Exploring Electricity and Magnetism

1. General Physics (PHY 2140) Introduction • Syllabus and teaching strategy • Electricity and Magnetism • Properties of electric charges • Insulators and conductors • Coulomb’s law Lecture 1. Chapter 15

2. Syllabus and teaching strategy Lecturer:Dr.Alan A. Sebastian, Physics Building Phone: 313-577-2720 (to leave a message with a secretary) e-mail: alansebastian@wayne.edu, Web: http://www.physics.wayne.edu/~alan Office Hours:TBD, Physics Building, , or by appointment. Grading:Reading Quizzes bonus Quiz section performance/Homework 10% Best Hour Exam25% Second Best Hour Exam25% Final40% Reading Quizzes:It is important for you to come to class prepared! Homework and QUIZ Sessions:The quiz sessions meet once a week; quizzes will count towards your grade. Hour Exams and Final Exam:There will be THREE (3) Hour Exams and one Final Exam. Online Content:Lectures will be made available to you as a supplemental reference.

3. Introduction • Knowledge of electricity dates back to Greek antiquity (700 BC). • Began with the realization that amber (fossil) when rubbed with wool, attracts small objects. • This phenomenon is not restricted to amber/wool but may occur whenever two non-conducting substances are rubbed together.

4. 15.1 Properties of Electric Charges - Discovery • Observation of “Static Electricity” • A comb passed though hair attracts small pieces of paper. • An inflated balloon rubbed with wool. • “Electrically charged” • Rub shoes against carpet/car seat to charge your body. • Remove this charge by touching another person/a piece of metal. • Two kinds of charges • Named by Benjamin Franklin (1706-1790) as positive and negative. • Like charges repel one another and unlike charges attract one another.

5. 15.1 Properties of Electric ChargesNature of Electrical Charge • Origin of charge is at the atomic level. • Nucleus : “robust”, positive. • Electrons : mobile, negative. • Usual state of the atom is neutral. • Charge has natural tendency to be transferred between unlike materials. • Electric charge is however always conserved in the process. • Charge is not created. • Usually, negative charge is transferred from one object to the other.

6. 15.1 Properties of Electric ChargesQuantization • Robert Millikan found, in 1909, that charged objects may only have an integer multiple of a fundamental unit of charge. • Charge is quantized. • An object may have a charge ±e, or ± 2e, or ± 3e, etc. but not ±1.5e. • Proton has a charge +1e. • Electron has a charge –1e. • Some particles such a neutron have no (zero) charge. • A neutral atom has as many positive and negative charges. • Units • In SI, electrical charge is measured in coulomb ( C). • The value of |e| = 1.602 19 x 10-19 C.

7. 15.2 Insulators and Conductors –Material classification • Materials/substances may be classified according to their capacity to carry or conduct electric charge • Conductors are material in which electric charges move freely. • Insulator are materials in which electrical charge do not move freely. • Glass, Rubber are good insulators. • Copper, aluminum, and silver are good conductors. • Semiconductors are a third class of materials with electrical properties somewhere between those of insulators and conductors. • Silicon and germanium are semiconductors used widely in the fabrication of electronic devices.

8. Mini-quiz: • Identify substances or materials that can be classified as • Conductors ? • Insulators?

9. 15.2 Insulators and Conductors – Charging by Conduction. • Consider negatively charge rubber rod brought into contact with a neutral conducting but insulated sphere. • Some electrons located on the rubber move to the sphere. • Remove the rubber rod. • Excess electrons left on the sphere. It is negatively charged. • This process is referred as charging by conduction.

10. 15.2 Insulators and Conductors – Earth/Ground. • When a conductor is connected to Earth with a conducting wire or pipe, it is said to be grounded. • Earth provides a quasi infinite reservoir of electrons: can accept or supply an unlimited number of electrons.

11. 15.2 Insulators and Conductors – Charging by Induction. • Consider a negatively charged rubber rod brought near a neutral conducting sphere insulated from the ground. • Repulsive force between electrons causes redistribution of charges on the sphere. • Electrons move away from the rod leaving an excess of positive charges near the rod. • Connect a wire between sphere and Earth on the far side of the sphere. • Repulsion between electrons cause electrons to move from sphere to Earth. • Disconnect the wire. • The sphere now has a positive net charge. • This process is referred as charging by induction. • Charging by induction requires no contact with the object inducing the charge.

12. 15.2 Insulators and Conductors – Charging by Induction. • Consider a negatively charged rubber rod brought near a neutral conducting sphere insulated from the ground. • Repulsive force between electrons causes redistribution of charges on the sphere. • Electrons move away from the rod leaving an excess of positive charges near the rod. • Connect a wire between sphere and Earth on the far side of the sphere. • Repulsion between electrons cause electrons to move from sphere to Earth. • Disconnect the wire. • The sphere now has a positive net charge. • This process is referred as charging by induction. • Charging by induction requires no contact with the object inducing the charge. Q: How does this mechanism work if we use a positively charged glass rod instead?

