A toroidal (ring) solenoid has a total number of turns of wire N, each of which carries a current I. The radius of the toroidal ring is R. The cross-sectional area of the solenoid is A. Here, we assume that the radius of the coils of wire which make up the solenoid are much smaller than the radius of the ring itself. This allows us to assume that the magnetic field strength within the solenoid itself (i.e., passing through its area) is approximately uniform.
(i) Write-down Ampere's law and use it to compute the strength of the magnetic field within: a) the centre of the solenoid (i.e., $r < R$); b) within the solenoid itself ($r = R$); and c) outside of the solenoid ($r > R$). Draw a rough sketch to show where the Amperian loops are being considered in each case.