Coulomb’s Law and Electric Field Chapter 24: all Chapter 25: all

2 Electric charge Able to attract other objects Two kinds Positive – glass rod rubbed with silk Negative – plastic rod rubbed with fur Like charges repel Opposite charge attract Charge is not created, it is merely transferred from one material to another Physics chapters

3 Elementary particles Proton – positively charged Electron – negatively charged Neutron – no charge Nucleus – in center of atom, contains protons and neutrons Quarks – fundamental particles – make up protons and neutrons, have fractional charge Physics chapters

4 ions Positive ions – have lost one or more electrons Negative ions – have gained one or more electrons Only electrons are lost or gained under normal conditions Physics chapters

5 Conservation of charge The algebraic sum of all the electric charges in any closed system is constant. Physics chapters

6 Electrical interactions Responsible for many things The forces that hold molecules and crystals together Surface tension Adhesives Friction Physics chapters

7 Conductors Permit the movement of charge through them Electrons can move freely Most metals are good conductors Physics chapters

8 Insulators Do not permit the movement of charge through them Most nonmetals are good insulators Electrons cannot move freely Physics chapters

9 Charging by induction See pictures on pages Physics chapters

10 Coulomb’s Law Point charge – has essentially no volume The electrical force between two objects gets smaller as they get farther apart. The electrical force between two objects gets larger as the amount of charge increases Physics chapters

11 Coulomb’s Law r is the distance between the charges q 1 and q 2 are the magnitudes of the charges k is a constant 8.99 x 10 9 N∙m 2 /C 2 Physics chapters

12 Coulombs SI unit of charge, abbreviated C Defined in terms of current – we will talk about this later Physics chapters

13 Coulomb’s law constant k is defined in terms of the speed of light k = c k = 1/4    0 is another constant that will be more useful later  0 = 8.85 x C 2 /N∙m 2 Physics chapters

14 The coulomb Very large amount of charge Charge on 6 x electrons Most charges we encounter are between and C 1  C = C Physics chapters

15 Examples See pages Physics chapters

16 Electric Field A field is a region in space where a force can be experienced.A field is a region in space where a force can be experienced. Or: a region in space where a quantity has a definite value at every point.Or: a region in space where a quantity has a definite value at every point. Physics chapters

17 Electric Field Produced by a charged particle.Produced by a charged particle. The force felt by another charged particle is caused by the electric field.The force felt by another charged particle is caused by the electric field. We can check for an electric field with a test charge, q t. If it experiences a force, there is an electric field.We can check for an electric field with a test charge, q t. If it experiences a force, there is an electric field. Physics chapters

18 Electric field The definite quantity is a ratio of the electric force experienced by a charge to the amount of the charge.The definite quantity is a ratio of the electric force experienced by a charge to the amount of the charge. Vector quantity measured in N/C.Vector quantity measured in N/C. Physics chapters

19 Electric field To determine the field from a point charge, Q, we place a test charge, q t, at some position and determine the force acting on it.To determine the field from a point charge, Q, we place a test charge, q t, at some position and determine the force acting on it. Qqtqt F Physics chapters

20 Direction of E If the test charge is positive, E has the same direction as F.If the test charge is positive, E has the same direction as F. If the test charge is negative, E has the opposite direction as F.If the test charge is negative, E has the opposite direction as F. Physics chapters

21 Electric Field - Point Charge Physics chapters

22 Electric Field The field is there, independent of a test charge or anything else!The field is there, independent of a test charge or anything else! The electric field vector points in the direction a positive charge would be forced.The electric field vector points in the direction a positive charge would be forced. Physics chapters

23 Example 1 Two charges, Q 1 = +2 x C and Q 2 = +3 x C are 50 mm apart as shown below.Two charges, Q 1 = +2 x C and Q 2 = +3 x C are 50 mm apart as shown below. What is the electric field halfway between them?What is the electric field halfway between them? Q1Q1 Q2Q2 50 mm E1E1 E2E2 Physics chapters

24 Example 1 At the halfway point, r 1 = r 2 = 25 mm.At the halfway point, r 1 = r 2 = 25 mm. Magnitudes of fields:Magnitudes of fields: Physics chapters

25 Example 1 E 1 = 2.9 x 10 5 N/CE 1 = 2.9 x 10 5 N/C E 2 = 4.3 x 10 5 N/CE 2 = 4.3 x 10 5 N/C E 1 is to the right and E 2 is to the left.E 1 is to the right and E 2 is to the left. E 1 = 2.9 x 10 5 N/CE 1 = 2.9 x 10 5 N/C E 2 = x 10 5 N/CE 2 = x 10 5 N/C E = E 1 + E 2 = x 10 5 N/CE = E 1 + E 2 = x 10 5 N/C Physics chapters

