A thin semicircular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B as shown in the figure. The potential difference developed across the ring when its speed is v, is (90)^ =1

Step-by-step solution

The motional emf induced in a conductor moving in a uniform magnetic field is given by = ( v B ) l , where l is the vector connecting the ends of the conductor. For the semicircular ring PQR, the effective length vector l is the straight line from P to R, which has a magnitude equal to the diameter of the semicircle. l_ eff = 2r Since v , B , and l are mutually perpendicular, the magnitude of the induced motional emf is: = B v l_ eff = 2rBv The polarity of the induced emf is determined by the direction of the magne