Question

A long conducting wire having a current I flowing through it, is bent into a circular coil of $N$ turns .Then it is bent into a circular coil of $n$ turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is :

• A. $n : N$
• B. $N : n$
• C. $N ^2: n ^2$
• D. $n^2: N ^2$

Answer 1

Answer: (C)

$N ^2: n ^2$

Answer 2

$I=(2\pi\ r)n$
$r∝(\frac{I}{n})$
$B=n(\frac{\mu_0i}{2r})∝(\frac{\mu_0i}{2L})n^2$
$\frac{B_1}{B_2}=(\frac{N^2}{n^2})$
So, the correct answer is (C) : $N^2:n^2$