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Sketch the Change in Flux, Emf and Force - Physics

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Sketch the change in flux, emf and force when a conducting rod PQ of resistance R and length l moves freely to and fro between A and C with speed v on a rectangular conductor placed in uniform magnetic field as shown in the figure

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Solution

The flux enclosed by the rod is

Φ = Blx        for 0 ≤ x ≤ b

= Blx           for b ≤ x ≤ 2b

Now, the magnitude of induced emf is

`epsilon=(dphi)/dt=-Bl(dx)/dt= -Blv`            for 0 ≤ x ≤ b

`=-Bl(db)/dt=0`                                  for b ≤ x ≤ 2b

Now, the magnitude of induced current when induced emf is non-zero is ε = IR

`:.I=epsilon/r=(Blv)/r`

The force required to keep the conductor in motion is F =  BIl

`:.F=B(Blv)/Rl=(B^2l^2v)/R`

`:.F=(B^2l^2v)/R`                      for b ≤ x < b

= 0                          for b ≤ x ≤ 2b

Therefore, the variation of flux, emf and force is

Concept: Force on a Current - Carrying Conductor in a Uniform Magnetic Field
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