1. 5. Electric potential 5.1 Electric (electrostatic) potential energy + a - b E
Electric force
Gravitational force
Conservative forces
Example

2. 5.2 Electric (electrostatic) potential and potential difference
Definitions:
Force – electric field
Energy - potential
Units:
Example

3. 5.3 Electric potential and electric field
Units:
Example E

4. 5.4 Potential due to a group of point charges
a) One charge
Usually we assume that
b) Several charges
(superposition)
c) Example (electric dipole) +Q -Q r- r+ d r

5. 5.5 Equipotential surfaces
Definition: V = const
Properties:
W = 0 for any motion along any equipotential surface
The electric field, E is always perpendicular to equipotential surfaces
The electric field, E points in the direction of decreasing potential
The surface of a conductor is always equipotential
All points of a conductor have the same potential
As you move away, the equipotentials look more and more like spheres because the conductor looks like a point charge
The electric field inside a conductor and
in an empty cavity inside a conductor is zero

6. V E y x E Examples: Topographic map of Mt. Fuji:
2D mapping of potential. Positive point charge. x y V E
30 V
20 V
10 V E

7. Example: What is the electric energy stored in a system of three charges q = 3.0 nC that form an equilateral triangle of side a = 1.0 cm?
This question can be reformulated:
How much energy has been put in the system to built it?
How much work was done to built it? q
The stored energy is: A) Positive B) Negative C) Zero a q q
We have to push the charges to arrange them like this → add energy.
Unless charges are somehow fixed, they will move to a situation with less energy (Uinfinity = 0).
External work done to bring a charge from infinity:
For the first charge:
For the second charge:
For the therd charge:

8. Example: Three charges q = 3
Example: Three charges q = 3.0 nC are initially fixed at the corners of an equilateral triangle of side a = 1.0 cm. One of them is released. Find its kinetic energy when it has doubled the distance to each of the other two charges. q q 2a a q q q q