Question

A square loop of side $a$ is placed at a distance $a$ length away from a long wire carrying a current $I_1$ . If the loop carries a current $I_2$ as shown in the figure. Then the nature of the force and its amount is

• A. $\frac{{\mu }_0{I}_1{I}_2}{2\pi a}$ , attractive
• B. $\frac{{\mu }_0{I}_1{I}_2}{4\pi }$ , attractive
• C. $\frac{{\mu }_0{I}_1{I}_2}{4\pi }$ , repulsive
• D. $\frac{{\mu }_0{I}_1{I}_2}{4\pi a}$ , repulsive

Answer 1

Answer: (B)

From the figure it is clear that $F_2$ & $F_4$ cancel each other, but $F_1>F_3$
$F_{net}=F_1-F_3$
$F_{net}=\frac{{\mu }_0{I}_1{I}_2}{2\pi a}a-\frac{{\mu }_0{I}_1{I}_2}{4\pi a}a$
$F_{net}=\frac{{\mu }_0{I}_1{I}_2}{4\pi }$