In the figure shown a long conductor carries constant current `I`. A rod `PQ` of length `l` is in the plane of the rod.The rod is rotated about point `P` with constant angular velocity `omega` as shown in the figure.Find the `e.m.f` induced in the rod in the position shown.Indicate which points is at high potential.

Answer

A, B, C

Explanation

Magnetic field `B` at point of differential element is `B=(mu_(0)i)/((2pi(a+x cos theta)) emf` induced in this element is `da= B V dx`
`rArr depsilon=(mu_(0)i omega)/(2pi).(xdx)/((1+x cos theta))`
`rArr epsilon=underset(0)overset(epsilon)int depsilon=(mu_(0)iomega)/(2pi cos theta)underset(0)overset(l)int (x/((a/cos theta)+x))dx`
`=(mu_(0)iomega)/(2pi cos theta)[l-a/costhetaln((a+l cos theta)/a)]`