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Q.

A wooden cubical block ABCDEFG of mass m and side a is wrapped by a square wire loop of perimeter 4a, carrying current I. The whole system is placed on frictionless horizontal surface in a uniform magnetic field B=BOj^ as shown in figure. In this situation, normal force between horizontal surface and block passes through a point at a distance x from centre. Choose correct statement(s).

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a

The block must not topple ifI<mgaBo

b

The block must not topple ifI<mg2aBo

c

x=a4ifI=mg2aBo

d

x=a4ifI=mg4aBo

answer is D, B.

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Detailed Solution

M=IAk^=ia2k^B=Boj^

τ=M×B=ia2B0(i^)

Ifτ¯mg,a2 the block must topple

ia2B0mga2i=mg2B0a

ifi<mg2B0a it must not topple

ifn=a4ia2B0=mg=a4

i=mg4B0a

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