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Home » A magnetic field B = Bo sin ωt k covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d. The wires are in the x-y plane. The wire AB (of length d) has resistance R and the parallel wires have negligible resistance. If AB is moving with velocity v, what is the current in the circuit? What is the force needed to keep the wire moving at constant velocity?
A magnetic field B = Bo sin ωt k covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d. The wires are in the x-y plane. The wire AB (of length d) has resistance R and the parallel wires have negligible resistance. If AB is moving with velocity v, what is the current in the circuit? What is the force needed to keep the wire moving at constant velocity?
CBSE | Class 12 | Electromagnetic Induction | ncert exemplar | Physics
A magnetic field B = Bo sin ωt k covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d. The wires are in the x-y plane. The wire AB (of length d) has resistance R and the parallel wires have negligible resistance. If AB is moving with velocity v, what is the current in the circuit? What is the force needed to keep the wire moving at constant velocity?

Allow wire AB to travel with velocity v at time t = 0.

x(t) = vt at time t

AB = e1 = Blv Motional emf across

(Bo sin t)vd = e1 (-j)

d(B)/dt = e2

e2 = -B0 cos tx (t)d e2 = -B0 cos tx (t)d e2 = -B0 cos tx

emf due to field change + motional emf across AB = total emf in the circuit

= Bod/R (x cost + v sint) is the formula for electric current in the clockwise direction.

Fext = Bo2d2/R (ꞷx cos ꞷt + v sin ꞷt)(sin ꞷt (i)

i

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