Electric field for a given charge density.

(See attached file for full problem description) --- A plastic sheet of thickness t has a uniform free charge density, +, embedded inside, and also one surface has a surface charge of -. Find the electric field and the potential as functions of distance from one surface. [Please neglect the issues of dielectric polarizability, the plastic simply functions to fix the charges in place].

Electric potential energy of a solid charged sphere

Calculate the electric potential energy of a solid sphere of uniform charge density rho; total charge Q and radius a using dU = dq(Vf - Vi). See attached file for full problem description with proper symbols.

Potential inside a box.

A rectangular box with x dimension a, y dimension b, and z dimension c is depicted in the diagram. If the electric potential on all sides except z=c is zero, and the potential on the side z=c is V(x,y), Find the potential inside the box.

Suppose we have a sphere of radius, a, centered on a dipole, p, at the origin. Integrate the energy density of the field outside the sphere, and show that U=p^2/(12 pi Eo a^3).

(See attached file for full problem description) --- Suppose we have a sphere of radius, a, centered on a dipole, p, at the origin. Integrate the energy density of the field outside the sphere, and show that U=p^2/(12 pi Eo a^3). ---

Conducting Sphere

Using method of images, find the force of attraction between an external point charge +Q and a conducting sphere of potential V_0. Take the charge to be a distance D from the center of the sphere. What value of V_0 makes the force equal 0?