Question

A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a circular loop of n turns. The magnetic field at the centre of the coil will be:

• A. $n B$
• B. $n² B$
• C. $2nB$
• D. $2n² B$

Hint:

When wire is made into multiple turns, radius decreases and field increases as $n²$.

Answer 1

The Correct Option is B

Step 1: For single turn, $B = \frac\mu₀ I2r$. For n turns, radius becomes $r/n$.

Step 2: $B' = n × \frac\mu₀ I2(r/n) = n² × \frac\mu₀ I2r = n² B$.