Summary

We started out summarizing the main concepts and laws in electrostatics (Coulomb's Law, Gauss' Law, definition of the electrostatic potential, energy of the electrostatic field, Poisson's Equation, Laplace's Equation).

We discussed Gauss units and SI units, and the significance of using one system or the other. See following link for Units

We gave expamples of different systems of coordinates, we gave the definition of solid angle, and we showed how to transform a vector from one system to the other. We discussed one practical example (a sphere with r-dependent charge density rho=k/r and/or rho=kr)

We discussed the meaning of irrotational fields, and defined the scalar potential. We solved the following exercise:
"Show that E=(6xy, 3x^2-y^2,0) is a possible electrostatic field by finding the function of which E is a gradient."
Our starting point for next classes will be to study the solutions to Poisson's eq. with boundaries at infinity. We will give examples with both spherical and cylindrical symmetries. We will next introduce the Green's functions.

We covered Sections 1.1-1.5, 1.7 of Jackson.

2nd Homework

1) Show that the average of the electrostatic potential taken over the surface of a spherical region of space that contains no charge is equal to the value of the potential in the center of the sphere.
Hint: Use Green's identities.

2) Two point charges q1 and q2 are located at distance r1 and r2 from a (grounded) conducting plane. The charges lie on a line perpendicular to the plane. (i) What is the force on q2? (ii) What is the surface charge density at the intersection with the line?

3) Show that the vector E=(2Rsin(f), 2Rcos(f)+3z,3Rsin(f)) is a possible electrostatic field by finding the function of which E is a gradient (the above coordinates are cylindrical coordinates). Change representation of E to both cartesian and spherical coordinates.