Question

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

• A. $ 2 \times {10} ^{-4} N$ repulsive
• B. $ 2 \times {10} ^{-7} N$ repulsive
• C. $ 2 \times {10} ^{-4} N$ attractive
• D. $ 2 \times {10} ^{-7} N$ attractive

Answer 1

Answer: (C)

Distance between two parallel wires
$( x )=10\, cm =0.1 \,m$;
Current in each wire $=I_{1}=I_{2}$
$=10\, A$ and length of wire $( l )=1 \,m$.
Force on the wire $( F )=\frac{\mu_{0} I_{1} \cdot I_{2} \times l}{2 \pi x}$
$=\frac{\left(4 \pi \times 10^{-7}\right) \times 10 \times 10 \times 1}{2 \pi \times 0.1}=2 \times 10^{-4} N .$
Since the current is flowing in the same direction, therefore the force will be attractive.