ELECTROSTATICS. the study of electric charges, forces and fields Static Electricity is Stationary Electricity or Accumulation of charge

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1 Electrostatics 1

2 ELECTROSTATICS the study of electric charges, forces and fields Static Electricity is Stationary Electricity or Accumulation of charge

3 Fundamental Rule Opposites attract, Likes Repel Things don t like having a net charge If objects don t like having a net charge, then how does it happen?

4 When objects get Charged: Must obey Law of Conservation of Charge Charges may be transferred among different atoms, materials, or objects but all charge is accounted for. NO NEW charges are created nor are any charges destroyed. Only electrons can move

5 Remember: An excess of electrons results in: A negative charge A shortage of electrons results in: A positive charge ONLY ELECTRONS MOVE

6 How Do Charges Behave in Materials? Conductor: Allows electrons to move easily Metals, why? Metals lose electrons, (not held tightly) Insulator: Does not allow electrons to move easily Non metals. Glass, plastic, dry wood. Why? Electrons held tightly

7 Semiconductors charges only move freely when certain conditions are met (i.e., heat, sufficient voltage, etc.) ex germanium, selenium, and silicon. Superconductors charges move effortlessly and cannot be stopped once they are moving

8 Objects become charged by Friction Electrons are rubbed off one insulator onto another insulator Conduction Induction Grounding With a credit card

9 FRICTION: e- rubbed off one insulator to another 9

10 Objects become charged by Friction Conduction Charging by CONTACT with a charged object Induction Grounding

11 Charging by Conduction Requires Contact Electrons transferred. Results in: Object with the same charge as original charged object. Some electrons leave rod and spread over sphere.

12 Objects become charged by Friction Conduction Induction Charging an object WITHOUT touching a charged object Grounding

13 Induction no contact occurs between charged object and neutral object.. Involves temporary rearrangement of electrons on neutral object Neutral Object becomes polarized but net charge remains the same If neutral polarized object is grounded, charge will become opposite of the charged object and is no longer temporary 13

14 Charging by Induction Neutral objects can be temporarily attracted to charged objects by a process called POLARIZATON.

15 A negatively charged balloon is brought near a neutral conducting sphere as shown below. As it approaches, charge within the sphere will distribute itself in a very specific manner. Which one of the diagrams below properly depicts the distribution of charge in the sphere?

16 What is grounding? Involves Transfer of excess electrons to and from the ground to neutralize it

17 Charging by Induction AND Grounding polarization grounding permanent charge The rod does not touch the sphere. It pushes electrons out of the back side of the sphere and down the wire to ground. The ground wire is disconnected to prevent the return of the electrons from ground, then the rod is removed. The charge on the object is opposite if grounded

18 Grounding is allowing charges to move freely along a connection between a conductor and the ground. The Earth (the ground) is a practically infinite reservoir of electric charge. Here a positively charge rod attracts electrons from the ground into the electroscope Here a negatively charge rod repels electrons into the ground from the sphere

19 Four fundamental forces in nature Gravity Weak nuclear Electromagnetic (electricity and magnetism) Strong nuclear

20 What exactly is CHARGE? It is physical property of matter. It comes in two flavors: plus and minus. What is the unit for charge? Coulombs (C) 20

21 Definition of Coulomb Abbreviation: C SI unit for charge One coulomb is NOT equal to the charge of 1 electron!!!! 1C ~ the charge of 6.25 x electrons It is the amount of charge to pass through a cross-section of wire in 1 second when 1 Ampere (A) of current is applied. (We ll cover the amp later.) Likewise the + charge of protons is associated with 6.25 x protons 21

22 Elementary Particles Particle Charge, (Coulombs per particle) # of particles in a Coulomb electron -1.6 x x proton +1.6 x x

23 Coulomb s Law Charles-Augustin de Coulomb used a torsion pendulum to establish his law. F k q q 1 d 2 2 rˆ 23

24 Electric Force F k q q d q charge, C (coulombs) 1 rˆ d distance between charges, m F electric force, N k electrostatic constant 9.00 x 10 9 Nm 2 /C

25 What happens to F as charge increases? Increase What happens to F as r increases? Decreases by inverse square Look at k c. Is this a large or small value? large How is q described for a proton? positive For an electron? negative

