Question

Two long straight wires, each carrying an electric current of 5 A, are kept parallel to each other at a separation of 2.5 cm. Find the magnitude of the magnetic force experienced by 10 cm of a wire.

• A. $4.0\times {10}^{-4}N$
• B. $3.5\times {10}^{-6}N$
• C. $2.0\times {10}^{-5}N$
• D. $2.0\times {10}^{-9}N$

Answer 1

Answer: (C)

$2.0\times {10}^{-5}N$

Given: $i_1=i_2=5A;d=2.5cm=0.025m;l=10cm=0.10m$

The magnetic force per unit length between two long straight parallel current carrying wires, placed in vacuum, separated by a distance $d$, is given by:

$F/l=\frac{{\mu }_0.i_1{i}_2}{2\pi d}$

$F=\frac{{\mu }_0.i_1{i}_{2}l}{2\pi d}$

Hence, $F=\frac{4\pi \times {10}^{-7}\times 5\times 5\times 0.10}{2\pi \times 0.025}=2.0\times {10}^{-5}N$