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Question

In the given figure, the four rods have λ resistance per unit length. The arrangement is kept in a magnetic field of constant magnitude B and directed perpendicular to the plane of the figure. Initially, the sides as shown form a square. Now each wire starts moving with constant velocity v towards the opposite wire.


Calculate the current flowing in the circuit.

A
Zero
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B
Bvλ
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C
Bv4λ
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D
4Bvλ
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Solution

The correct option is B Bvλ
Since, each rod is moving with velocity v, so the emf induced across each rod will be the same in magnitude and is given by,

e=Bvl .....(1)

The equivalent circuit can be drawn as,


Here, r is the resistance of each rod.

r=λl .....(2)

The current flowing in the circuit is,

i=eeqreq

i=[e+e+e+e](r+r+r+r)=er [ It is a series combination]

Using equations (1) and (2),

i=Bvlλl

i=Bvλ

Hence, option (B) is the correct answer.

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