Electrostatic Boundary Conditions

1. Electrostatic Boundary Conditions Consider a Gaussian pillbox at the interface between two different media: E2 DS E1 Total charge enclosed within the surface As the height of the pill-box ∆h tends to zero the volume contribution vanishes, and The normal component of E is discontinuous at a boundary carrying a surface charge. However, the tangential component is always continuous

2. Energy of the electric field The work done to move a charge: a q b The work done by an external agent to bring q2 from infinity to its position r2 against the field of q1 is: Therefore, the total energy of a set of charges is:

3. For a continuum with a charge density r, the energy is: energy density of the electric field:

4. Example: Find the energy of a uniformly charged spherical shell of a total charge q and radius R Another method: E=0 inside the sphere. For r>R Example: Find the energy per unit length for two long coaxial cylindrical shells, neglecting end effects. The inner and outer cylinders have radii a and b, and liner charge densities l and –l, uniformly distributed on the surface, respectively.