A long, hollow conducting pipe $($outer radius $=$ r$)$ is initially charged such that an electric field of magnitude E $($directed radially inward$)$ exists at its outer surface. After a thin charged rod is inserted along the axis of the pipe, the magnitude of the electric field remains the same but its direction is reversed. What is the linear charge density for the rod? State your answer in terms of the given variables, and use k for Colomb's constant.

To determine the electric field from the cylinder at location $<0,0,$w$>$ far from the tube, divide the tube into rings. An individual ring in the tube has thickness dz$.$

A$.$ How much charge dQ is on this ring?

dQ$=$