Electric Force and Coulombs Law

Transcription

1 Electric Force and Coulombs Law 1

2 Coulombs law is an inverse squared law prove this graphically / experimentally 2

3 NOTE: THIS IS ONLY FOR POINT CHARGES. Schematics I.) +5C 3C II.) Q Q 3

4 III.) more than two charges present gravity analogy with charges +Q Q Q 4

5 +Q Q Q 5

6 Mathematical examples Students DO 1.) A proton and an electron are separated by a distance of 5.3x10 2 nm. Find the magnitude of the electric force between them. 6

7 2.) 3 charges are located on an axis. A 20 µc charge is located at x=0 m, a 20 µc charge is located at x = 3 m and a 25 µc charge is located at x = 7 m. Determine the force acting on the charge located at x=3. 7

8 Students DO 3.) A 50 nc charge is placed 5 cm to the left of a 20 nc charge. A 35 nc charge is placed in the same line 15 cm to the right of the 20 nc charge. What is the force acting on the 35 nc charge. 8

9 Electric Field (E) (NOT force Fe) Gravity Analogy Electric Field 9

10 Graphical Representation of E fields

11 Rules for drawing field lines 1.) Lines are drawn based on the direction a + charge would be pushed (Field line come out from + objects and point in on objects) 2.) Field lines never cross 3.) When there is more than one charge, the lines will interact with each other and form curved patterns. 4.) The number of lines that are drawn in or out of the object must be proportion to the amount of charge each one has. (If a 2C charge is near a 1C charge, you have 2 x as many lines on the 2C one). The number chosen is arbitrary, as long as the proportion remains the same: 1 C vs 2 C 5 lines to 10 lines, or 6 line to 12 lines, or 10 line to 20 lines (Note: If a line comes out of one charge and goes into the other one, it should be included in the total count for each charge separately) 5.) Draw enough lines on the charges to give an accurate picture all around the charge (Minimum of 6 lines). 6.) The strength of the field is strongest where the lines are closest together. (next to the charge, the lines are very close) 11

12 Drawing E fields near in regions around charges +3C 2C +50μC +40μC Drawing E Fields at specific locations 3Q +3Q 12

13 Student Sheet Electric Fields 4.) Several electric field line patterns are shown in the diagrams below. Which of these patterns are incorrect? 5.) Consider the electric field lines shown in the diagram below. What is the charge on each object. 6.) Consider the electric field lines drawn at the right for a configuration of two charges. Several locations are labeled on the diagram. Rank these locations in order of the electric field strength from smallest to largest. 7.) Identify the sign of each charge below and also rank the objects according to which has the greatest magnitude of electric charge, beginning with the smallest charge. 13

14 The field around a charged conductor A conductor is in electrostatic equilibrium when the charge distribution (the way the charge is distributed over the conductor) is fixed. Basically, when you charge a conductor the charge spreads itself out. At equilibrium, the charge and electric field follow these guidelines: the excess charge lies only at the surface of the conductor the electric field is zero within the solid part of the conductor the electric field at the surface of the conductor is perpendicular to the surface charge accumulates, and the field is strongest, on pointy parts of the conductor Let's see if we can explain these things. Consider a negatively charged conductor; in other words, a conductor with an excess of electrons. The excess electrons repel each other, so they want to get as far away from each other as possible. To do this they move to the surface of the conductor. They also distribute themselves so the electric field inside the conductor is zero. If the field wasn't zero, any electrons that are free to move would. There are plenty of free electrons inside the conductor (they're the ones that are canceling out the positive charge from all the protons) and they don't move, so the field must be zero. A similar argument explains why the field at the surface of the conductor is perpendicular to the surface. If it wasn't, there would be a component of the field along the surface. A charge experiencing that field would move along the surface in response to that field, which is inconsistent with the conductor being in equilibrium. Why does charge pile up at the pointy ends of a conductor? Consider two conductors, one in the shape of a circle and one in the shape of a line. Charges are distributed uniformly along both conductors. With the circular shape, each charge has no net force on it, because there is the same amount of charge on either side of it and it is uniformly distributed. The circular conductor is in equilibrium, as far as its charge distribution is concerned. With the line, on the other hand, a uniform distribution does not correspond to equilbrium. If you look at the second charge from the left on the line, for example, there is just one charge to its left and several on the right. This charge would experience a force to the left, pushing it down towards the end. For charge distributed along a line, the equilibrium distribution would look more like this: The charge accumulates at the pointy ends because that balances the forces on each charge. 14

15 Special rules for charges on conductors in Estatic equilibrium (based on Gauss' Law, calculus based) also experimentally verifiable 1) charge distribution 2) E Field surface direction 3) Sharp points 4) E Field inside (faraday cage, microwave door) 5) point charge surrounded by hollow case 15

