A perfectly conducting ring of radius L is kept fixed on a horizontal surface. A vertical uniform magnetic field B_(0) exists in the region. A conducting rod (AB) of length L is hinged at the centre of the ring at A and its other end (B) touches the ring. The ring and the end A of the rod are connected to an external circuit having resistance R and capacitance C. The rod is made to rotate at a constant angular speed omega_(0). Neglect friction and self inductance of the circuit. (i) Find work done by the external agent in rotating the rod by the time the capacitor acquires a charge q_(0). (ii) Find heat generated in resistance R by the time the capacitor acquires a charge q_(0).

A perfectly conducting ring of radius L is kept fixed on a horizontal

1.	A perfectly conducting ring of radius L is kept fixed on a horizontal surface. A vertical uniform magnetic field B_(0) exists in the region. A conducting rod (AB) of length L is hinged at the centre of the ring at A and its other end (B) touches the ring. The ring and the end A of the rod are connected to an external circuit having resistance R and capacitance C. The rod is made to rotate at a constant angular speed omega_(0). Neglect friction and self inductance of the circuit. (i) Find work done by the external agent in rotating the rod by the time the capacitor acquires a charge q_(0). (ii) Find heat generated in resistance R by the time the capacitor acquires a charge q_(0).
Answer» ANSWER :(i) `(1)/(2) q_(0)B_(0) omega_(0)L^(2)` (ii) `(1)/(2) q_(0) [B_(0)omega_(0)L^(2) -(q_(0))/(C)]`

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