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
  1. $\frac{1}{r^{3}}$
  2. $\frac{1}{r}$
  3. $\frac{1}{r^{4}}$
  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 $\begin{aligned} & B=\frac{\mu_{0}}{4 \pi} \cdot \frac{2 M}{r^{3}} \\ \therefore \quad & B \propto \frac{1}{r^{3}} \end{aligned}$ *

Asked in: MHT CET 2020 (13 Oct Shift 1)

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