Question

An electric current is flowing through a circular coil of radius R. The ratio of the magnetic field at the center of the coil and that at a distance $2\sqrt{2}R$ from the center of the coil and on its axis is:

Answer 1

Magnetic field at a point x on its axis $B_x=\frac{B_o{R}^3}{(R^2+x^2{)}^{3/2}}$

where $B_o$ is the magnetic field at the centre

So ratio $\frac{B_x}{B_o}=\frac{R^3}{(R^2+x^2{)}^{3/2}}$

$\frac{B_x}{B_o}=\frac{R^3}{(R^2+(2\sqrt{2}R{)}^2{)}^{3/2}}=\frac{1}{(9{)}^{3/2}}=\frac{1}{27}$