1. Electrostatic potential and energy fall EM lecture, week 2, 7. Oct
Electrostatic potential and energy fall EM lecture, week 2, 7.Oct.2002, Zita, TESC
Homework and quiz
Review electrostatics, Gauss’ Law: charges  E field
Conservative fields and path independence  potential V
Boundary conditions (Ex. 2.5 p.74, Prob p.90)
Electrostatic energy (Prob p.106), capacitors (Ex p.104)
Start Ch.3: Techniques for finding potentials: V  E
Poisson’s and Laplace’s equations (Prob. 3.3 p.116), uniqueness
Method of images (Prob. 3.9 p.126)
Your minilectures on vector analysis (choose one prob. each)

2. Ch.2: Electrostatics (d/dt=0): charges  fields  forces, energy
Charges make E fields and forces
charges make scalar potential differences dV
E can be found from V
Electric forces move charges
Electric fields store energy (capacitance)
F = q E = m a
W = qV, C = q/V

3. Conservative fields admit potentials
depends only on endpoints.
Therefore
Easy to find E from V
is independent of choice of reference point V=0
V is uniquely determined by boundary conditions
Every central force (curl F = 0) is conservative (prob 2.25)
Ex.2.5 p.74: parallel plates

4. Parallel plates

5. Electrostatic boundary conditions:
E is discontinuous across a charge layer: DE = s/e0
E|| and V are continuous
Prob 2.30 (a) p.90: check BC for parallel plates

6. Electrostatic potential: units, energy
Prob p.106: Energy between parallel plates
Ex p.104: Find the capacitance between two metal plates of surface area A held a distance d apart.

7. Ch.3: Techniques for finding electrostatic potential V
Why?
Easy to find E from V
Scalar V superpose easily
How?
Poisson’s and Laplace’s equations (Prob. 3.3 p.116)
Guess if possible: unique solution for given BC
Method of images (Prob. 3.9 p.126)
Separation of variables (next week)

8. Poisson’s equation Gauss: Potential: combine to get Poisson’s eqn:
Laplace equation holds in charge-free regions:
Prob.3.3 (p.116): Find the general solution to Laplace’s eqn. In spherical coordinates, for the case where V depends only on r.
Do the same for cylindrical coordinates, assuming V(s).
(See Laplacian on p.42 and 44)

9. Method of images
A charge distribution r induces s on a nearby conductor.
The total field results from combination of r and s.
Guess an image charge that is equivalent to s.
Satisfy Poisson and BC, and you have THE solution.
Prob.3.9 p.126 (cf 2.2 p.82)

10. 1.1.1 Vector Operations - by

11. 1.1.2 Vector Algebra - by

12. Triple Products - by