13. 15.2 Insulators and Conductors – Polarization. • Polarization is realignment of charge within individual molecules. • Produces induced charge on the surface of insulators. • how e.g. rubber or glass can be used to supply electrons.

14. ? + Mini-quiz A positively charged object hanging from a string is brought near a non conducting object (ball). The ball is seen to be attracted to the object. • Explain why it is not possible to determine whether the object is negatively charged or neutral. • What additional experiment is needed to reveal the electrical charge state of the object?

15. - + Explain why it is not possible to determine whether the object is negatively charged or neutral. • Two possibilities: • Attraction between objects of unlike charges. • Attraction between a charged object and a neutral object subject to polarization. + - + - + - + + -

16. ? 0 What additional experiment is needed to reveal the electrical charge state of the object? • Two Experiments: • Bring a known neutral ball near the object and observe whether there is an attraction. • Bring a known negatively charge object near the first one. If there is an attraction, the object is neutral, and the attraction is achieved by polarization. -+ + + - + -- -+ + +

17. q1 q2 15.3 Coulomb’s Law - Observation • Charles Coulomb discovered in 1785 the fundamental law of electrical force between two stationary charged particles. • An electric force has the following properties: • Inversely proportional to the square of the separation, r, between the particles, and is along a line joining them. • Proportional to the product of the magnitudes of the charges |q1| and |q2| on the two particles. • Attractive if the charges are of opposite sign and repulsive if the charges have the same sign. r

18. 15.3 Coulomb’s Law – Mathematical Formulation • ke known as the Coulomb constant. • Value of ke depends on the choice of units. • SI units • Force: the Newton (N) • Charge: the coulomb ( C). • Current: the ampere (A =1 C/s). • Distance: the meter (m). • Experimentally measurement: ke = 8.9875´109 Nm2/C2. • Reasonable approximate value: ke = 8.99´109 Nm2/C2.

20. Example • 1e = -1.60 ´10-19 c • Takes 1/e=6.6 ´1018 protons to create a total charge of 1C • Number of free electrons in 1 cm3 copper ~ 1023 • Charge obtained in typical electrostatic experiments with rubber or glass 10-6 C = 1 mc • A very small fraction of the total available charge

21. r + + r F21 q1 F21 q2 - q2 F21 + F21 q1 15.3 Coulomb’s Law – Remarks • The electrostatic force is often called Coulomb force. • It is a force (thus, a vector): • a magnitude • a direction. • Second example of action at a distance.

22. Mini-Quiz • Name the first action at a distance force you have encountered in physics so far.

23. Example: Electrical Force Question: The electron and proton of a hydrogen atom are separated (on the average) by a distance of about 5.3x10-11 m. Find the magnitude of the electric force that each particle exerts on the other.

24. Question: The electron and proton of a hydrogen atom are separated (on the average) by a distance of about 5.3x10-11 m. Find the magnitude of the electric force that each particle exerts on the other. Observations: • We are interested in finding the magnitude of the force between two particles of known charge, and a given distance of each other. • The magnitude is given by Coulomb’s law. • q1 =-1.60x10-19 C • q2 =1.60x10-19 C • r = 5.3x10-11 m

25. Question:The electron and proton of a hydrogen atom are separated (on the average) by a distance of about 5.3x10-11 m. Find the magnitude of the electric force that each particle exerts on the other. Observations: • We are interested in finding the magnitude of the force between two particles of known charge, and a given distance of each other. • The magnitude is given by Coulomb’s law. • q1 =-1.60x10-19 C • q2 =1.60x10-19 C • r = 5.3x10-11 m Solution: Attractive force with a magnitude of 8.2x10-8 N.

26. Superposition Principle • From observations: one finds that whenever multiple charges are present, the net force on a given charge is the vector sum of all forces exerted by other charges. • Electric force obeys a superposition principle.

27. y F31 F32 4.00 m 37.0o q2 - + q3 3.00 m q1 x + Example: Using the Superposition Principle Consider three point charges at the corners of a triangle, as shown below. Find the resultant force on q3 if q1 = 6.00 x 10-9 C q2 = -2.00 x 10-9 C q3 = 5.00 x 10-9 C

28. y F31 F32 4.00 m 37.0o q2 - + q3 3.00 m q1 x + Consider three point charges at the corners of a triangle, as shown below. Find the resultant force on q3. Observations: • The superposition principle tells us that the net force on q3 is the vector sum of the forces F32 and F31. • The magnitude of the forces F32 and F31 can calculated using Coulomb’s law.

