Question

An electric current is flowing in a circular wire of radius a. At What distance from the centre on the axis of the circular wire will the magnetic field be 1/8th of it's value at the centre

Answer 1

$B_1=\frac B8,$

$B_1=\frac{\mu_0}{2}\frac{a^2I}{(a^2+x^2)^{\frac 32}},$

$B=\frac{\mu_0 I}{2a},$

$\frac{a^2}{(a^2+x^2)^{\frac 32}}=\frac1{8a},$

$4a^2=a^2+x^2,$

$3a^2=x^2,$

$x=±a\sqrt 3.$