Question

A circular current carrying coil has a radius $r$. At what distance from the centre of the coil, on the axis of the coil, the magnetic induction will be $\frac{1}{8}$th of the value as at the centre of the coil?

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

Answer 1

The correct option is A $r\sqrt{3}$

For the distance measured from the circumference
$B\propto \frac{1}{d^3}$
So, field will be $\frac{1}{8}$th at a distance $2r$ as shown in the figure
so, the distance along the axis
$x=\sqrt{{\left(2r\right)}^2-{\left(r\right)}^2}=r\sqrt{3}$