Question

Two straight parallel wires both carrying $10A$ current in the same direction attracts each other with a force of $1\times 10^{-3}N$ . If both currents are doubled, the force of attraction will be

• A. $1\times 10^{-3}N$
• B. $2\times 10^{-3}N$
• C. $4\times 10^{-3}N$
• D. $0.25\times 10^{-3}N$

Answer 1

Answer: (C)

Force between two parallel current carrying wires on their unit length
$F=\frac{{\mu }_0}{4\pi }\frac{{\dot{i}}_1{i}_2}{r}$
Hence, $F\propto {\dot{i}}_1{i}_2$
or $\frac{F_1}{F_2}=\frac{i_1{i}_2}{2i_1\cdot 2i_2}$
or $\frac{1\times 10^{-3}}{F_2}=\frac{10\times 10}{2\times 10\times 2\times 10}$
or $F_2=4\times 10^{-3}N$