Understanding Electric Potential and Capacitors in Physics

1. Key Points from Chapter 30

2. Point charges and capacitor plates share some common qualities… E lines point away from the positive towards the negative The positive point/plate creates the area of higher potential Areas of electric potential difference create voltage across which work is done on moving charges (q) from low potential to high potential (from the negative plate to the positive plate)

3. Remember… Voltage (potential difference)is related to potential energy through the equation ΔV = ΔU/q Volts=(Joules/Coulombs) Potential and field are just two perspectives on how source charges alter space around them.

4. Other relationships… • Potential energy is defined in terms of work done by a force on a charge as it moves from position initial to position final. ΔU= -W = -∫F (ds)

5. We can also use a E vs. s graph to calculate potential difference. The area under the curve is equal to potential difference. (voltage)

6. In a battery, the most common source of electric potential… ΔV = Wchem/ q For example, a 9volt battery uses 9 joules of “work” to move 1 coulomb of charge from the negative terminal to the positive terminal.

7. Batteries joined in series will produce larger potential differences calculated by adding or subtracting their known voltages

8. OLD: formulas for calculating electric field due to different shaped capacitors still apply!! NEW: calculate electric field from the Voltage vs. distance graph… E= -slope of the V vs. x

9. Example: • Plot the following data and than plot the corresponding E versus x x V 0 50 1 -75 2 0 3 100

10. Homework… • Page 935 # 1,3,4,6,9

11. Chapter 30#21-42

12. The change in potential can be calculated by finding the negative area under the E versus x curve… Plot the following information and then calculate the change in potential difference: E x 0 0 500.0 0.5 1000.0 1.0 1500.0 1.5

13. Significance of equipotential lines… • they connect areas of equal potential • they are perpendicular to the electric field • they take the shape of the conducting surface • Equipotential lines will have higher value near the positive plate of a capacitor and decrease as you near the negative plate

14. A capacitor attached to a battery will gain “charge” until the voltage of the capacitor is equal to the voltage of the battery • REMEMBER: V=Es and E=Q/εA • Combing these old formulas allows us to calculate the charge on a capacitor place if we know the voltage of the battery Q=εAV/d

15. Capacitance is Q/V OR ε0A/d • Unit of capacitance is farad

16. Example: • Two 2.0cm x 2.0cm square aluminum electrodes are spaced 0.50mm apart. The electrodes are connected to a 100V battery. • What is the capacitance? • What is the charge on each electrode?

17. Just like batteries, capacitors can be connected in series or parallel. • Capacitors in parallel all have the same ΔV Cp= C1 + C2 + C3 + … • Capacitors in series all have the same Q Cs= (1/ C1 + 1/ C2 + 1/ C3 + …)-1 ** If there are a combination of capacitors…solve for series first!!

18. C for parallel= Q/V + Q/V + Q/V…. • C for series = (V/Q + V/Q + V/Q….)-1

19. Homework: • Page 935-938 # 19,21,22,23,27,28,34,36,58

20. Chapter 30#43-54

21. Potential energy in a capacitor is similar to the potential energy of a spring: Uc= ½ CV2(if voltage is from a battery source) Uc = ½ Q2/ C Uc = (½ εoA/ d) (Ed)2

22. Example: • To what potential should you charge a 1.0 microfarad capacitor to store 1.0J of energy?

23. Example: • The flash unit on a camera uses two 1.5V batteries to charge a capacitor. The capacitor is then discharged through the flashlamp. The discharge takes 10 microseconds and the average power dissipated is 10W. What is the capacitance of the capacitor? (P=W/t)

24. If a substance is placed between the plates of a capacitor the E within the capacitor weakens E= Eo/k Eo is field strength without the dielectric in place K is a dielectric constant based on specific material present

25. Homework: Page 938-939 # 65,71