Question

A square coil of edge l having n turns carries a current 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. Find Minimum value of B for which the coil will start tipping over ?

• A. ${\left(\frac{mg}{nil}\right)}^2$
• B. $\frac{2mg}{nil}$
• C. $\frac{mg}{2nil}$
• D. $\frac{mg}{nil}$

Answer 1

Answer: (C)

$\frac{mg}{2nil}$

Deflecting torque = niAB sin 90
$=ni{l}^{2}B$
Restoring torque $=mg\frac{l}{2}$
For tipping $ni{l}^{2}B\ge \frac{mgl}{2}$
$\Rightarrow B\ge \frac{mg}{2nil}$
$\therefore B_{min}=\frac{mg}{2nil}$