BITSAT2019PhysicsElectromagnetic InductionActual
A semicircular wire of radius r rotates in uniform magnetic field B about its diameter with angular velocity ω . If the total resistance of the circuit is R , then the mean power generated per period of rotation is
Options
- Aπ B r 2 ω 2 8   R
- Bπ B r ω 2 8 R
- Cπ B r ω 2 8   R
- D0
Correct answer
A. π B r 2 ω 2 8   R
Step-by-step solution
The flux linked with coil (made of wire of radius r ) of area A and magnetic field B , is given by ϕ = B A   cos   θ = B   π r 2 2   cos   ω t ϕ = π B r 2 2   cos   ω t [ ∵         A = π r 2 2 and θ = ω t ] By Faraday's law of electromagnetic induction, induced emf, e = - d ϕ d t Hence, after differentiating, e = - d d t π B r 2 2   cos   ω t = π B r 2 ω 2   sin