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Figure shows a wire frame PQSTXYZ placed...

Figure shows a wire frame `PQSTXYZ` placed in a time varying magnetic field given as `B=betat`, where `beta` is a positive constant.Resistance per unit length of the wire is `lambda`.Find the current induced in the wire and draw its electrical equivalent diagram.

Text Solution

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Induced emf in part `PQST=betaa^(2)`(in anticlockwise direction, from Lenz's Law)
Similarly induced emf is part `TXYZ=betab^(2)`(in anticlockwise direction from Lenz's Law)
Total resistance of the part `PQST=lambda4a`.
Total resistance of the part `TXYZ=lambda4b`. The equivalent circuit is as shown in the following diagram.

writing KVL along the current flow
`betab^(2)=betaa^(2)-lambda4ai-lambda4bi=0`
`i=(beta)/(4lambda)(b-a)`
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