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}}
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}}

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}