Question

A long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having n turns. If the same current is passed in both the cases, the ratio of magnetic field produced at the centre for one turn to that of n turns is

• A. \(1:n\)
• B. \(n:1\)
• C. \(1:n^2\)
• D. \(n^2:1\)

Hint:

The same wire length is used, so the radius becomes R/n when there are n turns.

Answer 1

The Correct Option is C

Step 1: Two effects
Turns increase by n, and radius decreases by n, each raising the field by n.

Step 2: Combine
$B \propto N/r$ increases by $n \times n = n^2$.

Step 3: Ratio
$B_1 : B_n = 1 : n^2$. Option (C).

Final Answer:
Option (C). \[ \boxed{1 : n^2} \]