Correct option is
B $\sqrt{3} \mathrm{a}$
Magnetic field due to the circular current (I) carrying coil of radius $\mathrm{a}$, at a distance $r$ from the center of the coil is given by:
$$
B_{1}=\frac{\mu_{0}}{4 \pi} \frac{2 \pi a^{2} I}{\left(z^{2}+a^{2}\right)^{3 / 2}}
$$
Now the field at a point $P . B_{1} w i l l b e \frac{1}{8}^{\text {th }}$ times the field at the center:
So, $B=8 B_{1}$
or, $\frac{\mu_{0} \mathrm{I}}{2 \mathrm{a}}=8 \times \frac{\mu}{4 \pi} \frac{2 \pi \mathrm{a}^{2} \mathrm{I}}{\left(\mathrm{z}^{2}+\mathrm{a}^{2}\right)^{3 / 2}}$ for, $\mathrm{z}=\sqrt{3} \mathrm{a}$
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 $\frac{1}{8}$ of its value at the centre?
A $3 \mathrm{a}$
в $\sqrt{3} a$
c $\frac{\mathrm{a}}{3}$
D $\frac{\mathrm{a}}{\sqrt{3}}$
A $3 \mathrm{a}$
в $\sqrt{3} a$
c $\frac{\mathrm{a}}{3}$
D $\frac{\mathrm{a}}{\sqrt{3}}$
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 $\frac{1}{8}$ of its value at the centre?
A $3 \mathrm{a}$
в $\sqrt{3} a$
c $\frac{\mathrm{a}}{3}$
D $\frac{\mathrm{a}}{\sqrt{3}}$
A $3 \mathrm{a}$
в $\sqrt{3} a$
c $\frac{\mathrm{a}}{3}$
D $\frac{\mathrm{a}}{\sqrt{3}}$