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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
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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
Solution:
1608 Upvotes
Verified Answer
The correct answer is:
$\frac{1}{r^{3}}$
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
$$
\begin{aligned}
& B=\frac{\mu_{0}}{4 \pi} \cdot \frac{2 M}{r^{3}} \\
\therefore \quad & B \propto \frac{1}{r^{3}}
\end{aligned}
$$
$$
\mathrm{B}=\frac{\mu_{0}}{4 \pi} \cdot \frac{2 \mathrm{M}}{\left(\mathrm{R}^{2}+\mathrm{r}^{2}\right)^{3 / 2}}
$$
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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