26 The Product of q 1 and q 2 If the product, q 1 q 2,is negative then the force is attractive. If the product, q 1 q 2,is positive then the force is repulsive. 26

27 Ex 2: Two negatively charged balloons are 0.70m apart. If the charge of each is 2.0 x 10-6 C, What is the electric force between the two balloons? q 1 = q 2 = 2.0 x 10-6 C d = r = 0.70 m F k q 1 q 2 r 2 F = 9.0 x 10 9 N m 2 /C 2 (-2.0 x 10-6 C) 2 (0.70m) 2 F = N An attracting or repelling force?

28 Ex.3: Two equally charged balloons repel each other with a force of 4.0 x 10-3 N. If they are m apart, what is the charge of the each balloon? F = 4.0 x 10-3 N F k q q d = m q 2 = Fd 2 k q 2 = (4x10-3 N)(0.015m) 2 (9x10 9 Nm 2 /C 2 ) q 1 = q 2 = 1.0 x 10-8 C r

29 Ex 4: How many Coulombs are in a µc? 1 x 10-6 Two charges are separated by 3.0 cm. Object A has a charge of +6.0 µc. Object B has a charge of -6.0 µc. What is the force on Object A? Is the force attractive or repelling? -360N, attractive

30 Ex 5 Two electrons exert an electrical force of 1.0 x 10-8 N on one another. Is this an attractive or repelling force? Repelling Calculate the distance between them. Rearrange formula to solve for d Use known charge for an electron 1.5 x m

31 Two charges create a force on one another. If the charge of one object is doubled, how does the resulting force change? F will double What if charge of one object is tripled? F will triple F k q q 1 d 2 2 rˆ

32 Two charges create a force on one another. If the distance between the objects is increased by a factor of 2, the force changes by a factor of? F will decrease by a factor of 4 What if distance between the objects is tripled? F will decrease by a factor of 9 F k q q 1 d 2 2 rˆ

33 Review. How many electrons in one Coulomb? 6.25 x electrons What is the charge of one electron -1.6 x Coulombs (C) How many protons in one Coulomb? 6.25 x protons What is the charge of one proton +1.6 x Coulombs (C).

34 Review. How many electrons in one Coulomb? 6.25 x electrons Calculate the charge of one electron -1.6 x Coulombs (C) How many protons in one Coulomb? 6.25 x protons Calculate the charge of one proton +1.6 x Coulombs (C).

35 Force and Fields Contact forces What we mostly deal with Objects touch each other directly Ex. A tennis racket hits a tennis ball F=ma

36 Forces can occur without contact! Action at a distance Can you think of anything that applies a force without touching? 36

37 Gravity demonstrates action at a distance What happens if you get too far away from the mass exerting the force? The effects are less 37

38 What else applies an action at a distance? Magnets! 38

39 What else applies an action at a distance? 39

40 Attracting and repelling forces of charges 40

41 The space that surrounds these things is altered Examples: Magnets Sun Planets Electric charge

42 Action at a distance depends on a field of influence An object within the field may be affected by it Can be scalar or vector Magnitude only Ex. Heat Can be vector Magnitude and direction Ex. Gravity (one direction only since only attracts) Ex. Electric (more than one direction; attracts and repels 42

43 Fields are NOT Force, they exert the force Ex. A person pushes a box. The person is not the force, he exerts the force! 43

44 Electric field A field that exerts force that surrounds an electric charge or group of charges Magnitude and direction (vector)

45 Electric field How would you detect and measure an electric field around a charge? Place another one nearby and see what happens! Since all charges produce fields, come up with a model 45

46 Electric field model Source charge: charge producing the field. Usually designated with a capital Q Test charge: a mathematical creation Always positive Symbol: q Doesn t exist Infinitely small, thus produces no field of its own 46

47 What is the source charge if The test charge q moves towards it? Negative (attracts) The test charge q moves away from it? Positive (repels) How would I draw these? 47

48 Where do you think the field is strongest? 48

49 What if I had more than one source charge? What would the field lines look like? 49

50

51 Think: Where is the electrical potential energy of a positive test charge (q+) higher, at the point A or B? Why? Point A. Because of it s location, it is not where it wants to be. It took work to get it there!

