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  • Magnetic field at two points on the axis of a circular coil at a distance of 0.005m and 0.2m from the centre are in the ratio 8:1. The radius of coil is ___ Option: 1 0.2 m Option: 2 0.15 m <strong

Magnetic field at two points on the axis of a circular coil at a distance of 0.005m and 0.2m from the centre are in the ratio 8:1. The radius of coil is ___
Option: 1 0.2 m
Option: 2 0.15 m
Option: 3 0.1 m
Option: 4 1 m

Answers (1)

best_answer

We know, the magnetic field on the axis of a current-carrying circular ring is given by

\mathrm{B}=\frac{\mu_{0}}{4 \pi} \frac{2 \mathrm{NIA}}{\left(\mathrm{R}^{2}+\mathrm{x}^{2}\right)^{3 / 2}}

\therefore \frac{\mathrm{B}_{1}}{\mathrm{~B}_{2}}=\frac{8}{1}=\left[\frac{\mathrm{R}^{2}+(0.2)^{2}}{\mathrm{R}^{2}+(0.05)^{2}}\right]^{3 / 2}

\begin{array}{l} 4\left[\mathrm{R}^{2}+(0.05)^{2}\right]=\left[\mathrm{R}^{2}+(0.2)^{2}\right] \\ 4 \mathrm{R}^{2}-\mathrm{R}^{2}=(0.2)^{2}-4 \times(0.05)^{2} \\ 4 \mathrm{R}^{2}-\mathrm{R}^{2}=(0.2)^{2}-(0.1)^{2} \\ 3 \mathrm{R}^{2}=0.3 \times 0.1 \\ \mathrm{R}^{2}=(0.1)^{2} \\ \Rightarrow \mathrm{R}=0.1 \end{array}

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