1. ELECTRICITY AND MAGNETISM Phy 220 Chapter1: ELECTRIC FIELDS

2. 10/20/20152 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.

3. 10/20/20153 1.1 Properties of Electric Charges Observation of “Static Electricity” A comb passed though hair attracts small pieces of paper. A comb passed though hair attracts small pieces of paper. An inflated balloon rubbed with wool. An inflated balloon rubbed with wool. Two kinds of charges Named by Benjamin Franklin (1706-1790) as positive and negative. Named by Benjamin Franklin (1706-1790) as positive and negative. Like charges repel one another and unlike charges attract one another. Electric charge is however always conserved. Charge is neither created nor disappeared. Charge is neither created nor disappeared. Usually, negative charge (electron) is transferred from one object to the other. Usually, negative charge (electron) is transferred from one object to the other.

4. 10/20/20154 Robert Millikan found, in 1909, that charged objects may only have an integer multiple of a fundamental unit of charge. Charge is quantized. Charge is quantized. An object may have a charge  e, or  2e, or  3e, etc but not say  1.5e. An object may have a charge  e, or  2e, or  3e, etc but not say  1.5e. Proton has a charge +1e. Proton has a charge +1e. Electron has a charge –1e. Electron has a charge –1e. Some particles such a neutron have no (zero) charge. Some particles such a neutron have no (zero) charge. A neutral atom has as many positive and negative charges. A neutral atom has as many positive and negative charges.Units In SI, electrical charge is measured in coulomb ( C). In SI, electrical charge is measured in coulomb ( C). The value of |e| = 1.602 19 x 10 -19 C. The value of |e| = 1.602 19 x 10 -19 C.

5. 10/20/20155 1.2 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. 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 |q 1 | and |q 2 | on the two particles. Proportional to the product of the magnitudes of the charges |q 1 | and |q 2 | on the two particles. Attractive if the charges are of opposite sign and repulsive if the charges have the same sign. Attractive if the charges are of opposite sign and repulsive if the charges have the same sign. q1q1 q2q2 r

6. 1.2 Coulomb’s Law – Mathematical Formulation k e known as the Coulomb constant. Value of k e depends on the choice of units. SI units – Force: the Newton (N) – Distance: the meter (m). – Charge: the coulomb ( C). – Current: the ampere (A =1 C/s). Experimentally measurement: k e = 8.9875  10 9 Nm 2 /C 2. Reasonable approximate value: k e = 8.99  10 9 Nm 2 /C 2. 10/20/20156 How do we know the units of k e ?

7. 10/20/20157 Example: Fun with units Recall that units can be manipulated:

8. Example 1e = -1.60  10 -19 c Takes 1/e=6.6  10 18 protons to create a total charge of 1C Number of free electrons in 1 cm 3 copper ~ 10 23 Charge obtained in typical electrostatic experiments with rubber or glass 10 -6 C = 1  c 10/20/20158 Charge and Mass of the Electron, Proton and Neutron. Particle Charge ( C) Mass (kg) Electron -1.60  10 -19 9.11  10 -31 Proton +1.60  10 -19 1.67  10 -27 Neutron0

9. 1.2 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. 910/20/2015 + + r q1q1 q2q2 + - r q1q1 q2q2

10. 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. 10/20/201510

11. 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. 1110/20/2015 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. q 1 =-1.60x10 -19 C q 2 =1.60x10 -19 C r = 5.3x10 -11 m

12. 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. q 1 =-1.60x10 -19 C q 2 =1.60x10 -19 C r = 5.3x10 -11 m Solution: Attractive force with a magnitude of 8.2x10 -8 N. 10/20/201512

13. 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. 10/20/201513

14. Example: Using the Superposition Principle Consider three point charges at the corners of a triangle, as shown below. Find the resultant force on q 3 if q 1 = 6.00 x 10 -9 C q 2 = -2.00 x 10 -9 C q 3 = 5.00 x 10 -9 C 10/20/201514 + x y -+ q2q2 q1q1 3.00 m 4.00 m q3q3 F 32 F 31 37.0 o

