The force per unit length between two parallel current carrying straight conductors separated by $2 d$ is given by the formula

• Correct answer
  A

  $\frac{\mu_0}{4 \pi} \frac{i_1 i_2}{d}$
• B

  $\frac{\mu_0}{4 \pi} \frac{i_1 i_2}{2 d}$
• C

  $\frac{\mu_0}{\pi} \frac{i_1 i_2}{2 d}$
• D

  None of these

Solution

Force per unit length between the two parallel current carrying wires
$\frac{F}{L}=\frac{\mu_0}{2 \pi r} i_1 i_2$ $=\frac{\mu_0}{2 \pi(2 d)} i_1 i_2=\frac{\mu_0 i_1 i_2}{4 \pi d} \quad[\because r=2 d]$

Hence, the correct answer is option: 'A'.