An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as given by the following expression where rho0, a, and b are positive constants and r is the distance from the axis of the cylinder. rho = rho0 a − r b Use Gauss's law to determine the magnitude of the electric field at the following radial distances. (Use the following as necessary: ε0, rho0, a, b, r, and R.)

Four point charges each having charge q are located at the corners of a square having sides of length a. find symbolic expressions for the following. (a) the total electric potential at the center of the square due to the four charges (use any variable or symbol stated above along with the following as necessary: ke.) vtotal= (b) the work required to bring a fifth charge p from infinity to the center of the square (use any variable or symbol stated above along with the following as necessary: w=