Question

Magnetic field at the centre of a circular coil of radius $R$ due to current $I$ flowing through it is $B$. The magnetic field at a point along the axis at distance $R$ from the centre is........

• A. $\frac {B} {\sqrt{8}}$
• B. $\sqrt{8}B$
• C. $\frac{B}{2}$
• D. $\frac{B}{4}$

Answer 1

Answer: (A)

$\frac {B} {\sqrt{8}}$

Answer 2

The magnetic field at a point along the axis at distance $R$ from the centre of a circular coil of radius $R$ carrying current $i$ is
$B_{A} =\frac{\mu_{0} 2 \pi i R^{2}}{4 \pi\left(R^{2}+R^{2}\right)^{3 / 2}}$
$=\frac{\mu_{0} \dot{z}}{2 \sqrt{8} R}$
$=\frac{B}{\sqrt{8}}$
$\left[B_{\text {centre }}=B=\frac{\mu_{0} i}{2 R}\right]$