4.1 Electric (electrostatic) potential energy 4. Electric potential 4.1 Electric (electrostatic) potential energy Compare electric force and gravitational force Conservative forces We can introduce potential energy: Example: + + + + + + a - - - - - - b E

4.2 Electric potential and potential difference Definitions: electric field – force potential – energy Units (Volt): Example:

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

4.4 Potential due to a group of point charges a) One charge Usually we assume that b) Several charges (superposition)

4.5 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

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? The stored energy is: A) Positive B) Negative C) Zero q Explanation: 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? 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 a q q Solution: 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