1. Christopher Crawford PHY 416 2014-10-08
§2.3 Electric potential
Christopher Crawford
PHY 416

2. Outline Electric flow Meaning of Electric potential
5 Formulations Continue with flow derivations
Recover Coulomb Green’s functions Helmholtz theorem

3. Meaning of electric potential
Analogy with gravitational field
Potential energy per mass or charge
Equipotential contours

4. Flow: Circulation vs. Conservative fields

5. Curl of E Direct calculation – E is irrotational Potential V
Inverse Poincaré
Stokes’ theorem
Flow from a to b is unique
Fund. thm. of vector calc.
What is V ?

6. Integration of V
Direct calculation – Coulomb’s law is “exact” (1/r2 is a perfect differential)
Inverse: gradient of V

7. Poisson’s equation Combine div. & curl eq’s
Into 2nd order differential equation
Only scalar fields: V, ρ
Formal solution of Poisson’s eq
Expand as delta fn’s
Invert Laplacian to Green’s fn’s

8. Putting it all together…
Solution of Maxwell’s equations