Physics General Physics II Electricity, Magne/sm, Op/cs and Modern Physics Review Lecture Chapter Spring 2017 Semester

Transcription

1 Physics General Physics II Electricity, Magne/sm, Op/cs and Modern Physics Review Lecture Chapter Spring 2017 Semester Prof. Andreas Jung

2 Reminder Addi=onal help session tonight: 6:30-8:30pm, PHYS 12 Example problems online as of this morning The first mid-term exam will be on Thursday, February 16 th, 8-10pm, room 114. Equa=on sheet will be provided, no need for your own Material to be covered is chapters 14 and 15 Coulomb s law Electric poten=al energy Electric field Electric poten=al Capacitors

3 Electrosta5cs Electrosta=cs is concerned with the proper=es of charges that are not moving. For example, forces on charged objects Most objects have no, or very small net electric charge so we don t no=ce these forces. They are small compared with gravity In the 1700 s, people began the systema=c study of these forces induced by sta=c electricity. But what is electric charge?

4 More Realis5c Picture Example 1 : Carbon atom Example 2 : Sodium ion Net charge = 0 Net charge = +e

5 Electric Charge

6 Electric Charge How do objects become electrically charged? The addi$on or removal of electrons creates nega$vely or posi$vely charged objects. Except under extreme condi=ons, protons stay in place and electrons are moved or transferred. Example: - + =1 e =1 p Net electric charge: 0

7 Key Points ü Charge is said to be quan/zed it is always observed as an integer mul=ple of e, the magnitude of the charge of one electron or one proton. ü Charge can be redistributed, but cannot be created or destroyed. ü An object is charged when it has an imbalance between electrons and protons.

8 Key defini5ons CONDUCTOR: an object or material in which charge can flow freely (e.g.. metals) INSULATOR: an object or material in which charge does not move freely also called dielectrics (e.g.. glass or plas=c) GROUND: a name given to a large, conduc=ng reservoir of charge. Its proper=es do not change when charge is added or removed. An object that gets connected to ground is no longer an isolated system. The charge of the object changes as it flows to/from ground.

9 Inducing an Electric Charge without direct contact In an insulator, the electrons cannot move freely. A charged object will polarize the molecules in the insulator. The nega=ve ends will be aaracted to a posi=ve charge The nega=ve ends will be repelled by a nega=ve charge.

10 A Force is a Push or a Pull. We prefer to measure force in Newton's. Both gravity and the electrosta=c force are non-contact forces. They act on objects that do not touch each other.

11 The Electrosta5c Force: Coulomb s Law Only applies to point charges! We assume that the charges are stuck down and can t move. If they moved, then r would change, F would be a func=on of =me and we would need calculus! Force is a vector it has a direc=on. We need to define a coordinate system.

12 Example Two pieces of lint have a charge of +1 nc. If they are located 3 cm apart, what is the electrosta=c force they exert on each other? The force will be along the line joining the two point charges. The magnitude will be equal. The direc=ons will be opposite.

13 More than two charges Principle of superposi=on: Calculate the force on one charge due to each of the other charges using Coulomb s law The net force is the vector sum of the individual forces.

14 More than two charges Vector addi=on: Graphical: join the vectors head-to-tail Numerical: resolve vectors into components along the x and y axes and add them up.

15 Physics General Physics II Electricity, Magne/sm, Op/cs and Modern Physics Review Lecture Chapter Electric Poten$al Energy Spring 2017 Semester Prof. Andreas Jung

16 Mechanics Review Nega=ve work (you do something to increase the poten=al energy of the system): You carry water up a hill You compress a spring You climb stairs Posi=ve work (the system uses its poten=al energy to do work for you): The water flows downhill and turns a turbine The spring unwinds (and does something for you) You slide down the handrail (increase kine=c energy)

17 Mechanics Review The gravita=onal force is called conserva$ve: The poten=al energy only depends on the posi=on of an object. The poten=al energy does not depend on the path the object takes. Other conserva/ve forces: Spring force, F= kx (Hooke s law) Electrosta/c force Forces that are not conserva=ve: Fric=on Viscous damping These dissipate energy rather than store energy.

