Answer to Question #282933 in Electricity and Magnetism for BIGIRMANA Elie

Question

A circular current–carrying coil has a radius R. Determine the distance in terms of R, of a point on the axis from the centre of the coil where the magnetic field produced by the coil is 1/8 of its value at the centre of the coil.

Answer 1

$B(z)=\frac{\mu_0}2\frac{IR^2}{(z^2+R^2)^{\frac 32}},$

$\frac{B_0}{B_1}=\frac{(z^2+R^2)^{\frac 32}}{R^3}=8,$

$z=\sqrt3R.$