Question

Two straight wire A and B of lengths 10 m and 12 m 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 × 10-5 N, attractive
• B. 2.4 × 10-5 N, repulsive
• C. 1.2 × 10-5 N, attractive
• D. 1.2 × 10-5 N, repulsive

Answer 1

Answer: (B)

2.4 × 10-5 N, repulsive

Answer 2

The lengths of the two wires are quiet large as compared to the separation between them the two wires may be regarded as infinitely long wires the forces per unit length of wires B due to A,

$\mathrm { f } = \frac { \mu _ { 0 } \mathrm { I } _ { 1 } \mathrm { I } _ { 2 } } { 2 \pi \mathrm { r } } = \frac { 4 \pi \times 10 ^ { - 7 } \times 4 \times 6 } { 2 \pi \times 3 \times 10 ^ { - 2 } } = 1.6 \times 10 ^ { - 4 } \mathrm { Nm } ^ { - 1 }$

Force on 15cm or 0.15 cm section of B,

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