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AP EAMCET · PHYSICS · Magnetic Effects of Current

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

  1. A \(2 \times \frac{\mu_0}{2 \pi} i_1 i_2\)
  2. B \(\frac{\mu_0}{2 \pi} i_1 i_2 \ln [2]\)
  3. C \(\frac{\mu_0}{2 \pi} i_1 i_2 \ln [4]\)
  4. D 0
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\mu_0}{2 \pi} i_1 i_2 \ln [2]\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} \text { Work done } & =\int_d^{2 d} F \cdot d x=\int_d^{2 d} \frac{\mu_0 i_1 i_2}{2 \pi x} \cdot d x \\ & =\frac{\mu_0 i_1 i_2}{2 \pi}\left[\log _e x\right]_d^{2 d}=\frac{\mu_0 i_1 i_2}{2 \pi}\left(\log _e 2\right)\end{aligned}\)