB}{dt}=-(0.02)Ts^{-1}$

area of loop, A = l × b = (8cm × 2cm) = 16cm² = 1.6 × 10^-3 m² [ see figure ]

induced emf in the loop,

$\xi=-\frac{d\phi}{dt}=-A\frac{dB}{dt}$

= -1.6 × 10^-3 (-0.02) = 3.2 × 10^-5 Volts.

induced current in the closed loop,

I = $\frac{\xi}{R}$

= 3.2 × 10^-5/1.6 = 20μA.

power dissipated by the loop as heat, P = I²R

= (20 × 10^-6)² × 1.6

= 6.4 × 10^-10 W

The source of the power is work done in changing magnetic field.

Answer 2

Answer:

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