16 16

17 Working with Parallel Plates From gausses law, we also get vs

18 Calculating Electric Field Strength (Magnitude) 2 possibilities for electric fields 1.) A uniform field, 2.) A field created by a charge Q 18

19 Quick review of E Field 19

20 Direction of charge motion 20

21 Examples 1.) (a) What is the E field strength 1 m away from a + 2 C charge (b) If a 20 C charge was placed at this location, what would be the force acting on it. 21

22 Students Do REVISED 2.) A proton is placed near a charged sphere. The magnitude of the E field at this location is 200 N/C. (a) How much force acts on the proton. (b) what is the protons initial acceleration (c) If the proton is located 2 cm away from the charged sphere, what is the charge d) how would the answers differ if an electron was placed here? 22

23 Students Do 3.) 10 electrons are grouped together and placed in a uniform field of 3 x 10 3 N/C. (a) What force acts on the charge (b) If the group of electrons are free to move, how far would they move in 30 ns Electron mass 9.11x10-31 kg 23

24 E field with more than 1 point charge present 24

25 25

26 4.) A + 50 µc charge is placed 10 cm away from a 30 µc charge on the left of it. (a) Draw the field lines (b) What is the magnitude and direction of the electric field at the location of the 30uC charge. (c) What is the magnitude and direction of the field 5 cm to the right of the 30 µc charge. (c) How much force would act on and electron if it was placed at this location. 26

27 Students DO 5.) A sphere has 5 µc on it. (a) 10 electrons are grouped together and placed 30 cm away from the charge, what is the strength of the field at that location. (b) If 50 electrons were grouped and placed at that same 30 cm location what would the strength of the E field be. 27

28 setup only 6.) A +50μC charge is located at x = 0 and a 50 μc charge is placed at x = 52 cm. Determine the fiel d strength at (0,30) 28

29 Students DO 7.) Two charged spheres are placed 25 cm apart. Sphere A on the left has a charge of +20 μc and sphere B on the right has a charge of 50 μc. (a) Sketch the spheres and draw field lines around them (b) Find the magnitude of the field 10 cm to the right of A (c) How much force would act on an electron placed 10 cm to the right of A (d) The spheres are touched together. Explain in terms of the # of electrons or protons what occurs (e) The spheres from d are separated again to 25 cm. Draw the field lines 29

30 8.) A point charge (m = 1.0 g) at the end of an insulating string of length 55 cm is observed to be in equilibrium in a known uniform horizontal electric field, E = 8900 N/C, when the pendulum has swung so it is 1.0 cm high. If the field points to the right, determine the magnitude and sign of the point charge. 30

31 Parallel Plate Questions 9.) Two oppositely charged horizontal plates have an electric field between them. +4e worth of charge bunched together is placed at rest in the field (e = elementary charge). The charge floats suspended between the plates. (a) Draw a sketch of the plates with the charge inbetween them. Draw a FBD of the charge and label which plate is + and which plate is. (b) Redraw the plates and draw the E field between the plates. Then find the magnitude of the field. 31

32 Charges moving through parallel plates act like projectiles. 32

33 B2003B4. (15 points) An electric field E exists in the region between the two electrically charged parallel plates shown above. A beam of electrons of mass m, charge q, and velocity v enters the region through a small hole at position A. The electrons exit the region between the plates through a small hole at position B. Express your answers to the followin questions in terms of the quantities m, q, E, θ, and v. Ignore the effects of gravity. (a) i. On the diagram of the parallel plates above, draw and label a vector to show the direction of the electric field E between the plates. ii. On the following diagram, show the direction of the force(s) acting on an electron after it enters the region between the plates. iii. On the diagram of the parallel plates above, show the trajectory of an electron that will exit through the small hole at position B. (b) Determine the magnitude of the acceleration of an electron after it has entered the region between the parallel plates. (c) Determine the total time that it takes the electrons to go from A to position B. (d) Determine the distance d between positions A and B. (e) Now assume that the effects of gravity cannot be ignored in this problem. How would d change the distance for an electro entering the region A at and leaving B? at Explain your reasoning. 33

34 Electrical Energy = U e 34

35 Electric Potential (V) 35

36 E Field is a possibility ==> A possibility of force Potential is a possibility ==> A possibility of NOT A VECTOR Common Misconception Wimshurst vs Electric Outlet 36

37 Potential Difference. ΔV Water Analogy, Rollercoaster Analogy Crappy rollercoaster > need energy possibility difference to accomplish anything Have energy, but no energy difference Have energy, but no energy difference Electrical Outlet 37

