1. Electrical Potential Energy & Electrical Potential  Work, Potential Energy and the Electric Force  Electrical Potential  Equipotential Surfaces  Dielectrics, Capacitors, and Energy

2. Electrical Potential Energy & Electrical Potential  Work, Potential Energy and the Electric Force  Electrical Potential  Equipotential Surfaces  Dielectrics, Capacitors, and Energy

3. Work, Potential Energy, and the Electric Force Consider a positive charge q, moving west through a displacement S at a constant velocity in a region occupied by a uniform eastward electric field E.

4. Work, Potential Energy, and the Electric Force The charge experiences an eastward electric force. For it to move at constant velocity, an equal westward force is required.

5. Work, Potential Energy, and the Electric Force Work done by the westward force: Work done by the electrical force: Net work =  kinetic energy = zero

6. Work, Potential Energy, and the Electric Force The electric force is conservative. Its work does not change the energy of the object. The westward force is nonconservative. Its work changes the total energy:

7. Work, Potential Energy, and the Electric Force The increase, qES, in the energy of the object is electrical potential energy (EPE). Like any other form of energy, it has SI units of joules (J). Every conservative force is associated with a form of potential energy.

8. Work, Potential Energy, and the Electric Force The work done by the forces is the same, even if we go from the starting to the ending point by a meandering path. Work done by a conservative force is path-independent.

9. Work, Potential Energy, and the Electric Force The increase in electrical potential energy (EPE) is also unaffected by our choice of path.  EPE depends only on E, q, and the endpoint locations.

10. Work, Potential Energy, and the Electric Force Call the endpoints of our travel A (beginning) and B (end). Travel from A to B with a “test charge” q 0. Divide through by q 0 :

11. Work, Potential Energy, and the Electric Force Define a new quantity, electrical potential: and SI units of electrical potential:

12. Electrical Potential Energy & Electrical Potential  Work, Potential Energy and the Electric Force  Electrical Potential  Equipotential Surfaces  Dielectrics, Capacitors, and Energy

13. Electrical Potential Since we’ve talked about the electrical potential of points A and B, let’s look at what that means. Consider a positive point charge, Q, and a point A that is a distance r from Q:

14. Electrical Potential What is the electrical potential at point A? To answer that question, we need to know how much work is required to bring a test charge from a point infinitely distant from Q, to point A.

15. Electrical Potential The force required to move the test charge at a constant velocity is not constant with the distance x from Q: In fact, the force isn’t even linear with x … so we can’t calculate and use an average force.

16. Electrical Potential Calculating the potential at point A is a calculus problem. The work required to move the test charge an infinitesimal distance dx is dW:

17. Electrical Potential Integrate to calculate W:

18. Electrical Potential The potential of a point is relative to zero potential, which is located infinitely far away. When more than one charge is present, the potential is the algebraic sum of the potentials due to each of the charges, individually. “Electric potential” is not the same thing as “electrical potential energy.”

19. Electrical Potential Gravitational Electrical Another way to express the magnitude of the electric field: as a “potential gradient:”

20. Electrical Potential Energy & Electrical Potential  Work, Potential Energy and the Electric Force  Electrical Potential  Equipotential Surfaces  Dielectrics, Capacitors, and Energy

21. Equipotential Surfaces Equipotential surface: a collection of points that all have the same electrical potential.

22. Equipotential Surfaces The electric field vector is everywhere perpendicular to equipotential surfaces. Why?

23. Equipotential Surfaces The electric force does no work on charges moving on an equipotential surface. Why?

24. Electrical Potential Energy & Electrical Potential  Work, Potential Energy and the Electric Force  Electrical Potential  Equipotential Surfaces  Dielectrics, Capacitors, and Energy

25. Dielectrics, Capacitors, and Energy Consider a parallel-plate capacitor, with a charge q and a plate area A, the plates separated by a distance d. The internal electric field: A constant electric field E, and a distance d between the plates, gives the potential difference between the plates:

26. Dielectrics, Capacitors, and Energy Solve for the ratio of the charge to the voltage, and define a new quantity, capacitance: SI units: coulomb/volt = C 2 /J = farad (F)

27. Dielectrics, Capacitors, and Energy Dielectric material: fancy term for an insulating material. Separation of surface charge causes a reduction of the internal electric field by a factor of , the dielectric constant:

28. Dielectrics, Capacitors, and Energy Fill the capacitor with a dielectric: Its capacitance is increased by a factor of , the dielectric constant.

29. Dielectrics, Capacitors, and Energy Springs Capacitors Work is required to compress a spring Work is required to charge a capacitor Work per unit length increases linearly with compression Work per unit charge increases with the amount of charge Energy: