Question

Two conducting circular loops A and B are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is:

• A. \( \frac{\mu_0 \pi a^2}{2b} \)
• B. \( \frac{\mu_0}{2\pi} \cdot \frac{b^2}{a} \)
• C. \( \frac{\mu_0 \pi b^2}{2a} \)
• D. \( \frac{\mu_0}{2\pi} \cdot \frac{a^2}{b} \)

Answer 1

The Correct Option is A

The magnetic flux (\(\phi\)) through loop B due to current in loop A is given by:

\[ \phi = M \cdot i = B \cdot A \]

The mutual inductance is:

\[ M = \frac{\mu_0 \pi a^2}{2b} \]

where \(a\) is the radius of loop A, \(b\) is the distance between the loops, and \(\mu_0\) is the permeability of free space.