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  • 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.

Q6.11 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 0.3T  at the rate of   0.02\: T s^{-1}. If the cut is joined and the loop has a resistance of 1.6\Omega , how much power is dissipated by the loop as heat? What is the source of this power?

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best_answer

Given,

Area of rectangular loop which is held still:

A = l*b=(0.08)(0.02)m^2=16*10^{-4}

The resistance of the loop:

R=1.6\Omega

The initial value of the magnetic field :

B_{initial}= 0.3T

Rate of decreasing of this magnetic field:

\frac{dB}{dt}=0.02T/s

Induced emf in the loop :

e=\frac{d\phi }{dt}=\frac{d(BA)}{dt}=A\frac{dB}{dt}=16*10^{-4}*0.02=0.32*10^{-4}V

Induced Current :

I_{induced}=\frac{e}{R}=\frac{0.32*10^{-4}}{1.6}=2*10^{-5}A

The power dissipated in the loop:

P=I_{induced}^2R=(2*10^{-5})^2*1.6=6.4*10^{-10}W

The external force which is responsible for changing the magnetic field is the actual source of this power.

Posted by

Pankaj Sanodiya

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