Question

A circular coil of radius $R$ carries an electric current $I$. The magnetic field due to the coil at a point on the axis of the coil located at a distance $r$ from the centre of the coil, such that $r>>R$, varies as

• A. $\frac{1}{r}$
• B. $\frac{1}{r^{3/2}}$
• C. $\frac{1}{r^2}$
• D. $\frac{1}{r^3}$

Answer 1

The correct option is D $\frac{1}{r^3}$

The magnetic field at distance $r$ from the centre along the axis of circular loop $($radius $=R)$ of the current carrying conductor is given by,

$$B=\frac{{\mu }_0}{4\pi }\frac{2\pi I{R}^2}{(R^2+r^2{)}^{3/2}}$$
$\because R<<r$

$\therefore R^2+r^2\approx r^2$

$\Rightarrow B\propto \frac{1}{r^3}$

Hence, option $\left(D\right)$ is the correct answer.