Question

An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current $i$ along the same direction is shown in fig. Magnitude of force per unit length on the middle wire 'B' is given by

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

Answer 1

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

Magnetic force per unit length on one wire due to another wire is given by,
$F=\frac{{\mu }_0{i}_1{i}_2}{2\pi d}$
$F_1=\frac{({\mu }_{0}i)i}{2\pi d}=\frac{{\mu }_0{i}^2}{2\pi d}=F_2$

$F_{net}=\sqrt{F_1^2+F_2^2}=\frac{{\mu }_0{i}^2}{\sqrt{2}\pi d}$