The magnetic induction at the centre of a circular coil of radius 10 cm is $5 \sqrt{5}$ times the magnetic induction at a point on its axis. The distance of the point from the centre of the coil, in cm is:

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answer is C.

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Detailed Solution

$B_{c} = 5 \sqrt{5} B; \frac{μ_{0} i}{2 a} = 5 \sqrt{5} \frac{μ_{0} {ia}^{2}}{2 {(a^{2} + x^{2})}^{3 / 2}},$
Here, a = 0.1 m
${(a^{2} + x^{2})}^{3 / 2} = 5 \sqrt{5} a^{3} \Rightarrow x = 20 cm$

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