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

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

5.3 Electric potential and electric field a) Uniform field b) General relations Example E Units:

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- 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. The electric field inside a conductor and in an empty cavity inside a conductor is zero. As you move away, the equipotentials look more and more like spheres because the conductor looks like a point charge.

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

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 q q a The stored energy is: A) Positive B) Negative C) Zero 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 (U infinity = 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 = 3.0 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 q a q q q 2a2a