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Byju's Answer

Standard XII

Physics

Motional EMF

A wire is ben...

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 :

increase with time

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decrease with time

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remain constant

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always be zero

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Solution

The correct option is B remain constant
Induced EMF
$E = B v L$
$i = \frac{E}{R}$
Ohm's Law
$i = \frac{B v L}{R}$
Now
since resistance of wire =0
$R = R_{r o d}$
If $λ$ = resistance per unit length of rod
$i = \frac{B v L}{λ L}$
$i = c o n s t .$
As the potential increases, the resistance also increases in the same proportion maintaining constant current.

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The correct option is B remain constantInduced EMFE=BvLi=EROhm's Lawi=BvLRNowsince resistance of wire =0R=RrodIf λ = resistance per unit length of rodi=BvLλLi=const.As the potential increases, the resistance also increases in the same proportion maintaining constant current.