A circular coil of radius R carries a current I. What is the ratio of the magnetic field at the cent

Question

A circular coil of radius R carries a current I. What is the ratio of the magnetic field at the centre of the coil to the magnetic field at a distance R on the axis of the coil?

Professor PC Thomas Classes · Answer

$B_{center} = \frac{\mu_0 I}{2R}$. $B_{axis}(R) = \frac{\mu_0 I R^2}{2(R^2 + R^2)^{3/2}} = \frac{\mu_0 I}{4\sqrt{2} R}$. Ratio is $\frac{\mu_0 I / 2R}{\mu_0 I / 4\sqrt{2} R} = 2\sqrt{2}$.