JEE Main2004PhysicsElectromagnetic InductionActual
In a uniform magnetic field of induction B a wire in the form of semicircle of radius r rotates about the diameter of the circle with angular frequency . The axis of rotation is perpendicular to the field. If the total resistance of the circuit is R the mean power generated per period of rotation is
Options
- AB r^2 2 R
- B(B r^2 )^2 2 R
- C( B r )^2 2 R
- D(B r ^2 )^2 8 R
Correct answer
B. (B r^2 )^2 2 R
Step-by-step solution
Magnetic flux =B A =B r^2 2 t aligned & _ ind =- d dt = 1 2 ~B r ^2 t & P = _ ind ^2 R = B ^2 ^2 r ^4 ^2 ^2 t 4 R aligned Now, =1 / 2 (mean value) P = ( B r ^2 )^2 8 R .