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Suppose the loop in Textual Exercise 4 i...

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 ?

Text Solution

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Area of loop `=8xx 2= 16cm^(2)= 16 xx 10^(-4)m^(2)`
Rate of change of magnetic field `(dB)/(dt)=0.02T/S`
Resistance of loop `R= 1.62Omega`
Induced emf of loop `e=(dphi)/(dt)=(d)/(dt) (BA) (therefore phi=BA)`
`e=A (dB)/(dt) Rightarrow e=16xx10^(-4) xx 0.02 Rightarro e=0.32 xx 10^(-4)V`
Induced current in the loop `I=e/R=(0.32xx10^(-4))/(1.6)=0.2 xx 10^(-4)A
Power of source as heat `P=I^(2)R=(0.2xx10^(-4))x1.6=6.4xx10^(-10)W Rightarrow P=6.4xx10^(-10)W`
The agency which changing the magnetic field with time is the source of this power.
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