Question

Two long solenoids of radii \( r_1 \) and \( r_2 \) (\( > r_1 \)) and number of turns per unit length \( n_1 \) and \( n_2 \) respectively are co-axially wrapped one over the other. The ratio of self-inductance of inner solenoid to their mutual inductance is:

• A. \( \frac{n_1}{n_2} \)
• B. \( \frac{n_2}{n_1} \)
• C. \( \frac{n_1 r_1^2}{n_2 r_2^2} \)
• D. \( \frac{n_2 r_2^2}{n_1 r_1^2} \)

Hint:

Inductance is proportional to the number of turns and the square of the radius of the solenoid.

Answer 1

The Correct Option is C

Step 1: The setup. The self-inductance \( L \) of a solenoid is proportional to the square of the radius and the number of turns per unit length. The mutual inductance depends on the relative arrangement of the solenoids and their radii.

Step 2: Applying the formula. Using the general formula for inductance, the ratio of the self-inductance to the mutual inductance is \( \frac{n_1 r_1^2}{n_2 r_2^2} \), corresponding to option .