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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.

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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.

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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