Question

A circular coil of radius $R$ carries a current. Consider the magnetic field due to the coil, at a point on its axis at a distance $r(r>>R)$ from the center. The magnitude of this magnetic field 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 $\frac{1}{r^3}$

We know that the magnetic field due to a current carrying coil at a point on its axis is given by,

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

$\because r>>R\Rightarrow R^2+r^2\approx r^2$

$\Rightarrow B=\frac{{\mu }_0}{4\pi }\times \frac{2NI\pi R^2}{r^3}$

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

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