Two parallel conductors each carrying a current of 10 mA in opposite directions are placed at a distance 10 cm apart. The force per unit length between two conductors is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 10 \times 10^{-4}\left(\displaystyle\frac{\mu_0}{2\pi}\right)\,\mathrm{N/m} \)
Each wire lies in the magnetic field of the other, so each feels a force. The force per unit length between two long parallel currents is
\( \displaystyle \frac{F}{l} = \frac{\mu_0}{2\pi}\,\frac{I_1 I_2}{d} \)
The currents are opposite, so the force is repulsive; its magnitude is the same.
\( I_1 = I_2 = 10\,\mathrm{mA} = 10^{-2}\,\mathrm{A} \)
\( d = 10\,\mathrm{cm} = 0.1\,\mathrm{m} \)
\( \displaystyle \frac{F}{l} = \frac{\mu_0}{2\pi} \times \frac{10^{-2} \times 10^{-2}}{0.1} = 10^{-3}\left(\frac{\mu_0}{2\pi}\right) = 10 \times 10^{-4}\left(\frac{\mu_0}{2\pi}\right)\,\mathrm{N/m} \)