Question

n 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

The correct option is B $R\sqrt{3}$

$\frac{B_{centre}}{B_{axis}}={(1+\frac{x^2}{R^2})}^{\frac{3}{2}},also{B}_{axis}=\frac{1}{8}{B}_{centre}$
$\Rightarrow \frac{8}{1}={(1+\frac{x^2}{R^2})}^{\frac{3}{2}}\Rightarrow 2={(1+\frac{x^2}{R^2})}^{\frac{1}{2}}$
$\Rightarrow 4=1+\frac{x^2}{R^2}\Rightarrow 3=\frac{x^2}{R^2}\Rightarrow x^2=3R^2\Rightarrow x=\sqrt{3}R$