MHT CET · Physics · Magnetic Effects of Current
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
- A \(\frac{1}{r^{3}}\)
- B \(\frac{1}{r}\)
- C \(\frac{1}{r^{4}}\)
- D \(\frac{1}{r^{2}}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{r^{3}}\)
Step-by-step Solution
Detailed explanation
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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