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 (\(\phi\)) in loop B, resulting from the current in loop A, is calculated as:

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

The mutual inductance is defined as:

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

Here, \(a\) represents the radius of loop A, \(b\) denotes the separation distance between the loops, and \(\mu_0\) is the magnetic permeability of vacuum.