Chapter 20 Electric Potential and Electric Potential Energy

Transcription

1 Chapter 20 Electric Potential and Electric Potential Energy 1

2 Overview of Chapter 20 Electric Potential Energy and the Electric Potential! Energy Conservation! The Electric Potential of Point Charges! Equipotential Surfaces and the Electric Field! Capacitors and Dielectrics! Electrical Energy Storage 2

3 20-1 Electric Potential Energy and the Electric Potential Electric force has a potential energy associated with it It takes work to move an electric charge parallel to an electric field (going against the force due to the field): As usual, the change in potential energy is the negative of the work done by the field 3

4 20-1 Electric Potential Energy and the Electric Potential Sine we define the electric field, it is useful to define the electric potential (potential energy per unit of charge): The electron volt is a unit of energy: 4

5 20-1 Electric Potential Energy and the Electric Potential The electric field is related to how rapidly the potential is changes over distance 5

6 20-2 Energy Conservation In general, for a mass moving from A to B where potential+kinetic energy are conserved: For the electric force, so that 6

7 20-2 Energy Conservation V = V f U = U f V i U i A free charge in an electric field will move to region of lowest potential energy, ΔU is negative! 1) Positive charges accelerate in the direction of decreasing electric potential, ΔV negative 2) Negative charges accelerate in the direction of increasing electric potential, ΔV positive 7

8 20-3 The Electric Potential of Point Charges Potential energy between 2 charges is: The difference in potential energy between points A and B is 8

9 20-3 The Electric Potential of Point Charges Therefore, the electric potential of a point charge is: shown here for a positive and negative charge, respectively 9

10 20-3 The Electric Potential of Point Charges The electric potential of a group of point charges is the algebraic sum of the potentials of each charge. 10

11 20-4 Equipotential Surfaces and the Electric Field Lines of equal electric potential (equipotential) are shown by green lines! Electric field is perpendicular to these equipotential lines.. 11

12 20-4 Equipotential Surfaces and the Electric Field For two point charges: 12

13 20-4 Equipotential Surfaces and the Electric Field There are electric fields inside the human body; the body is not a perfect conductor, so there are also potential differences. An electrocardiograph plots the heart s electrical activity: 13

14 20-5 Capacitors and Dielectrics A capacitor is two conducting plates separated by a finite distance: 14

15 20-5 Capacitors and Dielectrics The capacitance relates the charge to the potential difference: 15

16 20-5 Capacitors and Dielectrics A simple type of capacitor is the parallel-plate capacitor. It consists of two plates of area A separated by a distance d. By calculating the electric field created by the charges ±Q, we find that the capacitance of a parallel-plate capacitor is: 16

17 20-5 Capacitors and Dielectrics The general properties of a parallel-plate capacitor that the capacitance increases as the plates become larger and decreases as the separation increases are common to all capacitors. 17

18 20-5 Capacitors and Dielectrics A dielectric is an insulator; when placed between the plates of a capacitor it gives a lower potential difference with the same charge, due to the polarization of the material. This increases the capacitance. 18

19 20-5 Capacitors and Dielectrics Polarization of the dielectric results in a lower electric field! New field given by dividing the original field by the dielectric constant κ: Therefore, the capacitance becomes: 19

20 20-5 Capacitors and Dielectrics The dielectric constant is a property of the material.! Here are some examples. 20

21 20-5 Capacitors and Dielectrics If the electric field in a dielectric becomes too large, it can tear the electrons off the atoms, thereby enabling the material to conduct. This is called dielectric breakdown; the field at which this happens is called the dielectric strength. 21

22 20-6 Electrical Energy Storage The total energy stored in the capacitor: 22

23 20-6 Electrical Energy Storage Energy stored in a capacitor can be put to a number of uses: - Camera flash, cardiac defibrillator and others. - Capacitors form an essential part of most electrical devices used today.! Divide the stored energy by the volume of the capacitor, find the energy per unit volume. Result is valid for any electric field: 23

24 Answer a): 0 J Answer b): -11 J Answer c): -11 J 24

25 Answer a): 0 V Answer b): -4.1 MV Answer c): -4.1 MV 25

26 Answer a): - 2 Q Answer b): Negative 26

27 Answer a): 0.86 J Answer b): Less Answer c): J 27

28 Answer a): 1.87 µm Answer b): 6.9 µm 28

29 Answer a): 0.29 C Answer b): 48 J 29