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A long thin wire carrying a varying curr...

A long thin wire carrying a varying current `I = i_(0) sin omegat` lies at a distance `y` above one edge of a rectangular wire loop of length `L and W` lying in the `x-z` plane. What emf is induced in the loop?

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`(di)/(dt)=l_(@)omega cos omegat B=(mu_(0)i)/(2pi(y^(2)+z^(2))^(1//2))`
`dphi=B(dA)cos theta =B(W dz)cos theta =(mu_(0)i)/(2pi(y^(2)+z^(2))^(3/2)) (W dz) cos theta`
`phi=(mu_(0)iW)/(2pi)underset(0)overset(L)intZ/(y^(2)+z^(2))dz =(mu_(0)iW)/(4pi)[ln(y^(2)+z^(2))]_(0)^(L) =(mu_(0)iW)/(4pi)ln[(y^(2)+L^(2))/y^(2)]`
`epsilon=(dphi)/(dt)= =(mu_(0)iW)/(4pi)ln[(y^(2)+L^(2))/y^(2)] (di)/(dt)`
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