Question

At what distance on the axis, from the centre of a circular current carrying coil of radius $r$, the magnetic field becomes $1 / 8$ th of the magnetic field at centre?

• A. $\sqrt{2} r$
• B. $2^{3 / 2} r$
• C. $\sqrt{3} r$
• D. $3 \sqrt{2} r$

Answer 1

Answer: (C)

$\frac{1}{8} \frac{\mu_{0} i}{2 r}=\frac{\mu_{0} r^{2}}{2\left(r^{2}+x^{2}\right)^{3 / 2}}$
$\Rightarrow \left(r^{2}+x^{2}\right)^{3 / 2}=8 r^{3}$
$\Rightarrow \left(r^{2}+x^{2}\right)=\left(8 r^{3}\right)^{2 / 3}$
$\Rightarrow r^{2}+x^{2}=4 r^{2}$
$\Rightarrow 3 r^{2}=x^{2}$
$\Rightarrow x=r \sqrt{3}$