Physics of Technology PHYS 1800

1. Physics of TechnologyPHYS 1800 Lecture 29 Electricity and Charge

2. PHYSICS OF TECHNOLOGYSpring 2009 Assignment Sheet *Homework Handout

3. Physics of TechnologyPHYS 1800 Lecture 29 Electric Fields and Potentials Electrostatic Force

4. The Electrostatic Force: Coulomb’s Law • Coulomb measured how the electrostatic force varies with distance and quantity of charge. • Since the electrostatic force is so weak, he had to develop special techniques, involving a torsion balance. • The degree of twist of the wire measures the repulsive force between the two charges. • Determining the amount of charge on the balls was more difficult.

5. Historical Perspective on Gravity Cavendish Developed a clever way to measure the weak gravitational force between small masses. Confirmed Newton’s Law of Universal Gravitation (and in essence measured the mass of the Earth in comparison to the kg mass standard). The effect the 320 kg balls of the 1.5 kg balls was about that of a grain of sand! That’s 20 parts per billion precision!!! Wikeapedia has a nice description of the experiment.

6. Coulomb’s Law: Amounts of Charge • Although he could not measure absolute quantities of charge on the balls, Coulomb was able to measure the effects due to different relative amounts of charge. • By bringing two identical metal balls into contact, one charged and the other initially uncharged, Coulomb knew he had equal amounts of charge on both balls. • By repeating the process, he could get a ball with exactly half that charge, or one-fourth, etc. • He could then measure how the strength of the electrostatic force varied when the amount of charge was doubled, quadrupled, etc., in addition to how the force varied with distance between the balls.

7. Coulomb’s Law • The electrostatic force between two charged objects is proportional to the quantity of each of the charges and inversely proportional to the square of each distance between the charges.

8. Two positive charges, one 2 C and the other 7 C, are separated by a distance of 20 cm. What is the magnitude of the electrostatic force that each charge exerts upon the other? • 0.32 N • 0.63 N • 0.70 N • 2.02 N • 3.15 N

9. The Electrostatic and Gravitational Forces • The electrostatic force has the same inverse-square dependence on distance as Newton’s law of gravitation. • If we double the distance between the charges, the force falls to one-fourth of the original. • The gravitational force depends on the masses, and the electrostatic force depends on the charges. • Gravity is always attractive; there is no such thing as negative mass. • Gravity is much weaker than the electrostatic force. • Physicists are still trying to understand the reasons for the relative strengths of the fundamental forces. • The search for a unified field theory that would explain the relationships between all of the fundamental forces is a major area of research in modern theoretical physics.

10. Three positive charges are located along a line as shown. What is the magnitude of the force exerted on the 0.02-C charge by the 0.10-C charge? • 2.25 x 106 N • 4.5 x 106 N • 9.0 x 106 N • 1.8 x 107 N • 2.7 x 108 N

11. Three positive charges are located along a line as shown. What is the magnitude of the force exerted on the 0.02-C charge by the 0.04-C charge? • 1.8 x 106 N • 3.6 x 106 N • 7.2 x 106 N • 1.44 x 107 N • 2.88 x 107 N

12. Three positive charges are located along a line as shown. What is the net force exerted on the 0.02-C charge by the other two charges? • 2.25 x 106 N • 4.5 x 106 N • 9.0 x 106 N • 1.8 x 107 N • 2.7 x 108 N

13. Physics of TechnologyPHYS 1800 Lecture 29 Electric Fields and Potentials Electric Fields

14. The Electric Field • How do the charges exert forces on each other, when they are not even touching? • The concept of an electric field describes how one charge affects the space around it, which then exerts a force on another charge. • The electric field at a given point in space is the electric force per unit positive charge that would be exerted on a charge if it were placed at that point. • It is a vector having the same direction as the force on a positive charge placed at that point. • Compare this to the gravitational field E

15. Two point charges, 3 C and 2 C, are separated by a distance of 30 cm. A third charge q0 is placed between them as shown. The force exerted by q1 on q0 is 10.8 N, and the force exerted by q2 on q0 is 1.8 N.What is the net electrostatic force acting on q0? • 1.8 N to the left • 9 N to the right • 10.8 N to the right • 12.6 N to the right • 12.6 N to the left

16. What is the electric field at the location of the charge q0 due to the other two charges? • 2.25 N/C to the left • 3.0 N/C to the left • 4.5 N/C to the left • 2.25 N/C to the right • 3.0 N/C to the right • 4.5 N/C to the right

17. Forces and the Electric Field • We can then use the electric field to find the force on any other charge placed at that point: • If the charge q is negative, the minus sign indicates that the direction of the force on a negative charge is opposite to the direction of the field. • The direction of the electric field is the direction of the force exerted on a positive test charge. • We can talk about the field at a point in space even if there is no charge at that point. • The electric field can exist even in a vacuum. • The field concept can also be used to define a gravitational field or a magnetic field, as well as others.

