Question

A metallic rod of ‘L’ length is rotated with angular frequency of ‘ω’ with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius L, about an axis passing through the centre and perpendicular to the plane of the ring. A constant and uniform magnetic field B parallel to the axis is present everywhere. Deduce the expression for the emf between the centre and the metallic ring.

Answer 1

Consider the infinitesimally small length dx at a distance x.So speed of this part is ωx.Induced small emf = Bωx dx (since emf = vBl)The emf between the ends of the rotating rod