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 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
$(x)=10cm=0.1m$;
Current in each wire $=I_1=I_2$
$=10A$ and length of wire $(l)=1m$.
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.