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A rod of length l is rotating with an an...

A rod of length `l` is rotating with an angular speed `omega` about its one end which is at a distance `a` from an infinitely long wire carrying current `i`.Find the `emf` induced in the rod at the instant shown in the figure.

Text Solution

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Consider a small segment of rod of length `dx`,at a distance `x` from one end of the rod.`Emf` induced in the segment
`dE=(mu_(0)i)/(2pi(x+a))(xomega)dx`
`thereforeE=underset(0)overset(l)int (mu_(0)i)/(2pi(x+a))(xomega)dx=(mu_(0)iomega)/(2pi)[l-aln((l+a)/a)]`
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