1. non-uniformly charged hollow cylinder (double points problem) consider an infinitely long charged hollow cylindrical object with outer radius 4a and inner radius a. let the axis of the cylindrical object be the z axis. between r = a and r = 4a, the charge per unit volume is rho(r) = rho0( 4r a − r 2 a 2 − 3) where rho0 > 0 is a constant. (a) sketch a plot showing rho(r) vs r. on the vertical axis, label the values of rho(r) at r = a, r = 2a, r = 3a, and r = 4a. (b) calculate the electric field e~ (~r) at all points in space. (you may need to write different expressions for different regions.)