Question

A current of $2\text{A}$ is flowing through a circular coil of radius $1\text{m}$.

Find the magnitude of magnetic field at a point on its axial line which is at $\sqrt{3}\text{m}$ distance away from its center.

​​​​​​​$[$1 Mark$]$

• A. ${\mu }_0$
• B. $2{\mu }_0$
• C. $8{\mu }_0$
• D. $\frac{{\mu }_0}{8}$

Answer 1

The correct option is D $\frac{{\mu }_0}{8}$

The magnitude of magnetic field at a point on the axial line of the circular current carrying coil is given by

$B=\frac{{\mu }_{0}i{r}^2}{2{(r^2+x^2)}^{3/2}}$

Where,

$i=$ current through the circular coil
$r=$ radius of the circular coil
$x=$ distance of the point on the axial line from the center of the circular coil

So,

$B=\frac{{\mu }_0\cdot \left(2\right)\cdot (1{)}^2}{2\cdot [1^2+(\sqrt{3}{)}^2{]}^{3/2}}$

$\Rightarrow B=\frac{{\mu }_0}{8}\text{T}$