shows a straight, long wire carrying a current I and a rod of length l coplanar with the wire and perpendicular to it. The rod moves with a constant velocity v in a direction parallel to the wire. The distance of the wire from the centre of the rod is x. Find the motional emf induced in the rod.

Explanation

In this case vec b varies, so we consider a small element at centre of rod of length dx at a distance x form the wire.`
`vec b =(mu_0 i)/(2pi r)`
`so, dE=(mu_0 i_/(2 pi r)xx vx dx`
`:. E= int _(0)^(theta) dE`
`=(mu_0 v)/(2 pi)[In (x=(1/2))-In (x-(1/2))]`
`=(mu_0 v)/(2 pi)In[(x=(1/2))/(x-(1/2))].`