Avery thin plastic ring (radius r) has a constant linear charge density, and total charge q. the ring spins at angular velocity ω about its center (which is the origin). what is the current i, in terms of given quantities? what is the volume current density j in cylindrical coordinates? (this may be a little tricky, since the ring is "very thin", there will be some δ functions. i suggest writing down a formula for rho(r,φ,z) first. and, remember that j should be a vector! ) now let’s take some currents and find the corresponding b field.

b) compute the magnetic field b(0,0,z) along the z-axis for a current loop (current i, radius r, sitting in x-y plane, centered around the z-axis). this is the same situation as part a-ii above, but here just solve in terms of a given current i.