52 The electric field is strongest in regions where the lines are close together and weak when the lines are further apart.

53 These fields can be detected in lab Threads floating on oil bath become polarized and align themselves with the electric field.

54 54

55 55

56 56

57 How do I measure the strength of the electrical field around a source charge (Q)? What factors do you think the electrical field strength is dependent on? 1. Force (Push or Pull) of Source Charge on Test Charge 2. Distance Between Source Charge and Test Charge

58 First let s consider effect of force 58

59 Electric Field Intensity (Strength) E F q' E - Electric Field Strength or Intensity (N/C) F - Force experienced by a test charge at that location (N) q - magnitude of the test charge placed at that location (C).

60 Ex 6 A test charge has a magnitude of 1 x C. It experiences a force of 2N in an electrical field. What is the Intensity of the field? Variables: F = 2N q = 1 x C E = F/q E = 2N/ 1 x C E = 2 x N/C

61 Ex 7 A test charge of 6 x uc is placed 200 mm from a proton (this is the source charge). What is the electrical force between them? What is the Field strength at this point? What is the direction of the field? Variables: q = 6 x µc p+= 1.6 x C d = 200 mm Variables: q = 6 x C p+= 1.6 x C d = 0.2m Now we can solve. This is a 2 step problem. Step 1: Solve for force using Coulombs Law Step 2: Use the calculated force and solve for Field Intensity

62 Ex 7 cont A test charge of 6 x µc is placed 200 mm from a proton (this is the source charge). What is the electrical force between them? What is the Field strength at this point? What is the direction of the field? Variables: q = 6 x C p+= 1.6 x C d = 0.2m F = kqq d 2 F = (9 x 10 9 C)(6 x C)(1.6 x C) 0.2m 2 F = 2.16 x N E = F/q E = 2.16 x N / 6 x C E = 3.6 x 10-8 N/C

63 Remember: The direction of the electric field at a point in space is the same as the direction in which a positive charge would move if it were placed at that point. The electric field lines or lines of force indicate the direction. + -Q Electric field line flow Out of positive charges and into Negative charges.

64 The electric field intensity E at a distance d from a source charge Q can be found without knowing the test charge!: Units: N/C

65 EX 8: What is the electric field intensity at a distance of 2 m from a source charge of -12 μc? Include direction. d = 2 m q = -12 μc q = -12μC To determine the direction of the field, ask If the source charge is negative do the field lines go out or in? E kq d x10 ( 12x10 ) = 2.7x10 4 N/C, towards q 2 2 or to the left

66 How do I determine the field strength if there are multiple charges? 66

67 When more than one charge contributes to the field, the resultant field is the vector sum of the contributions from each charge. E kq d 2 Where k : 9x10 9 Nm 2 /C 2 Units: N/C Note we will look at direction of the field to know whether fields add or subtract at a point.

68 Remember this? + -Q Electric field line flow Out of positive charges and into Negative charges.

69 Ex 9: Two charges q 1 =-8 μc and q 2 =+12 μc are placed 120 mm apart in the air. What is the electric field at the midpoint between them? q 1 = -8 μc q 2 = +12 μc r = m - E T E 1 E 2 X q 1 + q 2 E kq d 2 = kq 1 + kq 2 r 2 r 2 = (9 x 10 9 )(8 x 10-6 ) + (9 x 10 9 )(12 x 10-6 ) (0.06) 2 (0.06) 2 E= 2.0 x x 10 7 = 5.0 x 10 7 N/C to the left

70 Ex.10: Two charges q 1 =+8 μc and q 2 =+12 μc are placed 120 mm apart in the air. What is the electric field at the midpoint between them? q 1 = + 8 μc q 2 = +12 μc r = m + E T E 1 E 2 X q 1 + The fields are in opposite directions so they subtract q 2 E kq = kq 1 - kq 2 r 2 r 2 r 2 = (9 x 10 9 )(8 x 10-6 ) - (9 x 10 9 )(12 x 10-6 ) (0.06) 2 (0.06) 2 E= 2.0 x x 10 7 = -1.0 x 10 7 N/C E = 1.0 x 10 7 N/C to the left

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