Question

A wooden cubical block ABCDEFG of mass m and side a is wrapped by a square wire loop of perimeter 4a, carying current I. The whole system is placed at frictionless horizontal surface in a uniform magnetic field `vecB=B_0hatj` as shown in fig. In this situation, normal force between horizontal surface and block passes through a point at a distance x from centre. Choose correct statement (s).

A. The block must not topple if `Ilt (mg)/(aB_0)`
B. The block must not topple if `Ilt (mg)/(2aB_0)`
C. `x=a/4 if I=(mg)/(2aB_0)`
D. `x=a/4 if I=(mg)/(4aB_0)`

Answer 1

Correct Answer - (b,d)
Torque of magnetic field : `tau=MB_0=Ia^2B_0`
For rotation equilibrium: `tau=mgx implies Ia^2B_0=mgx`
`implies x=(Ia^2B_0)/(mg)`
For the block not to topple:
`xlta/2 implies Ilt(mg)/(2aB_0)`