Magnetic field at centre of a circular loop

Field at the centre of a circular current: $B = \frac{\mu_0 I}{2r}$
Equivalent current: $I = \frac{e}{T} = ne$
$B = \frac{\mu_0 ne}{2r}$

Field at the centre of each coil: $B_1 = \frac{\mu_0I}{2R}$ and $B_2 = \frac{\mu_0(2I)}{2R}$
The planes are perpendicular, so the two fields are perpendicular to each other.
$B = \sqrt{B_1^2 + B_2^2} = \sqrt{\left(\frac{\mu_0I}{2R}\right)^2 + \left(\frac{2\mu_0I}{2R}\right)^2} = \frac{\sqrt5\mu_0I}{2R}$