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A square loop ACDE of area 20 cm^2 res...

A square loop `ACDE` of area `20 cm^2 ` resistance `5Omega` is rotate in as magnetic field `B=2T` through `180^@` (a) in `0.01s` and (b) in `0.02 s`
Find the magnitudes of averasge values of e i and `/_\q` in both the cases.

Text Solution

Verified by Experts

Let us take the area vector `S` perpendicular to plane of loop inwards. So initially `S uarr uarr B` and when it is rotated by `180^@ Suarr darrB`. Hence initial flux passing through the loop,
`phi_i=BScos0^@=(2)(20xx10^-4)(1)=4.0xx10^-3Wb`
Flux passing through the loop when it is rotated by `180^@`
`phi_f=BScos180^@=(2)(20xx10^(-4))(-1)=-4.0xx10^(-3)Wb`
Therefore, change in flux,
`/_\phi_B=phi_f-phi_i=-8.0xx10^-3Wb`
(a) Given `Delta t=0.01s, R=5Omega`
`:. |e|=|-(/_\phi_B)/(/_\t)|=(8.0xx10^-3)/0.01=0.8V`
`i=(|e|)/R=0.8/5=0.16A`
and `/_\q=i/_\t=0.16xx0.01=1.6xx10^-3C`
b. `/_\=0.02s`
`:. |e|=|-(/_\phi_B)/(/_\t)|=(8.0xx10^-3)/0.02=0.4V`
`i=(|e|)/R=0.4/5=0.08A`
and `/_\q=i Delta t=(0.08)(0.02)`
`=1.6x10^-3C`
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