Question

A square coil of edge $I$ 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 $m$ . The minimum value of $B$ for which the coil will start tipping over

• A. $\left(\frac{m g}{n i l}\right)^{2}$
• B. $\frac{2 m g}{n i l}$
• C. $\frac{m g}{2 \, n i l}$
• D. $\frac{m g}{n i l}$ '

Answer 1

Answer: (C)

Deflecting torque $=ni​ABsin90$
$=nil^{2}B$
Restoring torque $=mg\frac{l}{2}$
For tipping $nil^{2}B\geq \frac{m g l}{2}$
$\Rightarrow B\geq \frac{m g}{2 n i l}$
$\therefore B_{m i n}=\frac{m g}{2 n i l}$