A magnetic field B = B0sin (ωt)k covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d (figure). 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 = B0sin (ωt)k covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d (figure). 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?

This is a long answer type question as classified in NCERT Exemplar
Let us assume that parallel wires at are y=0 i.e along x-axis and y=d.at t=0, AB has x=0 i.e along y-axis and moves with a velocity v
Motional emf across AB is = (B0sinwt)vd (-j)
Emf due to change in field along OBAC = -B0wcoswt x (t)d
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Kindly go through the solution
Bv = B sin 60°
->
M = φ? /I? = (B? A? )/I? = [ (μ? I? /2R? )πR? ²]/I?
[Diagram of two concentric coils]
M = (μ? πR? ²)/ (2R? )
M ∝ R? ²/R?
(A) The magnet's entry
R =
L = 2 mH
E = 9V
Just after the switch ‘S’ is closed, the inductor acts as open circuit.
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Physics Ncert Solutions Class 12th 2023
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