Question

A rigid square of loop of side $a$ and carrying current $I_2$ is lying on a horizontal surface near a long current $I_1$ carrying wire in the same plane as shown in figure. The net force on the loop due to the wire will be

• A. Repulsive and equal to $\frac{{\mu }_0{I}_1{I}_2}{2\pi }$
• B. Zero
• C. Repulsive and equal to $\frac{{\mu }_0{I}_1{I}_2}{4\pi }$
• D. Attractive and equal to $\frac{{\mu }_0{I}_1{I}_2}{3\pi }$

Answer 1

The correct option is C Repulsive and equal to $\frac{{\mu }_0{I}_1{I}_2}{4\pi }$

Let forces on the loops is $F_1\&F_2$ as shown below


Net force on the loop is
$F=F_1-F_2=\frac{{\mu }_0}{2\pi }(\frac{I_1{I}_2}{a}-\frac{I_1{I}_2}{2a})\times a$
$F=\frac{{\mu }_0{I}_1{I}_2}{4\pi }$ $(\text{Repulsive}$)