Question

Two straight parallel wires both carrying $ 10\,A $ 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 $\frac{F_{1}}{F_{2}}=\frac{i_{1} i_{2}}{2 i_{1} \cdot 2 i_{2}}$
or $\frac{1 \times 10^{-3}}{F_{2}}=\frac{10 \times 10}{2 \times 10 \times 2 \times 10}$
or $F_{2}=4 \times 10^{-3} N$