Discussion Forum



1)

A circular current-carrying coil has a radius R.The distance from the centre of the coil on the axis, where the magnetic induction will be $\frac{1}{8}$ th to its value at the centre of the coil is 


A) $\frac{R}{\sqrt{3}}$

B) $R \sqrt{3}$

C) $2\sqrt{3}R$

D) $\frac{2}{\sqrt{3}}R$

Answer:

Option B

Explanation:

 Here the ratio, $\frac{B_{centre}}{B_{axis}}=\left(1+\frac{x^{2}}{R^{2}}\right)^{3/2}$

Also, $B_{axis}=\frac{1}{8}B_{centre}$

$\frac{8}{1}=\left(1+\frac{x^{2}}{R^{2}}\right)^{3/2} \Rightarrow   4=1+\frac{x^{2}}{R^{2}}$

$3=\frac{x^{2}}{R^{2}} \Rightarrow X^{2}=3R^{2}$

or ,$x= \sqrt{3}R$