26 Example 2 For the charges in Example 1, where is the electric field equal to zero?For the charges in Example 1, where is the electric field equal to zero? Since the fields are in opposite directions between the charges, the point where the field is zero must be between them.Since the fields are in opposite directions between the charges, the point where the field is zero must be between them. Q1Q1 Q2Q2 E1E1 E2E2 Physics chapters

27 Example 2 r 1 + r 2 = s, so r 2 = s – r 1 Physics chapters

28 Example 2 Physics chapters

29 Field Diagrams To represent an electric field we use lines of force or field lines.To represent an electric field we use lines of force or field lines. These represent the sum of the electric field vectors.These represent the sum of the electric field vectors. Physics chapters

30 Field Diagrams Physics chapters

31 Field Diagrams Physics chapters

32 Field Diagrams At any point on the field lines, the electric field vector is along a line tangent to the field line.At any point on the field lines, the electric field vector is along a line tangent to the field line. Physics chapters

33 Field Diagrams Physics chapters

34 Field Diagrams Lines leave positive charges and enter negative charges. Lines leave positive charges and enter negative charges. Lines are drawn in the direction of the force on a positive test charge.Lines are drawn in the direction of the force on a positive test charge. Lines never cross each other.Lines never cross each other. The spacing of the lines represents the strength or magnitude of the electric field.The spacing of the lines represents the strength or magnitude of the electric field. Physics chapters

35 Point Charges Lines leave or enter the charges in a symmetric pattern.Lines leave or enter the charges in a symmetric pattern. The number of lines around the charge is proportional to the magnitude of the charge.The number of lines around the charge is proportional to the magnitude of the charge. Physics chapters

36 Point Charges Physics chapters

37 Point Charges Physics chapters

38 Gauss’s Law Electric flux through a closed surface is proportional to the total number of field lines crossing the surface in the outward direction minus the number crossing in the inward direction.Electric flux through a closed surface is proportional to the total number of field lines crossing the surface in the outward direction minus the number crossing in the inward direction. Physics chapters

39 Example 25-9 (see page 563) Field of a charged sphere is the same as if it were a point charge Physics chapters

40 Example (see page 564) Field of a infinite line of charge is Physics chapters

41 Other scenarios See table on page 567See table on page 567 Physics chapters

42 Example 3 Two parallel metal plates are 2 cm apart.Two parallel metal plates are 2 cm apart. An electric field of 500 N/C is placed between them.An electric field of 500 N/C is placed between them. An electron is projected at 10 7 m/s halfway between the plates and parallel to them.An electron is projected at 10 7 m/s halfway between the plates and parallel to them. How far will the electron travel before it strikes the positive plate?How far will the electron travel before it strikes the positive plate? Physics chapters

43 Example 3 Two charged parallel plates create a uniform electric field in the space between them.Two charged parallel plates create a uniform electric field in the space between them. Physics chapters

44 Example 3 E vovo This is just like a projectile problem except that the acceleration is not a given value. Physics chapters

45 Example 3 = 8.8 x m/s 2 Physics chapters

46 Example x m/s 2 is the vertical acceleration of the electron.8.8 x m/s 2 is the vertical acceleration of the electron. Horizontally, the acceleration is zero.Horizontally, the acceleration is zero. x = vtx = vt v = 1 x 10 7 m/s & t = ?v = 1 x 10 7 m/s & t = ? Physics chapters

47 Example 3 Back to vertical direction:Back to vertical direction: y = y o + v o t + 1 / 2 at 2y = y o + v o t + 1 / 2 at 2 y = 1 / 2 at 2y = 1 / 2 at 2 = 1.5 x s Physics chapters

48 Example 3 Back to horizontal direction:Back to horizontal direction: x = vtx = vt x = (1 x 10 7 m/s)(1.5 x 10 –8 s)x = (1 x 10 7 m/s)(1.5 x 10 –8 s) x = 0.15 m = 15 cmx = 0.15 m = 15 cm Physics chapters

49 Dipoles A pair of charges with equal and opposite sign.A pair of charges with equal and opposite sign. Induced dipoles, molecular dipoles, etc.…Induced dipoles, molecular dipoles, etc.… Physics chapters