1. Electric Potential
The scalar function V determines the vector field E!
The reference point O is arbitrary, where V(O)=0.
It is usually put at infinity.

2. Example 2.6 Potential inside and outside of a uniformly charged
spherical shell.

3. Point charge:
Superposition:
Continuous charge
distribution:

4. Example 2.7
Find the potential of a uniformly charged spherical shell.

5. The surfaces of constant potential are called
The field lines are parallel to
and, hence, perpendicular to the equipotentials.

6. Units Do not confuse the electric potential V
[force]=Newton (N)
[charge]=Coulomb (C)
[electric field]=N/C=V/m
[potential]=N m/C=Volt (V)
Do not confuse the electric potential V
With the potential energy QV!

7. Differential form:
Poisson’s equation:
Laplace’s equation:
Integral form:

8. Boundary conditions at a charged surface
normal component:
parallel components:

9. All the relations hold only very near the boundary.

11. POISSON, Siméon Denis

12. Work and Energy Mechanical work to move Q from a to b:
from infinity to a:

13. Work to assemble a collection of point charges:

14. energy of a continuous charge distribution:
The energy is stored in
the electrical filed.

15. Example 2.8
Energy of a uniformly charged sphere of charge q and radius R .

16. Energy of combined charge distributions
superposition
no superposition

17. The self-energy problem:
of an isolated point charge is infinite!
The field energy
Way out: The elementary particles (quarks, electrons) are given.
They change only their relative position (interaction energy).
It is not important how much energy it takes to make an
elementary particle and the field it carries carries along.