Question

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 1

Answer: (B)

$R\sqrt{3}$

Here, the ratio, $\frac{B_{centre}}{B_{axis}}={(1+\frac{x^2}{R^2})}^{3/2}$
Also, $B_{axis}=\frac{1}{8}{B}_{centre}$
$\frac{8}{1}={(1+\frac{x^2}{R^2})}^{3/2}\Rightarrow 4=1+\frac{x^2}{R^2}$
$3=\frac{x^2}{R^2}\Rightarrow x^2=3R^2$
or, $x=\sqrt{3}R$