The endpoints of a conducting string (shaped as a circular loop) of constant length are being pulled at a constant velocity v as shown in the figure. There exists a uniform magnetic field B in space which is perpendicular to the circular loop. If the loop always remains circular during the motion of its endpoints, then the emf induced in the loop at t = π R 2 v is

Question

The endpoints of a conducting string (shaped as a circular loop) of constant length are being pulled at a constant velocity v as shown in the figure. There exists a uniform magnetic field B in space which is perpendicular to the circular loop. If the loop always remains circular during the motion of its endpoints, then the emf induced in the loop at t = π R 2 v is, 2 B R v, B R v, 4 B R v, 0.5 B R v

MARKS App · Accepted Answer

At any instant, the radius of the loop r , will satisfy the following relation 2 π r + 2 v t = 2 π R ⇒ r = R - v t π The flux of the magnetic field at any instant, will be ϕ B = π r 2 B So, the induced emf is Ε = - d ϕ d t = 2 π B r d r d t ⇒ Ε = 2 π B R - v t π v ⇒ Ε = B R v

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