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Question

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 at frictionless horizontal surface in a uniform magnetic field B=B0^j as shown in fig. In this situation, normal force between horizontal surface and block passes through a point at a distance x from center. Choose correct statement(s)

166520.png

A
The block must not topple if I<mgaB0
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B
The block must not topple if I<mg2aB0
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C
x=a4 if I=mg2aB0
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D
x=a4 if I=mg4aB0
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Solution

The correct options are
A x=a4 if I=mg4aB0
C The block must not topple if I<mg2aB0
Torque of magnetic field; τ=MB0=Ia2B0
For rotational equilibrium: τ=mgxIa2B0=mgx
x=Ia2B0mg
For the block not to topple:
x<a2I<mg2aB0

If I=mg4aBo, substituting value we get
x=a/4

278071_166520_ans_5637cbd942af4aa9bfb1651c0dc0fa24.PNG

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