(a) Using Biot-Savarts law, derive an expression for the magnetic field at the centre of a circular coil of radius $$R$$, number of turns $$N$$, carrying current $$i$$.
(b) Two small identical circular coils marked 1, 2 carry equal currents and are placed with their geometric axes perpendicular to each other as shown in the figure. Derive an expression for the resultant magnetic field at $$O$$.