Question

The radius of a circular current carrying coil is $R$. At what distance from the centre of the coil on its axis, the intensity of magnetic field will be $\frac{1}{2 \sqrt{2}}$ times that at the centre?

• A. $2 \,R$
• B. $\frac{3 R}{2}$
• C. $R$
• D. $\frac{R}{2}$

Answer 1

Answer: (C)

$\frac{\mu_{0} i R^{2}}{2\left(R^{2}+x^{2}\right)^{3 / 2}}=\frac{1}{2 \sqrt{2}} \frac{\mu_{0} i}{2 R}$
$2 \sqrt{2} R^{3}=\left(R^{2}+x^{2}\right)^{3 / 2}$
$(2 \sqrt{2})^{2 / 3} R^{2}=R^{2}+x^{2}$
$x^{2}=2 R^{2}-R^{2}=R^{2} $
$\Rightarrow x=R$