An infinitely long solid cylindrical insulator of radius a has nonuniform volume charge density Mr) = 190(1 - E) where r is the radial distance from the axis of the cylinder and p0 is a positive constant. (a) Use Gauss's law to find the electric field inside and outside the cylinder. (Hint: the charge density is nonuniform, like in Problem 2, so you have to integrate to find the charge enclosed by the Gaussian surface.) (b) Find the value Off at which the electric field is maximum and find the value of that maximum field. (c) The cylindrical insulator is placed within an infinitely long hollow cylindrical conductor with inner radius 2a and outer radius 3a. The cylinders are coaxial. The conductor is neutral. 2a 36: Find the surface charge densities on the inner and outer surfaces of the conductor 4. Three point charges are located at the corners of a rectangle. The electric potential at the empty corner of the rectangle is zero. 91 92 = 2.5 JC 93 = -3 JC a a = 3mm b = 4mm 92 b 93 (a) Determine the value of q1. (b) What is the electric potential energy associated with q1? (c) What is the electric potential at the center of the rectangle? (d) What is the total electric potential energy of this collection of charges