Question

Magnetic field at the center 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 center

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

Answer 1

The correct option is C $\frac{B}{\sqrt{8}}$

Given: A circular coil of radius R.

Solution: As we know, magnetic field at the center of a circular coil carrying current $I$ of radius $R$ is given by,

$B=\frac{\mu 2\pi I}{4\pi R}=\frac{\mu I}{2R}$ (1)

So, magnetic field at a point along axis of circular coil at distance $R$ from the center is given by,

$B_a=\frac{\mu 2\pi I{R}^2}{4\pi (R^2+R^2{)}^{\frac{3}{2}}}$

$=\frac{\mu I}{2\sqrt{8}R}$

$=\frac{B}{\sqrt{8}}$ (From (1))

Hence, the correct option is (C).