Separation of variables and laplaces equation in electrostatics

The problem has to do with the potential inside a square. Separation of variables is to be used to find the general solution to the problem and then the boundary conditions need to be applied. The constant needs to be found then as well. The problem is attached. I have also attached the picture of the problem.

Electrostatics: Surface charge density and electric field

Two part question involving a spherical cavity inside a shell and calculating: a) the surface charge density b) the electric field Problem is attached in word format. Diagram is included in jpeg.

Electrostatics: Method of images for a grounded sphere

Use the method of images to find: a) the electric field at a point P. b) force on the real charge q Problem is in word format. Diagram is a jpeg.

A large conducting spherical shell has fixed surface charge density, has a small circular hole in the surface. Using integration over the surface of the sphere find the electric field in the hole at its center.

A large conducting spherical shell of radius a, and fixed surface charge density (sigma), has a small circular hole in the surface of radius b< ...continues

Electrostatics: Unequal Charge density on parallel plates

(See attached file for full problem description) --- 1. Consider two infinite parallel plane conducting plates, of finite thickness, with separation d. Suppose a charge density of sigma; is placed on one plate, while the other plate has -2sigma. A) Determine the resulting charge densities on each of the 4 surfaces B) De ...continues

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 dielec ...continues

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?