Question

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

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

Answer 1

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

$B_{axis}$ $=\frac{{\mu }_{0}I{r}^2}{2{\left(r^2+x^2\right)}^{3/2}}$

$B_{center}$ $=\frac{{\mu }_{0}I}{2r}$

$B_{axis}$ $=$ $\frac{1}{8}$ $B_{center}$

$\frac{r^2}{{\left(r^2+x^2\right)}^{3/2}}=\frac{1}{8r}$

${\left(2r\right)}^2=r^2-x^2$

$x=r\sqrt{3}$

Hence,

option $\left(C\right)$ is correct answer.