A square coil of edge I having n turns carries a curent i. it is kept on a smooth horizontal plate. A uniform magnetic field B exists in a direction parallel to an edge the total mass of the coil is M. What should be the minimum value of B for which the coil will start tipping over?

Explanation

Deflecting torque due to current
`tau_(1) = (n i A)B sin 90^(@) = niL^(2)B`
Restoring torque
`tau_(2) = Mg (L)/(2)`
`tau_(1) ge tau_(2)`
`niL^(2) B ge Mg.(L)/(2)`
`B ge (Mg)/(2niL)`
`B_(min) = (Mg)/(2niL)`
Note: `vec(M)` is along `+z`-axis and `vec(B)` is along `+x`-axis. The magnetic moment vector `vec(M)` tries to align along `vec(B)` through smaller angle to have minimum potential energy so coil rotates clockwise about line `BC`.