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Question

A wire is bent in the form of a V shape and placed in a horizontal plane. There exists a uniform magnetic field B perpendicular to the plane of the wire. A uniform conducting rod starts sliding over the V shaped wire with a constant speed v as shown in the figure. If the wire has no resistance, the current in rod will :

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A
increase with time
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B
decrease with time
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C
remain constant
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D
always be zero
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Solution

The correct option is B remain constant
Induced EMF
E=BvL
i=ER
Ohm's Law
i=BvLR
Now
since resistance of wire =0
R=Rrod
If λ = resistance per unit length of rod
i=BvLλL
i=const.
As the potential increases, the resistance also increases in the same proportion maintaining constant current.
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