    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 BvλSince, 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.  Suggest Corrections  0      Explore more