99 Percentile Qs Bank for JEE MainPhysicsElectromagnetic Induction
In a uniform magnetic field of induction B , a wire, in the form of a semicircle of radius r , rotates about the diameter of the circle with angular frequency ω . 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 π r 2 ω 2 R
- BB π r 2 ω 2 8 R
- CB π r ω 2 2 R
- DB π r ω 2 2 8 R
Correct answer
B. B π r 2 ω 2 8 R
Step-by-step solution
Magnetic flux linked = BA cos ω t = B π r 2 cos ω t 2 ∴ Induced emf e = - d ϕ dt = - 1 2 B π r 2 ω sin ω t ∴ Power = e 2 R = B 2 π 2 r 4 ω 2 sin 2 ω t 4 R = B π r 2 ω 2 4 R sin 2 ω t ∵ < sin 2 ω t > = 1 / 2 ∴ Mean power generated = B π r 2 ω 2 4 R × 1 2 = B π r 2 ω 2 8 R .