Chapter 19

1. Chapter 19 Electric Potential Energy and The Electric Potential

2. Outline • Potential Energy • The Electric Potential Difference • The Electric Potential Difference Created by Point Charges • Equipotential Surfaces and their Relation to the Electric Field • Capacitors and Dielectrics

3. 1- Potential Energy

4. Work done by electric force on charge q from A to B: But DPE = change in potential energy = -W

5. 2- The Electric Potential Difference We define: So that

6. Example 1 Work, Potential Energy, and • Electric Potential • The work done by the electric force as the • test charge (+2.0x10-6C) moves from A to • B is +5.0x10-5J. • Find the difference in EPE between these • points. • Determine the potential difference between • these points.

7. (a) (b)

8. Conceptual Example 2 The Accelerations of Positive and Negative Charges A positive test charge is released from A and accelerates towards B. Upon reaching B, the test charge continues to accelerate toward C. Assuming that only motion along the line is possible, what will a negative test charge do when released from rest at B?

9. A positive charge accelerates from a region of higher electric potential toward a region of lower electric potential. A negative charge accelerates from a region of lower potential toward a region of higher potential.

10. Conservation of Energy • Note: the eV electron Volt is defined as the energy that the electron / proton gains when accelerated through a potential difference of 1 Volt

11. Example 4 The Conservation of Energy A particle has a mass of 1.8x10-5kg and a charge of +3.0x10-5C. It is released from point A and accelerates horizontally until it reaches point B. The only force acting on the particle is the electric force, and the electric potential at A is 25V greater than at C. (a) What is the speed of the particle at point B? (b) If the same particle had a negative charge and were released from point B, what would be its speed at A?

13. (a) (b)

14. When the electric field is directed downward, point B is at a lower potential than point A • A positive test charge that moves from A to B loses electric potential energy • It will gain the same amount of kinetic energy as it loses potential energy

15. Electric field Gravity

16. Field between two parallel plates

17. 3- The Electric Potential Difference Created by Point Charges • The electric potential created at A by a point charge q is: • VA is a scalar quantity. • For several point charges qi ,

18. Consider a charge q0 is brought from infinity to point A

19. If the charges have the same sign, DPE is positive • Positive work must be done to force the two charges near one another • The like charges would repel • If the charges have opposite signs, DPE is negative • The Coulomb force does positive work

20. Example 5 The Potential of a Point Charge Using a zero reference potential at infinity, determine the amount by which a point charge of 4.0x10-8C alters the electric potential at a spot 1.2m away when the charge is (a) positive and (b) negative.

21. (a) (b)

22. Example 6 The Total Electric Potential At locations A and B, find the total electric potential.

24. Potentials and Charged Conductors • No work is required to move a charge between two points that are at the same electric potential

25. Conductors in Equilibrium • E = 0 inside the conductor • The electric field just outside the conductor is perpendicular to the surface • The potential is a constant everywhere on the surface of the conductor • VA = VB = cst • The potential everywhere inside the conductor is constant and equal to its value at the surface • Vinside = Vsurface = cst

26. 4- Equipotential Surfaces and their relation to the Electric Field • An equipotential surface is a surface on which all points have the same electric potential. • Given some initial velocity, no work is required to move a charge at a constant speed on an equipotential surface. • The electric field at every point on an equipotential surface is perpendicular to the surface

28. rB r1 rA r2 Electric field lines Equipotential lines

30. Example 9 The Electric Field and Potential Are Related The plates of the capacitor are separated by a distance of 0.032 m, and the potential difference between them is VB-VA=-64V. Between the two equipotential surfaces shown in color, there is a potential difference of -3.0V. Find the spacing between the two colored surfaces.

32. 5- Capacitors and Dielectrics • Most common capacitors is the parallel plate capacitor. • With A being the area of each plate and d being the separation between the plates. • Thecapacitance, C, of a capacitor is defined as: • Units: Farad (F), 1 F = 1 C / V • Where Q is the charge accumulated on each plate and V is the potential difference between the 2 plates.

33. The symbol for a capacitor is • For a parallel-plate capacitor whose plates are separated by air:

34. Combination of Capacitors In parallel: For n capacitors in parallel:

35. In series: For n capacitors in series:

36. Capacitors with Dielectrics If a dielectric is inserted between the plates of a capacitor, the capacitance can increase markedly. Dielectric constant

37. Capacitance of Parallel Plate Capacitor Parallel plate capacitor filled with a dielectric

38. Conceptual Example 11 The Effect of a Dielectric When a Capacitor Has a Constant Charge An empty capacitor is connected to a battery and charged up. The capacitor is then disconnected from the battery, and a slab of dielectric material is inserted between the plates. Does the voltage across the plates increase, remain the same, or decrease?

39. The dielectric becomes polarized. • The presence of the positive charge on the dielectric effectively reduces some of the negative charge on the metal • This allows more negative charge on the plates for a given applied voltage, so Q increases due to the additional flow of charges. • So the capacitance increases when the dielectric is inserted between the plates.

40. Energy Stored in a Capacitor At t=0, small charges dq are transferred from 1 plate to another.