Question

Two straight wires A and B of lengths 10m and 12m carrying currents of 4.0 A and 6.0 A respectively in opposite direction, lie parallel to each other at a distance of 3.0 cm. The force on a 15 cm section of the wire B near its centre is

• A. 2.4 x ${10}^{-5}N$, attractive
• B. 2.4 x ${10}^{-5}N$, repulsive
• C. 1.2 x ${10}^{-5}N$, attractive
• D. 1.2 x ${10}^{-5}N$, repulsive

Answer 1

Answer: (B)

2.4 x ${10}^{-5}N$, repulsive

The lengths of the two wires are quite large as compared to the separation between them. The two wires may be regarded as infinitely long wires. The force per unit length of wire B due to A,
$f=\frac{{\mu }_0{I}_1{I}_2}{2\pi r}=\frac{4\pi \times {10}^{-7}\times 4\times 6}{2\pi \times 3\times {10}^{-2}}$
$=1.6\times {10}^{-4}N{m}^{-1}$
Force on 15 cm or 0.15 m section of ,

$F=fl=1.6\times {10}^{-4}\times 0.15=2.4\times {10}^{-5}N$, (repulsive)