29. y F31 F32 4.00 m 37.0o q2 - + q3 3.00 m q1 x + Consider three point charges at the corners of a triangle, as shown below. Find the resultant force on q3. 5.00 m Solution:

30. Lightning Review • Properties of electric charge • two types: positive and negative • always conserved and quantized • Insulators and conductors • charges move freely in conductors; opposite is true for insulators • conductors can be charged by conduction and induction; insulators can be polarized • Review Problem: Operating-room personnel must wear special conducting shoes while working around oxygen. Why? What might happen if personnel wore ordinary rubber shoes (sneakers)?

31. Example: Fun with units Recall that units can be manipulated:

32. 15.4 Electric Field - Discovery • Electric forces act through space even in the absence of physical contact. • Suggests the notion of electrical field (first introduced by Michael Faraday (1791-1867). • An electric field is said to exist in a region of space surrounding a charged object. • If another charged object enters a region where an electrical field is present, it will be subject to an electrical force.

33. 15.4 Electric Field – Quantitative Definition • A field : generally changes with position (location) • A vector quantity : magnitude and direction. • Magnitude at a given location • Expressed as a function of the force imparted by the field on a given test charge.

34. 15.4 Electric Field – Quantitative Definition (2) • Direction defined as the direction of the electrical force exerted on a small positive charge placed at that location. E + E • - • - - • - - - • - - • - + + + + + + + + + + + + + + + + + + + + + + + + +

35. 15.4 Electric Field – Electric Field of a Charge “q” • Given • One finds

36. If q>0, field at a given point is radially outward from q. r E qo + q • If q<0, field at a given point is radially inward from q. r - qo E q

37. Problem-Solving Strategy • Electric Forces and Fields • Units: • For calculations that use the Coulomb constant, ke, charges must be in coulombs, and distances in meters. • Conversion are required if quantities are provided in other units. • Applying Coulomb’s law to point charges. • It is important to use the superposition principle properly. • Determine the individual forces first. • Determine the vector sum. • Determine the magnitude and/or the direction as needed.

38. Example: • An electron moving horizontally passes between two horizontal planes, the upper plane charged negatively, and the lower positively. A uniform, upward-directed electric field exists in this region. This field exerts a force on the electron. Describe the motion of the electron in this region. - - - - - - - - - - - - - - - - - - - - - - vo - + + + + + + + + + + + + + + + + + + + + + +

39. - - - - - - - - - - - - - - - - - - - - - - vo - + + + + + + + + + + + + + + + + + + + + + + Observations: • Horizontally: • No electric field • No force • No acceleration • Constant horizontal velocity

40. - - - - - - - - - - - - - - - - - - - - - - vo - + + + + + + + + + + + + + + + + + + + + + + Observations: • Vertically: • Constant electric field • Constant force • Constant acceleration • Vertical velocity increase linearly with time.

41. - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + Conclusions: • The charge will follow a parabolic path downward. • Motion similar to motion under gravitational field only except the downward acceleration is now larger.

42. y E1 E P E2 0.400 m x q1 0.300 m q2 Example: Electric Field Due to Two Point Charges Question: Charge q1=7.00 mC is at the origin, and charge q2=-10.00 mC is on the x axis, 0.300 m from the origin. Find the electric field at point P, which has coordinates (0,0.400) m.

43. Question: Charge q1=7.00 mC is at the origin, and charge q2=-10.00 mC is on the x axis, 0.300 m from the origin. Find the electric field at point P, which has coordinates (0,0.400) m. Observations: • First find the field at point P due to charge q1 and q2. • Field E1 at P due to q1 is vertically upward. • Field E2 at due to q2 is directed towards q2. • The net field at point P is the vector sum of E1 and E2. • The magnitude is obtained with

44. Question: Charge q1=7.00 mC is at the origin, and charge q2=-10.00 mC is on the x axis, 0.300 m from the origin. Find the electric field at point P, which has coordinates (0,0.400) m. Solution:

45. 15.5 Electric Field Lines • A convenient way to visualize field patterns is to draw lines in the direction of the electric field. • Such lines are called field lines. • Remarks: • Electric field vector, E, is tangent to the electric field lines at each point in space. • The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region. E is large when the field lines are close together and small when far apart.

46. 15.5 Electric Field Lines (2) • Electric field lines of single positive (a) and (b) negative charges. a) b) + - q q

47. 15.5 Electric Field Lines (3) • Rules for drawing electric field lines for any charge distribution. • Lines must begin on positive charges (or at infinity) and must terminate on negative charges or in the case of excess charge at infinity. • The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge. • No two field lines can cross each other.

48. 15.5 Electric Field Lines (4) Electric field lines of a dipole. + -

49. Application: Measurement of the atmospheric electric field • The electric field near the surface of the Earth is about 100 N/C downward. Under a thundercloud, the electric field can be as large as 20000 N/C. • How can such a (large) field be measured? A

50. A A A A A A A A A A A A