A partial ring of circular shape centered at the origin is located in the first quadrant (0 < þ<π/2) of the x-y plane and carries a uniform surface charge density of ps = k, but only for a radius of a < p < b. The charge density is zero elsewhere. (k is a constant, and (p, , z) are the usual cylindrical coordinates.) Determine an expression for the the z-component of the electric field at any location on the z-axis. [NOTE: We are only asking for the z-component of the electric field. The x- and y-components exist but they are a little messy. You can certainly attempt to figure them out, but you don't have to.]

A partial ring of circular shape centered at the origin is located in the first quadrant (0 < þ<π/2) of the x-y plane and carries a uniform surface charge density of ps = k, but only for a radius of a < p < b. The charge density is zero elsewhere. (k is a constant, and (p, , z) are the usual cylindrical coordinates.) Determine an expression for the the z-component of the electric field at any location on the z-axis. [NOTE: We are only asking for the z-component of the electric field. The x- and y-components exist but they are a little messy. You can certainly attempt to figure them out, but you don't have to.]