Two very large, flat plates are parallel to each other. Plate A, located at y=1.0cm, is along the xz plane and carries a uniform surface charge density -1.00muC/m². Plate B is located at y= -1.0cm and carries a uniform surface charge density +2.00uC/m². Find the electric field vector at the point having x,y,z coordinates ( -0.50cm, 0.00cm, 0.00cm).

A charge distribution creates the following electric field throughout all space: E(r, 0, q) = (3/r) (r hat) + 2 sin cos sin 0(theta hat) + sin cos p (phi hat). Given this electric field, calculate the charge density at location (r, 0, p) = (ab.c).

A cylindrical shell of radius 7.00 cm and length 2.36 m has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 20.6 cm radially outward from its axis (measured from the midpoint of the shell) is 36.0 kN/C. (a) Find the net charge on the shell. nC (b) Find the electric field at a point 4.00 cm from the axis, measured radially outward from the midpoint of the shell. kN/C

A non-conducting solid sphere with a radius of 50.0 cm located at the origin has a charge of +3.00 µC spread uniformly throughout its volume. Concentric with the sphere is a conducting spherical shell that has an inner diameter of 2.00 m and an outer diameter of 2.50 m with a net charge of -2.50 µC. Calculate the magnitude and direction (either away or toward the origin) of the electric field at (a) r = 1.20 m, and (b) r = 3.00 m, where r is the distance from the origin. (c) What is the net charge on the inner and outer surfaces of the shell? (d) Include a diagram of the situation indicating both the sphere and the shell along with the Gaussian surfaces.