A conducting rod AB is bent in the form of a semicircle of radius R. It is kept in a region of uniform magnetic field B such that plane of semicircle is perpendicular to magnetic field. This rod is being moved with a constant speed v perpendicular to AB. Find the emf developed between the ends.

Explanation

Consider a small arc of length dl = `Rdphi` as shown

This section can be considered as a conductor of length dl.
The emf across this section is
`dV=B(v sinphi)dl`
`dV=BvRsinphi(dphi)`
The emf between A and B is `V_(AB)=intdV=int_(0)^(n)BvRsinphi dphi`
`V_(AB)=BvR[-cosphi]_(0)^(pi)=2BvR`