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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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A rectangular loop of sides 8cm and 2cm with a small cut is kept stationary in a uniform magnetic field directed normal to the loop. 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 0.02T^(-1) . If the cut is joined and the loop has a resistance of 1.6 Omega , how much power is dissipated by loop as heat ? What is the source of this power ?

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