Understanding Electrical Potential Energy and Capacitance

1. Chapter 18 Electrical Energy and Capacitance

2. 18.1 Electrical Potential Energy Objectives 1. Define electrical potential energy 2. Compare the electrical potential energy for various charge distributions

3. A Look Back atGravitational Potential Energy PEgrav = mgh PEgrav=mgh h PEgrav=0

4. Electric Potential Energy Potential associated with an object due to its position relative to a source of electric force

5. Consider: Uniform Electric Field

6. Charge Movement in E Field vs PEelectric

7. Electrical Potential Energy (in a uniform field) PEelectric = -qEd q = charge (C) E = electric field strength (N/C) d = displacement (m) from the reference point in the direction of the field

8. Electrical Potential Energy for a Pair of Charges PEelectric = kC q1q2 r …because point charges produce non-uniform electric fields

9. Regarding PEelectric for point charges… • The reference point for electrical potential energy is assumed to be at infinity. Note that PEelectric goes to zero as r goes to infinity. • Because like charges repel, positive work must be done to bring them together. So, PEelectric is positive for like charges and negative for unlike charges. • For determining PEelectric for more than two charges, calculate PEelectric for each pair then add the energies.

10. Problem: In one model of the hydrogen atom, an electron in its lowest energy state moves in a circular orbit about the nucleus (a single proton) at a distance of 5.29x10-11m. Find the electrical potential energy of the hydrogen atom. Which equation for PEelectric? PEelectric = kCq1q2 r Answer: PEelectric = -4.35x10-18 J

11. 18.2 Potential Difference Objectives • Distinguish between electrical potential energy, electric potential, and potential difference. • Compute the potential difference for for various charge distributions.

12. Water Analogy

13. Electric Potential …is the electrical potential energy associated with a charged particle divided by the charge of the particle V = PEelectric q

14. Potential Difference …is the change in electrical potential energy associated with a charged particle divided by the charge of the particle. V = PEelectric q units = J/C = volts (V)

15. What’s another name for PE? Hint:What do we have to do to a particle if we want to increase it’s PE? PE aka “Work” (W) So, ΔV = PEelec = W q q units for PE and for work = joules (J)

16. More About Potential Difference • Potential difference is often referred to as “voltage”. • As a 1C charge moved through a potential difference of 1V, the charge gains (or loses) 1J of energy. • Common potential differences (voltages) are 12V for a car battery and 120V between the two slots in a household electrical outlet.

17. Potential Difference in a Uniform Electric Field And PEelectric = -qEd (uniform field) PEelectric q We know V = So V = -qEd q V = -E d (where d is displacement from a reference point in the direction of the electric field)

18. V = -E d Notice…..new units for E !! V units is volts (V) d is in meters (m) ...therefore E units must be ?? E is in V/m

19. Potential Difference at Some Location Near a Point Charge PEelectric q We know V = And PEelectric = kCq1q2 (for point charges) r V = kCq1q2 q1r So V = kCq r (compares the potential difference between a point at infinity and some location near a point charge)

20. Questions 1. Find the potential difference between a point infinitely far away from and a point 1.0 cm from a proton. 2. A proton is released from rest in a uniform E-field with a magnitude of 8.0x104 V/m. The proton moves 0.50 m as a result. Find: a) The potential difference between the initial and final positions of the proton. b) The change in electrical potential energy of the proton as a result of this displacement.

21. Answers 1. 1.44 x 10-7 V • a) -4.0 x 104 V b) -6.4 x 10-15 J

22. PEelectric, Electric Potential, and Potential Difference in a Battery • The potential difference between the positive and negative terminals is 9V, where the electric potential at the negative terminal is 0V, and the electric potential at the positive terminal is 9V. • When hooked to an electrical device, the charge moves inside the battery from negative to positive terminal. The battery does work on the charge in order to move it from the (-) to the (+) terminal, so PEelectric increases.

23. More on PEelectric, Electric Potential and Potential Difference

24. 18.3 Capacitance Objectives • Relate capacitance to the storage of electrical potential energy in the form of separated charges • Calculate the capacitance of various devices • Calculate the energy stored in a capacitor

25. Capacitance …is the ability of a conductor to store energy in the form of electrically separated charges

26. Parallel-plate Capacitor Parallel conductive plates in a circuit with a charge source (V). Close the switch and the charge flows until the voltage across the plates equals the applied voltage. Charge flows from one plate to the other, leaving behind a plate that is equally (but oppositely) charged. Open the switch and charge (and electrical potential energy) are stored.

27. Capacitance – Basic Equation C = Q V capacitance = magnitude of charge on each plate potential difference C = farads (F) = C/V

28. Capacitance and PEelectric PEelectric = ½ Q V and since C = Q V PEelectric = ½ C V2 substituting gives us: PEelectric = Q2 2C and

29. Questions 1. A parallel-plate capacitor has a charge of 6.0x10-6 C when charged by a potential difference of 1.25V. a) Find its capacitance b) How much potential energy is stored when this capacitor is connected to a 1.5V battery? Answers: • 4.8x10-6 F • 5.4x10-6 J