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 $F_{1}>F_{3}$
$F_{n e t}=F_{1}-F_{3}$
$F_{n e t}=\frac{\mu _{0} I_{1} I_{2}}{2 \pi a}a-\frac{\mu _{0} I_{1} I_{2}}{4 \pi a}a$
$F_{n e t}=\frac{\mu _{0} I_{1} I_{2}}{4 \pi }$