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?

Options

A. `(Mg)/(niL)`
B. `(Mg)/(2niL)`
C. `(Mg)/(4niL)`
D. `(2Mg)/(niL)`

Answer

B

Explanation

Deflecting torque due to current,
`tau_(1)=(niA)B=sin90^(@)=niL^(2)B`
Restoring torque,
`tau_(2)=Mg""(L)/(2)impliestau_(1)getau_(2)`
`niL^(2)BgeMg""(L)/(2)impliesBge(Mg)/(2niL)`
`B_(min)=(Mg)/(2niL)`
Note M is along +Z-axis and B is along +X-axis. The magnetic mament vector M tries to align along B through smaller angle to have minimum potential energy. so coil rotates clockwise about line BC.