Question

Two parallel wires in free space are $10cm$ apart and each carries a current of $10A$ in the same direction. The force exerted by one wire on other per metre of length of the wire is

• A. $2\times {10}^{-6}N$
• B. $2\times {10}^{-4}N$
• C. $2\times {10}^{-3}N$
• D. $2\times {10}^{-2}N$

Answer 1

The correct option is B $2\times {10}^{-4}N$

Given,

$i_1=i_2=10A$

$d=10cm=0.1m$

$l=1m$

The force exerted by one wire on other is given by

$F=\frac{{\mu }_0{i}_1{i}_{2}l}{2\pi d}$

$F=\frac{4\pi \times {10}^{-7}\times 10\times 10\times 1}{2\pi \times 0.1}=2\times {10}^{-4}N$

The correct option is B.