18 Gravita5onal Poten5al Energy

19 Electrosta5c Poten5al Energy

20 Electrosta5c Poten5al Energy

21 Electrosta5c Poten5al Energy

22 Key Points It is important to use the signs associated with each charge. When the signs of the two charges are opposite, the poten=al energy of the pair is nega=ve. When the signs of the two charges are the same, the poten=al energy of the pair is posi=ve.

23 Examples

24 Key points poten5al energy Energy can be stored in the configura=on of two or more charges. The energy of the system can be increased or decreased by moving the charges around. Changing the electrical poten=al energy must be balanced by changes in other types of energy Kine=c Gravita=onal Chemical Thermal Etc

25 Physics General Physics II Electricity, Magne/sm, Op/cs and Modern Physics Review Lecture Chapter The Electric Field Spring 2017 Semester Prof. Andreas Jung

26 Electrosta5c Force and Poten5al Energy

27 The Electric Field

28 The Electric Field The electric field produced by a charge Q is a property only of Q and not of other charges we place in its vicinity. We define the electric field in terms of the electric force that acts on a test charge : F Q =k q test Q/ r 2 r E Q = F Q / q test

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30 Electric Field Now we can talk about electric fields that occupy a region of space. We do not need to specify the source of the electric field. Any charge that is placed in the electric field will experience a force. Units for electric field: Newtons/Coulomb.

31 Electric Fields

32 Electric Field Lines Electric Dipole: opposite signs but equal magnitude Two Posi=ve Charges: with equal magnitude

33 Electric Field Lines Opposite charges with unequal magnitudes: At very large distances, the electric field is the same as one produced by a single point charge with magnitude Q = +2q q=+q. Density of lines is propor=onal to the magnitude of the electric field.

34 Calcula5ng The Electric Field

35 Example

36 Example

37 Key points Electric field

38 Physics General Physics II Electricity, Magne/sm, Op/cs and Modern Physics Review Lecture Chapter Electric Poten$al Spring 2017 Semester Prof. Andreas Jung

39 Electric Poten5al Energy

40 Electric Poten5al

41 Electric Poten5al The electric poten=al at a point in space is the sum of the electric poten=als due to mul=ple sources (principle of superposi=on)

42 Visualizing Electric Poten5al The electric field is a vector field. At each point in space it has a magnitude and a direc=on. We drew pictures of the electric field using a) Vectors (lots of liale arrows) b) Electric field line diagrams The electric poten=al is a scalar field. At each point in space it has a value (posi=ve or nega=ve) but no direc=on

43 Visualizing Electric Poten5al Gravita=onal equipoten=al contour lines on a topographic map: Electrosta=c equipoten=al:

44 Electric Field Lines and Electric Poten5al Surfaces

45 Electrosta5c Equilibrium Charges will exert forces on each other Unless they are stuck to something, the force will cause them to move around They will move un=l the electrosta=c forces balance out So the net force ac=ng on them is zero When all the charges eventually stop moving, the system is in a state of electrosta/c equilibrium Usually this happens quickly, especially for small systems so fast that we usually won t worry about it. For example, in much less than 1 µs for something that is about 1 cm in size. Remember Faradays cage demonstra=on!

46 Example

47 Physics General Physics II Electricity, Magne/sm, Op/cs and Modern Physics Review Lecture Chapter Capacitors Spring 2017 Semester Prof. Andreas Jung

48 Capacitance

49 Parallel Plate Capacitor

50 Q Q Q Capacitors Suppose charge Q flows onto the top plate. The boaom plate is a conductor so it aaracts a charge Q. This is the same as a charge Q flowing away from the boaom plate. What is the resul=ng electric field and poten=al difference?

51 Capacitors

52 Capacitors In Parallel

53 Capacitance in Series

54 Dielectrics

55 Adding an Insula5ng Material (Dielectric)

56 PermiWvity

57 Summary Equa=ons will be provided you should have a understanding of what they mean

58 Reminder Addi=onal help session tonight: 6:30-8:30pm, PHYS 12 Example problems online as of this morning The first mid-term exam will be on Thursday, February 16 th, 8-10pm, room 114. Equa=on sheet will be provided, no need for your own Material to be covered is chapters 14 and 15 Coulomb s law Electric poten=al energy Electric field Electric poten=al Capacitors

59 Backup

60 Example