Question

Two long straight parallel conductors are carrying currents $i_{1}$ and $i_{2}$ in the same direction. Work done per unit length, when the distance between them is doubled is

• A. $2 \times \frac{\mu_{0}}{2 \pi} i_{1} i_{2}$
• B. $\frac{\mu_{0}}{2 \pi} i_{1} i_{2} \ln [2]$
• C. $\frac{\mu_{0}}{2 \pi} i_{1} i_{2} \ln [4]$
• D. 0

Answer 1

Answer: (B)

Work done $=\int_\limits{d}^{2 d} F \cdot d x=\int_\limits{d}^{2 d} \frac{\mu_{0} i_{1} i_{2}}{2 \pi x} \cdot d x$
$=\frac{\mu_{0} i_{1} i_{2}}{2 \pi}\left[\log _{e} x\right]_{d}^{2 d}$
$=\frac{\mu_{0} i_{1} i_{2}}{2 \pi}\left(\log _{e} 2\right)$