Magnetic fields at two points on the axis of a circular coil carrying current at a distance of 1m and 5m from the centre are in the ratio 27:1. The radius of the coil is

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2 m

$\sqrt{2} m$

$\frac{1}{\sqrt{2}} m$

1 m

answer is C.

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Detailed Solution

$\begin{array}{l} B_{A} = \frac{B_{0}}{{(1 + \frac{x^{2}}{r^{2}})}^{3 / 2}} \\ \frac{B_{1}}{B_{2}} = \frac{{(1 + \frac{25}{r^{2}})}^{3 / 2}}{{(1 + \frac{1}{r^{2}})}^{3 / 2}} = \frac{27}{1} \\ r = \sqrt{2} m \end{array}$

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