A square wire frame of side a is placed a distance b away from a long straight conductor carrying current I. The frame has resistance R and self-inductance L. The frame is rotated by ${180}^{\mathrm{o}}$ about OO' as shown in Fig. Find the electric charge flown through the frame -

• A

  $\frac{2{\mathrm{\mu }}_0\mathrm{i}{\mathrm{a}}^2}{2\mathrm{\pi }\mathrm{R}\mathrm{b}}$
• B

  $\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{\pi }\mathrm{R}}{\log }_{\mathrm{e}}\frac{\mathrm{b}+\mathrm{a}}{\mathrm{b}-\mathrm{a}}$
• Correct answer
  C

  $\frac{\mathrm{ }{\mathrm{\mu }}_0\mathrm{i}\mathrm{a}}{2\mathrm{\pi }\mathrm{R}}{\log }_{\mathrm{e}}\frac{\mathrm{b}+\mathrm{a}}{\mathrm{b}-\mathrm{a}}$
• D

  None of these

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