A. the rod and fur both gain mass. B. the rod and fur both lose mass.

1. When you rub a plastic rod with fur, the plastic rod becomes negatively charged and the fur becomes positively charged. As a consequence of rubbing the rod with the fur, A. the rod and fur both gain mass. B. the rod and fur both lose mass. C. the rod gains mass and the fur loses mass. D. the rod loses mass and the fur gains mass. E. none of the above

2. A positively-charged piece of plastic exerts an attractive force on an electrically neutral piece of paper. This is because A. electrons are less massive than atomic nuclei. B. the electric force between charged particles decreases with increasing distance. C. an atomic nucleus occupies only a small part of the volume of an atom. D. a typical atom has many electrons but only one nucleus.

3. + + Electric forces ARE strong: Comparing to the gravitational force between an electron and proton: Another example: 2 protons, one held at rest, another released r=2.5 mm Initial acceleration? a(t)? At rest

4. Superposition of electric forces For point charges in vacuum (or in air) – we can add forces as a vector sum q q Find a force acting on one of the charges from the other three q L q Electric field and Electric Forces Electric field E is the force per unit “test” charge: F=q2E Coulomb’s law is “exact” only in electrostatics! (source charges do not move)

5. Charge #2 Three point charges lie at the vertices of an equilateral triangle as shown. All three charges have the same magnitude, but Charge #1 is positive (+q) and Charges #2 and #3 are negative (–q). The net electric force that Charges #2 and #3 exert on Charge #1 is in –q Charge #1 +q y –q x Charge #3 A. the +x-direction. B. the –x-direction. C. the +y-direction. D. the –y-direction. E. none of the above

6. Some Definitions • Electric Field—Field set up by an electric charge in the space surrounding it, which will produce a force on any other charged particle brought into the field. • Vector Field—A field that has both magnitude and direction. It is symbolized by lines; vectors in space. • Test charge—A small positive charge used to determine the electric field. It has to be much smaller than the source charge so that it doesn’t affect the electric field. • Electric Field Lines—Lines that follow the same direction as the electric field vector at any point

7. Electric Field and Electric Forces But charges are finely balanced in nature: The number of protons in a 70 kg body = 2×1028 If two such bodies have that charge imbalanced by just 1%, then the repulsion force at the arm length of 0.5 m would be (9×109) ((2×1026)(1.6×10-19))2/0.52 ~ 1026 N - sufficient to lift a mass of ~ 1026/10 = 1025 kg – on the order of the Earth’s mass!!! It is the electric forces that make solids “solid” and work in chemical reactions, etc

8. Electric field strength – force acting on the unit charge Typical electric field magnitudes (N/C = V/m)

9. Michael Faraday (1791-1867). Field vs action-at-a-distance. In our everyday experiences, we tend to think of a force being exerted only when contact is made between material bodies, as when we push open a door. Newton's law of gravitation had already introduced the notion that a force could act at a distance. But this idea of "action at a distance" deeply troubled many thinkers. At any moment in time, the earth has to "know" instantaneously the sun's position and to "feel" the appropriate force. The phenomenon of electromagnetism demonstrated this apparent action at a distance even more dramatically. That magnets would act on each other while separated by empty space is most alluring to children, and to physicists as well. Like many of his predecessors and contemporaries, Faraday grappled with this philosophical problem and finally reached the following picture. He proposed that an electric charge produces around it an electric field of force. When another charge is introduced into this electric field, the field acts on this charge, exerting on it a force in accordance with Coulomb's law. The important point is that this electric field is to be thought of as a separate entity: The electric field produced by an electric charge exists, regardless of whether another charge is introduced to feel the effect of the field. Similarly, one envisages a magnetic field produced by a magnet or an electric current. Thus, Faraday introduced an intermediary: Two charges do not act "directly" on each other but they each produce an electric field that, in turn, acts on the other charge. (From A. Zee, “Fearful Symmetry”)

10. For non-point charges, we can “divide” a charged body into point charges Electric field of a point charge magnitude magnitude and direction Electric field – vector field, may change from point to point. Think of wind velocity in the atmosphere as an example of a vector field

11. Charge #1 Two point charges and a point P lie at the vertices of an equilateral triangle as shown. Both point charges have the same magnitude q but opposite signs. There is nothing at point P. The net electric field that Charges #1 and #2 produce at point P is in –q P y +q x Charge #2 A. the +x-direction. B. the –x-direction. C. the +y-direction. D. the –y-direction. E. none of the above

12. Example: Find the electric field at point P Reading Assignment :Chapter 21.1-21.4

13. James Clerk Maxwell (1831-1879). Field concept brings fruit. Maxwell put it all together in four mathematical statements, known ever since as Maxwell's equations. The equations specify how the electromagnetic field varies, in space and in time. Armed finally with the correct equations, Maxwell was able to go further. In a flash of insight, he made one of those truly amazing discoveries in physics: the existence of electromagnetic waves. Roughly speaking, if we have in a region of space an electric field changing in time, then a magnetic field is produced in the neighboring space. Its very production means that this magnetic field is also changing in time—and it generates an electric field. Thus, like a ripple on a pond spreading from a dropped pebble, an electromagnetic field propagates out in a wave, undulating between electric and magnetic energy. The value obtained theoretically for the speed of his electromagnetic wave coincides closely with the measured speed of light! And thus Maxwell proclaimed that the mysterious phenomenon of light is just a form of electromagnetic wave. In one stroke, optics as a field of physics was subsumed under the study of electromagnetism. Maxwell's discovery demonstrated conclusively the physical reality of the field and its claim to a separate existence. Indeed, the space around us is literally humming with packets of electromagnetic field hurrying hither and yon. In recent decades, physicists have come to the view that all physical reality is to be described in terms of fields, an idea we will come back to later. It is interesting how this concept originated in the vague philosophical unease physicists felt with the action-at-a-distance hypothesis. (From A. Zee, “Fearful Symmetry”)

14. Maxwell Equations All of the electromagnetism is contained in Maxwell equations! “From a long view of the history of mankind … there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics.” (R.P. Feynman)

15. Electric E and magnetic B fields are vector fields existing at each point of space surrounding charges and that can continuously change in space and time: We will spend time to study how (1) E and B are created by charges (2) Charges are affected by E and B

16. Forces and fields obey the superposition principle: Field from a group of particles is a vector sum of fields from each particle