A circular coil of radius 'R' carries an electric current 'I'. The magnetic field due to the coil at a point…
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 ' $\mathrm{r}^{\prime}$ from the centre of
the coil, such that $\mathrm{r} \gg \mathrm{R}$, the magnetic field at that point is proportional to
$\frac{1}{r^{3}}$
$\frac{1}{r}$
$\frac{1}{r^{4}}$
$\frac{1}{r^{2}}$
Solution
Magnetic field at a point on the axis of the coil is given by
$\mathrm{B}=\frac{\mu_{0}}{4 \pi} \cdot \frac{2 \mathrm{M}}{\left(\mathrm{R}^{2}+\mathrm{r}^{2}\right)^{3 / 2}}$
If $r>>R$ then
$\begin{aligned}
& B=\frac{\mu_{0}}{4 \pi} \cdot \frac{2 M}{r^{3}} \\
\therefore \quad & B \propto \frac{1}{r^{3}}
\end{aligned}$
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