Question

A rigid square 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 wire will be :

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

Answer 1

Answer: (B)

F${}_3$ & F${}_4$ cancel each other
Force on PQ will be F${}_1=I_2{B}_1$ a
$=I_2\frac{{\mu }_0{I}_1}{2\pi a}a$
$=\frac{{\mu }_0{I}_1{I}_2}{2\pi }$
Force on RS will be F${}_2$ = I${}_2{B}_2$ a
$=I_2\frac{{\mu }_0{I}_1}{2\pi 2a}a$
$=\frac{{\mu }_0{I}_1{I}_2}{4\pi }$
Net force = $F_1-F_2=\frac{{\mu }_0{I}_1{I}_2}{4\pi }$ repulsion
Option (2)