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 ω . The axis of rotation is perpendicular to the

Question

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 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

TestHub · Accepted Answer

Magnetic flux = B A cos θ = B ⋅ 2 π r 2 ​ cos ω t ​ ∴ ε ind ​ = − dt d ϕ ​ = 2 1 ​ B π r 2 ω sin ω t ∴ P = R ε ind 2 ​ ​ = 4 R B 2 π 2 r 4 ω 2 sin 2 ω t ​ ​ Now, < sin 2 ω t >= 1/2 (mean value) ∴ ⟨ P ⟩ = 8 R ( B π r 2 ω ) 2 ​ .

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