This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
ΜThe point P is on the axis of the circular coil, I suppose.  Let the center of the coil be O.  Let OP be equal to x.  Radius is a.  Current is I.  Let  dL be a small element of the coil.  So  r = distance between dL and P = √(a²+x²).

Let the angle made by the line joining dL and P with the axis  be θ.  Here the angle θ is same for all elements on the coil.  Also r is also same.  The angle between the vectors dL and r is 90 deg. always.  Let us say that the axis of the coil is x axis.

Cos θ = a / √(a² + x²) = a/r

Using Biot Savarts law: 
\vec{B}=\frac{\mu_0\ I}{4 \pi} \int\limits^{}_{} {\frac{\vec{dL} \times \vec{r}}{r^3}} \, {} \\\\B_x=\frac{\mu_0 I}{4 \pi}  \int\limits^{2\pi a}_{0} { \frac{\ Sin \frac{\pi}{2}\ Cos\theta}{r^2}} \, dL \\\\=\frac{\mu_0 I}{4 \pi} [2 \pi a\ cos \theta/r^2]\\\\B_x=\frac{\mu_0 I\ a^2}{2 (a^2+x^2)^{\frac{3}{2}}}\\\\B_x=\frac{\mu_0 I}{2a}cos^3\theta

The y and z components of the magnetic field induction By and Bz are zero, as the components along these axes will be cancelled by diametrically opposite elements.

B₀ at the center of the coil when x = 0, is:    μ₀ I / (2 a)
Bx at a distance x on the axis will be  B₀ / 8 when Cos θ = 1/2

ie.,  Cos² θ = 1/4 = a² / (a² + x²)
   =>  x² = 3 a²       
   =>  x = √3 a

1 5 1