(i) Consider an infinitely long solenoid parallel to the $z$-axis whose cross section is a simple closed curve of arbitrary shape. A current $I$, per unit length of the solenoid, flows around the solenoid parallel to the $x-y$ plane. Show using the relevant Maxwell equation that the magnetic field $\mathbf{B}$ inside the solenoid is uniform, and calculate its magnitude.

(ii) A wire loop in the shape of a regular hexagon of side length $a$ carries a current $I$. Use the Biot-Savart law to calculate $\mathbf{B}$ at the centre of the loop.