Question

Two solenoids A and B of equal number of turns have their lengths and radii in the same ratio \(1:3\). The ratio of the self-inductance of solenoid A to that of B will be

• A. \(1:1\)
• B. \(1:3\)
• C. \(1:9\)
• D. \(3:1\)

Hint:

L = mu0 N^2 A / l, so with the same N, L is proportional to r^2 / l.

Answer 1

The Correct Option is B

Step 1: Scaling
Radius scales by 3 so area by 9; length scales by 3.

Step 2: L change
$L \propto 9/3 = 3$ for B relative to A.

Step 3: Ratio
$L_A : L_B = 1 : 3$. Option (B).

Final Answer:
Option (B). \[ \boxed{1:3} \]