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

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

5.3 Electric potential and electric field Units: Example + + + + + - - - - - E

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 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

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

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:

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