Suppose the loop in Textual Exercise 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 `0.02Ts^(-1)` .If the cut is joined and the loop has a resistance of `1.6Omega` how much power is dissipated by the loop as heat ? What is the source of this power ?

Explanation

If A is the area of the loop and B is the magnetic field, then magnetic flux linked with the loop is
`phi=BA cos theta`
where `theta= "angle between normal to the loop and magnetic field"`.
As the field is directed normal to the loop, `theta=0^(@)`
`:. phi=BA`
Induced emf in the loop is given by
`epsilon=-(dphi)/(dt)=-(d)/(dt)(BA)=-A(dB)/(dt)`
(As A is constant)
Here, `A = 0.08 m xx 0.02 m = 16 xx 10^(-4) m^(2)`
`(dB)/(dt) = "Rate of change of magnetic field" = -0.02 T // s`.
If `R = 1.6 Omega` is the resistance of loop, then induced current is
`I=(epsilon)/(R)=(3.2 xx 10^(-5))/(1.6)=2 xx 10^(-5)A`
Power dissipated by loop as heat is
`P=I^(2)R=(2 xx 10^(-5))^(2) xx 1.6`
`6.4 xx 10^(-10) W`.
The source of this power is the external agent responsible for changing the magnetic field with time.