Question

An electric current $i$ is flowing in a circular coil of radius $a$. At what distance from the center of the axis of the coil will the magnetic field be ${\frac{1}{8}}^{th}$ of its value at the centre?

• A. $3a$
• B. $\sqrt{3}a$
• C. $\frac{a}{3}$
• D. $\frac{a}{\sqrt{3}}$

Answer 1

The correct option is B $\sqrt{3}a$

Magnetic field due to the circular current (I) carrying coil of radius a, at a distance r from the center of the coil is given by:
$B_1=\frac{{\mu }_0}{4\pi }\frac{2\pi a^{2}I}{(z^2+a^2{)}^{3/2}}$.
Now the field at a point $P.B_1$will be ${\frac{1}{8}}^{th}$ times the field at the center:
So, $B=8B_1$
or, $\frac{{\mu }_{0}I}{2a}=8\times \frac{{\mu }_0}{4\pi }\frac{2\pi a^{2}I}{(z^2+a^2{)}^{3/2}}$
for, $z=\sqrt{3}a$