Question

The ratio of magnetic inductions at the centre of a circular coil of radius $a$ and on its axis at a distance equal to its radius, will be -

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{\sqrt{2}}{1}$
• C. $\frac{1}{2\sqrt{2}}$
• D. $\frac{2\sqrt{2}}{1}$

Answer 1

The correct option is D $\frac{2\sqrt{2}}{1}$

Let us consider, $a=$ radius of circular coil $i=$ current flow in the circular coil
The magnetic field at the center of a circular coil is given by-
$B_1=\frac{{\mu }_{0}i}{2a}$
The magnetic field on its axis at a distance equal to the radius of the circular coil is given by-
$B_2=\frac{{\mu }_{0}i{a}^2}{2(a^2+a^2{)}^{\frac{3}{2}}}=\frac{{\mu }_{0}i}{2a\times 2^{\frac{3}{2}}}$
Ratio, $\frac{B_1}{B_2}=\frac{2\sqrt{2}}{1}$