Question

24.a current is flowing in a circular coil of radius r and the magnetic field at it's centre is B.at what distance from the centre on the axis of the coil,the magnetic field will be B/8 ?

Answer 1

The formula for the magnetic field B (flux density) at P at a distance d from the center of O the coil on the axis of the coil of radius r :

$B=\frac{\mu_0}{2} \frac{i*r^2}{(r^2+d^2)^{\frac{3}{2}}}\\\\\frac{B_{point\_P}}{B_{center\_O}}=\frac{r^3}{(r^2+d^2)^{\frac{3}{2}}}=\frac{1}{8}\\\\2r=\sqrt{r^2+d^2}\\\\d^2=3r^2\\\\d=\sqrt{3}\ r$