18. Electric Field and Field Lines • Although Maxwell was the major contributor to the electric field concept, Faraday also developed the idea of field lines as a means of visualizing both the direction and strength of the field. • The direction of the electric field lines around a positive charge can be found by imagining a positive test charge q0 placed at various points around the source charge. • The field has the same direction as the force on a positive test charge.

19. Electric Field and Field Lines • Although Maxwell was the major contributor to the electric field concept, Faraday also developed the idea of field lines as a means of visualizing both the direction and strength of the field. • The electric field lines associated with a positive charge are directed radially outward.

20. Electric Field and Field Lines • Although Maxwell was the major contributor to the electric field concept, Faraday also developed the idea of field lines as a means of visualizing both the direction and strength of the field. • A positive test charge is attracted to a negative charge. • The electric field lines associated with a negative charge are directed inward, as indicated by the force on a positive test charge, q0.

21. Dipole Electric Field and Field Lines • An electric dipole is two charges of equal magnitude but opposite sign, separated by a small distance. • You just add the vectors!!! • Electric field lines originate on positive charges and end on negative charges. • The field lines point away from the positive charge, and in toward the negative charge. • Near each charge, the electric field approximates the field due to a single point charge of the same sign.

22. Two charges, of equal magnitude but opposite sign, lie along a line as shown. What are the directions of the electric field at points A, B, C, and D? • A:left, B:left, C:right, D:right • A:left, B:right, C:right, D:right • A:left, B:right, C:right, D:left • A:right, B:left, C:left, D:right • A:right, B:left, C:right, D:right

23. Physics of TechnologyPHYS 1800 Lecture 29 Electric Fields and Potentials Electrostatic Potential

24. Electric Potential • The electrostatic force is a conservative force, which means we can define an electrostatic potential energy. • We can therefore define electric potential or voltage. • Two parallel metal plates containing equal but opposite charges produce a uniform electric field between the plates. • This arrangement is an example of a capacitor, a device to store charge.

25. Electric Potential • A positive test charge placed in the uniform electric field will experience an electrostatic force in the direction of the electric field. • An external force F, equal in magnitude to the electrostatic force qE, will move the charge q a distance d in the uniform field. • The external force does work on the charge and increases the potential energy of the charge. • The work done by the external force is qEd, the force times the distance. • This is equal to the increase in potential energy of the charge: PE = qEd. • This is analogous to what happens when a mass m is lifted against the gravitational force.

26. Electric Potential • Electric potential is related to electrostatic potential energy in much the same way as electric field is related to electrostatic force. • The change in electric potential is equal to the change in electrostatic potential energy per unit of positive test charge: • Electric potential and potential energy are closely related, but they are NOT the same. • If the charge q is negative, its potential energy will decrease when it is moved in the direction of increasing electric potential. • It is the change in potential energy that is meaningful.

27. Two plates are oppositely charged so that they have a uniform electric field of 1000 N/C between them, as shown. A particle with a charge of +0.005 C is moved from the bottom (negative) plate to the top plate. What is the change in potential energy of the charge? • 0.15 J • 0.3 J • 0.5 J • 0.8 J • 1.5 J

28. What is the change in electric potential from the bottom to the top plate? • 0.15 V • 0.3 V • 5 V • 30 V • 150 V

29. Relation between Electric Potential and Electric Field • The potential energy of a positive charge increases when we move it against the field. • For a uniform electric field, there is a simple relationship between the magnitude of the electric field and the change in electric potential: V = Ed. • For non-uniform fields, the relationship is more complicated, but the electric potential always increases most rapidly in the direction opposite to the electric field. • For a positive point charge, the electric potential increases as we move closer to the charge.

30. What is lightning? • Most thunderclouds generate a separation of charge resulting in a net positive charge near the top and a net negative charge near the bottom. • The charge separation produces strong electric fields in the cloud as well as between the cloud and earth. • Since moist earth is a reasonably good conductor, a positive charge is induced on the surface of the earth below the cloud.

31. Moving a charge in an electric field changes the electric PE and electric potential (the voltage!). Thus moving charge (current) is directly related to change in voltage.Sounds like circuits to me!!! Circuits and Electric Potential and Electric Field V= 30 V V= 0 V

32. Electric Potential and Electric Field of Lightning • The electric field generated can be several thousand volts per meter; the potential difference between the cloud’s base and the earth can easily be several million volts! • This creates an initial flow of charge (the “leader”) along a path that offers the best conducting properties over the shortest distance. • The leader ionizes some of the atoms in the air along that path. • The following strokes all take place along this same path in rapid succession. • The heating and ionizing produce the lightning we see. • The thunder (sound waves) is produced at the same time, but takes longer to reach us since sound travels slower than light.

33. Physics of Technology Next Lab/Demo: Electric Charge Electric Circuits Thursday 1:30-2:45 ESLC 46 Ch 12 and 13 Next Class: Wednesday 10:30-11:20 BUS 318 room Read Ch 13