Calculate the electric field at height h above the center of a square plate of size 2a x 2a with uniform surface charge density n (both direction and magnitude). Verify that in the limit of large a the result agrees with the field of an infinite uniformly charged plane.

Consider a long cylindrical charge distribution of radius R with a uniform charge density ρ. Calculate the magnitude of the electric eld at a distance R/2 from the axis.

Calculate the electric field at height h above the center of a square plate of size 2a×2a with uniform surface charge density η (both direction and magnitude). Verify that in the limit of large a the result agrees with the field of an infinite uniformly charged plane.

A solid insulating sphere of radius R =5.00 cm has a non-uniform charge density p = Por2, where r is measured from the center of the sphere and po is constant. Concentric with this sphere is a conducting spherical shell with inner radius a = 7.00 cm and outer radius b = 9.00 cm, having a net charge q = -1.00 µC. a) Find the value for the constant po (including units), given that the total charge on the insulating sphere is Q = 4.00 nC. Be sure to first derive expression in symbolic form in terms of Q, R. Box both the symbolic expression and the final answer. b) Derive an expression for electric field forr b. Box it. e) Draw an E vs. r graph and show the values for E at distances R, a, b.