Question

An arrangement of three parallel long straight wires placed perpendicular to plane of paper carrying equal current $‘i^{\prime }$ along the same direction as shown in figure. Magnitude of force per unit length on the wire $A$ due to other wires is given by

• A. $\frac{\sqrt{3}{\mu }_0{i}^2}{2\pi a}$
• B. $\frac{{\mu }_0{i}^2}{\sqrt{2}\pi a}$
• C. $\frac{\sqrt{2}{\mu }_0{i}^2}{3\pi a}$
• D. $\frac{3{\mu }_0{i}^2}{2\pi a}$

Answer 1

The correct option is A $\frac{\sqrt{3}{\mu }_0{i}^2}{2\pi a}$


Net force per unit length on $A$

$F=\sqrt{F_1^2+F_2^2+2F_1{F}_2\cos {60}^{\circ }}$

where, $F_1=\frac{{\mu }_0}{2\pi }\frac{i^2}{a}=F_2$

$F=2F_1\cos {30}^{\circ }=F_1\sqrt{3}$

$F=\frac{{\mu }_0}{2\pi }\frac{i^2}{a}\sqrt{3}$
Hence, option $\left(B\right)$ is correct.