5 Electric potential 5 1 Electric electrostatic potential

5. 2 Electric (electrostatic) potential and potential difference Definitions: Force – electric field Units:

5. 3 Electric potential and electric field a) Uniform field b) General relations Units:

5. 4 Potential due to a group of point charges a) One charge Usually

5. 5 Equipotential surfaces Definition: V = const Properties: • W = 0 for

Examples: Topographic map of Mt. Fuji: 2 D mapping of potential. Positive point charge.

Example: What is the electric energy stored in a system of three charges q

Example: Three charges q = 3. 0 n. C are initially fixed at the

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

5. 2 Electric (electrostatic) potential and potential difference Definitions: Force – electric field Units: Example Energy - potential

5. 3 Electric potential and electric field a) Uniform field b) General relations 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) r+ +Q r d -Q 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.

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

Example: What is the electric energy stored in a system of three charges q = 3. 0 n. C 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? The stored energy is: A) Positive B) Negative q C) Zero q a 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 therd charge:

Example: Three charges q = 3. 0 n. C 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 2 a a q q