Electric Potential and Potential Energy Concepts

1. There will be a quiz next class period, Feb 1, covering Ch 22 and the beginning of Ch 23 (what we cover in class today)

2. Definitions • Electric potential—Potential energy per unit charge at a point in an electric field • Path integral (line integral)—An integral performed over a path such as the path a charge q follows as it moves from one point to another • Volt—The unit of electric potential. 1V = 1 J/C • Electron volt (eV)—the energy that an electron (or proton) gains or loses by moving through a potential difference of 1 V. • Equipotential surface—A surface consisting of a continuous distribution of points having the same electric potential

3. Electric Potential • Electric force is a conservative force, therefore there is a potential energy associated with it. • We can define a scalar quantity, the electric potential, associated with it.

4. Electric Potential Energy Concepts of work, potential energy and conservation of energy For a conservative force, work can always be expressed in terms of potential energy difference Energy Theorem For conservative forces in play, total energy of the system is conserved

5. The line integral used to calculate V does not depend on the path taken from A to B; therefore pick the most convenient path to integrate over

6. Electric Potential • We can pick a 0 for the electric potential energy • U is independent of any charge q that can be placed in the Electric field • U has a unique value at every point in the electric field • U depends on a location in the E field only

7. Potential energy Uincreases as the test charge q0 moves in the direction opposite to the electric force : it decreases as it moves in the same direction as the force acting on the charge

8. Electric Potential Energy of Two Point Charges

9. Electric potential energy of two point charges

10. a-particle positron What is the speed at the distance ? What is the speed at infinity? Suppose, we have an electron instead of positron. What kind of motion we would expect? Example: Conservation of energy with electric forces A positron moves away from an a – particle Conservation of energy principle

11. Electric Potential Energy of the System of Charges Potential energy of a test charge q0 in the presence of other charges Potential energy of the system of charges (energy required to assembly them together) Potential energy difference can be equivalently described as a work done by external force required to move charges into the certain geometry (closer or farther apart). External force now is opposite to the electrostatic force

12. Electric potential is electric potential energy per unit charge Finding potential (a scalar) is often much easier than the field (which is a vector). Afterwards, we can find field from a potential Units of potential are Volts [V] 1 Volt=1Joule/Coulomb If an electric charge is moved by the electric field, the work done by the field Potential difference if often called voltage

13. Two equivalent interpretations of voltage: • Vab is the potential of a with respect to b, equals the work done • by the electric force when a UNIT charge moves from a to b. • 2. Vab is the potential of a with respect to b, equals the work that must • be done to move a UNIT charge slowly from b to a against the • electric force. Potential due to the point charges Potential due to a continuous distribution of charge Finding Electric Potential through Electric Field

14. Some Useful Electric Potentials • For a uniform electric field • For a point charge • For a series of point charges

15. Potential of a point charge Moving along the E-field lines means moving in the direction of decreasing V. As a charge is moved by the field, it loses it potential energy, whereas if the chargeis moved by the external forces against the E-field, it acquires potential energy

16. Negative charges are a potential minimum Positive charges are a potential maximum

17. Positive Electric Charge Facts • For a positive source charge • Electric field points away from a positive source charge • Electric potential is a maximum • A positive object charge gains potential energy as it moves toward the source • A negative object charge loses potential energy as it moves toward the source

18. Negative Electric Charge Facts • For a negative source charge • Electric field points toward a negative source charge • Electric potential is a minimum • A positive object charge loses potential energy as it moves toward the source • A negative object charge gains potential energy as it moves toward the source