Question

If $\overline{B}$ is the magnetic induction, at the centre of a circular coil of radius $r$ carrying a current is $1T$, then its value at a distance of $\sqrt{3}r$ on the axis from the centre of the coil is:

• A. $\frac{1}{8}T$
• B. $\frac{1}{16}T$
• C. $8T$
• D. $\frac{1}{4}T$

Answer 1

The correct option is A $\frac{1}{8}T$

Magnetic field induction at a general point on the axis of a circular coil is given by the formula,

$B=\frac{{\mu }_0}{2}\frac{I{r}^2}{{(z^2+r^2)}^{3/2}}$

At center of the coil, $z=0,B=1T$

$\therefore B=\frac{{\mu }_0}{2}\frac{I}{r}=1T$

At a distance $\sqrt{3}r$ on the axis from the center,

$B^{\prime }=\frac{{\mu }_0}{2}\frac{I{r}^2}{{(r^2+{\left(\sqrt{3}r\right)}^2)}^{3/2}}=\frac{{\mu }_0}{2}\times \frac{I}{r}\times \frac{1}{8}=\frac{1}{8}T$