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Question
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
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