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 `vecB=B_(0)hatj` as shown in figure. In this situation, normal force between horizontal surface and clock passes through a point at a distance x from centre. Choose correct statement (s).

Options

A. The block must not topple if `I lt (mg)/(aB_(0))`
B. The block must not topple if `Ilt(m g)/(2aB_(0))`
C. `x=a/4` if `I=(mg)/(2aB_(0))`
D. `x=a/4` if `I=(mg)/(4aB_(0))`

Answer

B, D

Explanation

For rotational equilibrium, taking torque about the point from where normal force passes.
`IaB_(0)a/2+IaB_(0)a/2-mgx=0,x=(Ia^(2)B_(0))/(mg)`
Fro the block not to topple `x lt a/2impliesIlt(mg)/(2aB_(0))`