38 Batteries B-Batteries Video Clip Batteries are not 'buckets full of charge' that empty as charge leaves them and then die out Chemical reaction maintains pot diff. between the two terminals so one is always high and one is always low and once charge is exposed to it, it flows Note that the charges that are made to move are not provided by the battery, they are already there inside the device, there are millions of them available. Its like a water hose full of water already... all the charge begins to move immediately and you dont have to wait for it to flow from the battery. Work is done by reaction to seperate the charges and create the potential difference 38

39 Charge moving between spheres examples Equal & Unequal sizes 39

40 The electronvolt (ev) 40

41 Summary Electric Energy Electric Potential Defined Variable Unit(s) 41

42 Electric Potential Math General Case Finding energy or Potential Difference 42

43 Example 1: Image you have a 100 N/C E field with a 5 C charge at a certain spot. This charge has electric potential energy at this spot (we don t know how much). The charge is moved 2 m against the E field. Determine the potential difference it is moved through. 43

44 Example 2: Move A B Move A C Move A D 44

45 Examples A.) 3 electrons are moved against an E field through a potential difference of 100 V. How much work is done on them. 45

46 Students Do B.) A charge of +200µC is moved 1.5 m against a uniform electric field of 13 N/C + (a) How much work is done on the charge (b) Determine the change in the potential energy of the charge after it was moved (c) What is the potential difference between beginning and start (d) How many electron volts of energy does the charge have. (e) How would the answers change if a negative charge was used instead? 46

47 Parallel Plates questions (using potential) Derive ΔV = E d 47

48 48

49 1.) An electron is accelerated horizontally from rest through an electron gun in a television picture tube by a potential difference of V. It then passes between two horizontal plates 6.5 cm long and 1.3 cm apart that have a potential difference of 250 V. The electron enters the plates horizontally and is deflected as it travels between them. What angle above the horizontal will the electron be traveling after it leaves the plates? 49

50 2.) A pair of horizontal plates have a potential difference of 1000 V and plate separation of 1 cm on the surface of the earth. (a) Compare the gravitational force on an electron placed midway between the plates in relation to the electric force. (b) What potential difference, acting over a distance of 1 cm, would be needed to balance the downward force of gravity so that an electron would remain stationary? (c) Ignoring the effects of gravity, what would the speed of the electron be when it struck a plate if it were released midway between the 1000 V plates. 50

51 Point charges Electrical Potential Energy for a point charge 51

52 More than 2 charges two possibilities 52

53 Calculating potential for point charges 53

54 Potential when more than one charge present 54

55 3.) A +50 μc charge is located at x=0 and a 50 μc charge is located at X=52 cm. (a) Determine the potential energy of the charge system. (b) What is the potential at (0cm,30cm) and at (26cm,30cm). (c) How much work would be required to bring an electron from infinity to point (0,30) cm (d) If the electron was released from (0, 30) after being placed here, what would its speed be when it returns to infinity (e) What would the energy of the system be if a third 50uC charge was placed at (0,30) 55

56 #4) A 5 uc is located at x=0 and a 10 uc charge is located at X=10 cm. a) Find the potential energy of the 2 charges b) Find the potential at the midpoint of the charges c) Determine the net E field at the midpoint An electron is brought to the midpoint of the charges. Answers 4.5 J 9x10 5 V 5.4x10 7 N/C d) How much work is needed to bring in the electron e) Determine the force exerted on an electron placed at the midpoint f) Find the speed of the electron released from the midpoint when it reaches infinity 1.44x10 13 J 8.64x10 12 N 5.6x10 8 m/s 56

57 Concepts With Potential Potential Difference Equipotentials 57

58 Graphs 58

59 Capacitors How is charge put on the plates? 59

60 Capacitance Dielectrics 60

61 Charge stored on a plate Energy stored in capacitor 61

62 C1.) A homemade capacitor is assembled by placing two 9 in diameter pie pans 10 cm apart and connecting them to the opposite terminals of a 9 V battery. ( r = 4.5 in = cm =.1143 m ) Estimate (a) the capacitance, (b) the charge on each plate, (c) the electric field halfway between the plates, (d) the work done by the battery to charge the plates. (e) Which of the above values change if a dielectric is inserted. 62

63 C2.) Dry air will break down (cause charge to leap from one plate to another across the air gap) if the electric field between capacitor plates exceeds 3x10 6 V/m. What amount of charge can be placed on Capacitor before break down will occur if the area of each plate is 56 cm 2 63

64 Moving Parallel Plates Isolated Plates. Plates connected to a battery 64

65 Vandegraaff Generator Vandegraaff Generator 65

66 Vandegraaff Generator 66

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