15. Consider three point charges at the corners of a triangle, as shown below. Find the resultant force on q 3. Observations: The superposition principle tells us that the net force on q 3 is the vector sum of the forces F 32 and F 31. The magnitude of the forces F 32 and F 31 can calculated using Coulomb’s law. 10/20/201515 + x y -+ q2q2 q1q1 3.00 m 4.00 m q3q3 F 32 F 31 37.0 o

16. 1610/20/2015 Consider three point charges at the corners of a triangle, as shown below. Find the resultant force on q 3. 5.00 m Solution: + x y -+ q2q2 q1q1 3.00 m 4.00 m q3q3 F 32 F 31 37.0 o

17. 1.3 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. 10/20/201517

18. 1.3 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. 10/20/201518

19. 1.3 Electric Field – Quantitative Definition (2) Direction defined as the direction of the electrical force exerted on a small positive charge placed at that location. 1910/20/2015 - - - - - - - - - - + + + + + + + + + + + + + + + + +

20. 1.3 Electric Field – Electric Field of a Charge “q” Given One finds 10/20/201520

21. 10/20/201521 + r q qoqo - r q qoqo If q>0, field at a given point is radially outward from q. If q<0, field at a given point is radially inward from q.

22. Problem-Solving Strategy Electric Forces and Fields – Units: For calculations that use the Coulomb constant, k e, 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. 10/20/201522

23. 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. 10/20/201523 - vovo - - - - - - - - - - - + + + + + + + + + + +

24. Observations: Horizontally: – No electric field – No force – No acceleration – Constant horizontal velocity 2410/20/2015 - vovo - - - - - - - - - - - + + + + + + + + + + +

25. 10/20/201525 - vovo - - - - - - - - - - - + + + + + + + + + + + Observations:Vertically: Constant electric field Constant electric field Constant force Constant force Constant acceleration Constant acceleration Vertical velocity increase linearly with time. Vertical velocity increase linearly with time.

26. 10/20/201526 - - - - - - - - - - - - + + + + + + + + + + + Conclusions: The charge will follow a parabolic path downward. Motion similar to motion under gravitational field only except the downward acceleration is now larger.

27. Example: Electric Field Due to Two Point Charges Question: Charge q 1 =7.00  C is at the origin, and charge q 2 =-10.00  C 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. 2710/20/2015 x y 0.300 m q1q1 q2q2 0.400 m P

28. Question: Charge q 1 =7.00  C is at the origin, and charge q 2 =-10.00  C 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 q 1 and q 2. Field E 1 at P due to q 1 is vertically upward. Field E 2 at due to q 2 is directed towards q 2. The net field at point P is the vector sum of E 1 and E 2. The magnitude is obtained with 2810/20/2015

29. Question: Charge q 1 =7.00  C is at the origin, and charge q 2 =-10.00  C 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: 2910/20/2015

30. 1.4 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: 1.Electric field vector, E, is tangent to the electric field lines at each point in space. 2.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. 10/20/201530

31. 1.4 Electric Field Lines (2) Electric field lines of single positive (a) and (b) negative charges. 10/20/201531 + q a) - q b)

32. 1.4 Electric Field Lines (3) Rules for drawing electric field lines for any charge distribution. 1.Lines must begin on positive charges (or at infinity) and must terminate on negative charges or in the case of excess charge at infinity. 2.The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge. 3.No two field lines can cross each other. 10/20/201532

33. 1.4 Electric Field Lines (4) 10/20/201533 Electric field lines of a dipole. + -

34. 10/20/201534 1.4 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. Glass, Rubber are good insulators. Copper, aluminum, and silver are good conductors. 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. Silicon and germanium are semiconductors used widely in the fabrication of electronic devices.

35. Conductors in Electrostatic Equilibrium Good conductors (e.g. copper, gold) contain charges (electron) that are not bound to a particular atom, and are free to move within the material. When no net motion of these electrons occur the conductor is said to be in electro-static equilibrium. 10/20/201535