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Question
Consider the situation shown in figure. The wire AB is slid on the fixed rails with a constant velocity. If the wire AB is replaced by a semicircular wire, the magnitude of the induced current will _____________ .
Options
increase
remain the same
decrease
increase or decrease depending on whether the semi-circle bulges towards the resistance or away from it
Solution
remain the same
The induced emf across ends A and B is given by
`E=Bvl`
This induced emf will serve as a voltage source for the current to flow across resistor R, as shown in the figure. The direction of the current is given by Lenz's law and it is anticlockwise.
`i=(Bvl)/R`
If the wire is replaced by a semicircular wire, the induced current will remain the same, as it depends on the length of the wire and not on its shape (when B, v and R are kept constant).
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