CHAPTER 18 ELECTRIC POTENTIAL

Transcription

1 CHAPTER 18 ELECTRIC POTENTIAL BASIC CONCEPTS: ELECTRIC POTENTIAL ENERGY ELECTRIC POTENTIAL ELECTRIC POTENTIAL GRADIENT POTENTIAL DIFFERENCE POTENTIAL ENERGY 1

2 h PE = U = mgh Or PE U KE K And U + K = total energy = constant 2

3 BOOK EXAMPLE 3

4 Charged Particle in Electric Field is similar 4

5 Consider a point charge q that sets up an electric field in space 5

6 Now a test charge q 0 is placed at position a a distance r a from q 0. Then q 0 moves to position b a distance r b from q 0. What is the change in potential energy? The change in potential energy is the negative of the work done to move the test charge from a to b. The force on the test charge is = 1 4 6

7 The work done is force times distance. But the force changes as q 0 moves away from q See Figure 18.6 Must integrate (Not necessary to understand but the procedure is in the box on the next page.) 7

8 Use = Then = = 1 4 = The change in potential energy, Δ, is the negative of this work. Δ= =

9 So difference in potential energy between two points is Δ= = Now define the potential energy to be zero when the two charged particles are separated by an infinite distance (b = ; U b = 0). 0 = Or = 1 4 9

10 = 4 1 Use = and replace the symbol a with r the distance from the charge providing the field to the charge. = 10

11 ELECTRIC POTENTIAL Start with: Difference in potential energy is Δ= = DEFINITION: ELECTRICAL POTENTIAL IS POTENTIAL ENERGY PER UNIT CHARGE = h Therefore divide all terms by 11

12 = Thus = =

13 Then for potential at a point The potential energy at a point is = = h U= = = = 13

14 POTENTIALS ADD (SCALERS) Just as we did with the electric field we can add the potentials for many charges in an area. EXAMPLE A 60cm 30cm 50µC -50 µc 14

15 What is the potential at A? = + = = =7.510 ELECTRON VOLT An electron volt is a unit for energy. It is the work necessary to move an electron 15

16 (charge =1.610 ) a potential difference of 1 volt. 1 Volt Batt The work to move a charge across a potential difference is = == =

17 Therefore 1=

18 MAJOR TOPICS CAPACITANCE AND DIELECTRICS Calculating Capacitance Capacitors in Circuits Energy Storage in Capacitors Dielectrics 18

19 Capacitors store: Charge Energy +Q + - -Q v V _- BATTERY 19

20 The battery supplies charge to the plates. The charge Q is proportional to V. Choose the proportionality constant C. = C is the CAPACITANCE of the capacitor. = 20

21 If there is charge on a plate there is an electric field E. +Q + - -Q + P v V _- BATTERY E at P due to + plate = 21

22 E at P due to - plate = Both fields point to the right d +Q + - -Q + P - + E v V _- = + = 22

23 For all capacitors = And for parallel plate capacitors = Parallel plate capacitors are easy: Area and distance between plates gives C. If know C then: Know Q can get V Know V can get Q 23

24 CAPACITORS IN CIRCUITS Series 24

25 = + = = = + 25

26 1 = Parallel 26

27 = + = = = + = + 27

28 ENERGY IN CAPACITOR AND ELECTRIC FIELD The potential difference across the capacitor is = Where U is the energy stored in the electric field of the capacitor and q is the charge on the plates. Thus the change in potential difference is Δ= Δ Now charge a capacitor 28

29 dq ΔW=VΔq = Δ= Δ Add up all of the work done to charge the capacitor to charge q 29

30 Once again we use calculus but only to show you how something is done. To add up the work. = 1 =1 2 = =

31 = 1 2 This is the amount of work to charge the capacitor from 0 charge to a charge of Q. This is the energy stored in the capacitor. = 1 2 Use definition of capacitance = 31

32 = Or = Then for parallel plate capacitors = and = = 1 2 = 1 2 =

33 = Energy density = Therefore = = = 33

34 DIELECTRICS Add material between plates and C increases. Increases by K the dielectric constant Parallel Plate Capacitor = Define = Then can use = 34

35 Other quantities Energy density = = 1 2 Charge on capacitor connected to V. V = Introduce dielectric 35

36 V dielectric = = = == Insert dielectric and Q increases if V remains constant. 36

37 Voltage across capacitor without battery. = 37

38 = = 38

39 = = But = So = When C not connected to battery inserting dielectric decreases V. 39

40 Electric Field in dielectric. = = = = 40

41 CAPACITOR SUMMARY 1 = = + = ENERGY = 1 2 =

42 = 1 2 ENERGY DENSITY = = 1 2 DIELECTRICS = = 42

43 = = = 43