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)

$R \sqrt{3}$

Answer 2

$\frac{B_{\text {centre }}}{B_{\text {axis }}}=\left(1+\frac{x^{2}}{R^{2}}\right)^{3 / 2}$
Also,
$B_{\text {axis }} =\frac{1}{8} B_{\text {centre }}$
$\frac{8}{1} =\left(1+\frac{x^{2}}{R^{2}}\right)^{3 / 2}$
$4 =1+\frac{x^{2}}{R^{2}}$
$3=\frac{x^{2}}{R^{2}}$
$x^{2} =3 R^{2}$
$x =\sqrt{3} R$