Q.1 (vi) A conducting rod of length l , rotates about one of its ends in a uniform magnetic field B , with a constant angular velocity ω . If the plane of rotation is perpendicular to B , the e.m.f. induced between the ends of rod is _____. A. 1/2Bω l² B. Bω l² C. 2Bω l² D. Bω l

Answer: A. 1/2Bω l² Answer: (a) 1/2Bω l² In one rotation (time T = 2π/ω ) the rod sweeps an area π l² , so the flux cut is Bπ l² . Hence e = Bπ l²/2π/ω = 1/2Bω l² . (Equivalently, the average speed of the rod is ω l/2 and e = B l (ω l/2) .)

A conducting rod of length \(l\), rotates about one of its ends in a uniform magnetic field \(B\), with a constant angular velocity \(\omega\). If the plane of rotation is perpendicular to \(B\), the e.m.f. induced between the ends of rod is _____.

Q.1 (vi) A conducting rod of length \(l\), rotates about one of its ends in a uniform magnetic field \(B\), with a constant angular velocity \(\omega\). If the plane of rotation is perpendicular to \(B\), the e.m.f. induced between the ends of rod is _____.

A. \(\dfrac{1}{2}B\omega l^2\)

B. \(B\omega l^2\)

C. \(2B\omega l^2\)

D. \(B\omega l\)

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Answer: A. \(\dfrac{1}{2}B\omega l^2\)

Answer: (a) \(\dfrac{1}{2}B\omega l^2\)

In one rotation (time \(T = 2\pi/\omega\)) the rod sweeps an area \(\pi l^2\), so the flux cut is \(B\pi l^2\). Hence \(e = \dfrac{B\pi l^2}{2\pi/\omega} = \dfrac{1}{2}B\omega l^2\). (Equivalently, the average speed of the rod is \(\omega l/2\) and \(e = B l\,(\omega l/2)\).)

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A conducting rod of length \(l\), rotates about one of its ends in a uniform magnetic field \(B\), with a constant angular velocity \(\omega\). If the plane of rotation is perpendicular to \(B\), the e.m.f. induced between the ends of rod is _____.

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