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If “B” is the magnetic induction, at the centre of a circular coil of radius “r” carrying a current is 1 T ,then its value at a distance of $\sqrt{3} r$ on the axis from the centre of the coil is

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$\frac{1}{4} T$

$\frac{1}{8} T$

$\frac{1}{16} T$

answer is A.

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Detailed Solution

$B_{A} = \frac{B_{o}}{{[1 + \frac{x^{2}}{R^{2}}]}^{\frac{3}{2}}}$
Given B_o = 1T

Here $x = \sqrt{3} r$ , $R = r$

$B_{A} = \frac{1}{{[1 + {(\frac{\sqrt{3} r}{r})}^{2}]}^{\frac{3}{2}}}$

$= \frac{1}{{[1 + 3]}^{\frac{3}{2}}}$

$= \frac{1}{{[4]}^{\frac{3}{2}}}$

$= \frac{1}{{[2^{2}]}^{\frac{3}{2}}} = \frac{1}{2^{3}}$

$\begin{array}{l} B_{A} = \frac{1}{8} T \end{array}$

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