Outline. March 2 is the day of the first midterm Heads up! Recap of electric forces Fields Examples. 2/17/17 Physics 132 1

Transcription

1 Outline March 2 is the day of the first midterm Heads up! Recap of electric forces Fields Examples 2/17/17 Physics 132 1

2 The Electric Field!!!! Fq ( r ) E (r ) = q 2/17/17 2 Physics 132

3 Foothold idea: Charge A hidden property of matter Matter is made up of two kinds of electrical matter (positive and negative) that usually cancel very precisely. Like charges repel, unlike charges attract. Bringing an unbalanced charge up to neutral matter polarizes it, so both kinds of charge attract neutral matter The total amount of charge (pos neg) is constant. 2/17/17 3 Physics 132

4 Foothold idea: Conductors and Insulators Insulators In some matter, the charges they contain are bound and cannot move around freely. Excess charge put onto this kind of matter tends to just sit there (like spreading peanut butter). Conductors In some matter, charges in it can move around throughout the object. Excess charge put onto this kind of matter redistributes itself or flows off (if there is a conducting path to ground). 2/17/17 4 Physics 132

5 Foothold idea: Coulomb s Law All objects attract each other with a force whose magnitude is given by F = F = k CqQ q Q Q q r qq 2 ˆr q Q k C is put in to make the units come out right. k C = N-m 2 / C 2 2/17/17 5 Physics 132

6 Making sense of Coulomb s Law It s about the force one point charge exerts on another It only works for point charges! It s proportional to the product of the two charges The direction is correctly given if the unit vector direction matches the labels on the force and the charges include their signs. F = F = k C qq q Q Q q It satisfies Newton s third law It gets weaker as the charges get farther apart like the square of the distance between them. 2/17/17 Physics r qq 2 ˆr q Q It points along the line joining the two charges (this is a unit vector only shows direction)

7 Making sense of Coulomb s Law It s about the force one point charge exerts on another It only works for point charges! It s proportional to the product of the two charges The direction is correctly given if the unit vector direction matches the labels on the force and the charges include their signs. F = F = k C qq q Q Q q It satisfies Newton s third law It gets weaker as the charges get farther apart like the square of the distance between them. 2/17/17 Physics r qq 2 ˆr q Q It points along the line joining the two charges (this is a unit vector only shows direction)

8 Three identical charges are lined up in a row. If we compare the electric force charge q 1 exerts on charge q 3 (F 1 3 ) to the force q 2 exerts on charge q 3 (F 2 3 ) 1. F 1 3 is twice as big as F F 1 3 is half as big as F F 1 3 is more than twice as big as F F 1 3 is less than half as big as F F 1 3 doesn t affect q 3 at all since q 2 is in the way.

9 Two small objects each with a net charge of +Q exert a force of magnitude F on each other (top figure). We replace one of the objects with another whose net charge is +4Q (bottom figure). The original magnitude of the force on the +Q charge was F. What is the magnitude of the force on the +Q now? 1. 16F 2. 4F 3. F 4. F/4 5. Something else.

10 In the original state we assumed Q was positive. If the symbol Q were taken to have a negative value, how would the forces change compared to the original state? 1. Would stay the same 2. Both would reverse 3. Only the left force would reverse 4. Only the right force would reverse 5. Something else

11 Foothold idea: Energies in charge clusters Atoms and molecules are made up of charges. The potential energy between two charges is U elec 12 = k Q Q C 1 2 r 12 The potential energy between many charges is elec U 12...N = N i< j=1 k C Q i Q j r ij 2/17/17 11 Physics 132

12 Electric energy If we start with a system of charge q 1, q 2,..., q N the electric potential energy of the system is U elec 1...N = i< j N j=1 k C q i q j r ij Electric energy of the system of charges q 1,,,q N Sum over all distinct pairs of charges Electric Potential Energy of the pair q i, q j 2/17/17 Physics

13 Adding a test charge. We are often interested to what happens to one last charge (a test charge ) when we add it to a system of already existing charges. Assuming that the charges 1...N don t move when we add a charge q 0, the new electric energy after adding the charge is U elec 01...N = U elec 1...N + U elec 0 = NX kc q 0 q j j=1 r 0j NX j=1 = q 0 kc q 0 q j r 0j 2/17/17 Physics NX 3 kc q j 5 j=1 r 0j

14 Why fields? Fields are a useful way to talk about forces that act without touching. It reduces the spookiness of objects interacting when they are far apart. The source object creates an effect (field) everywhere and the test object measures that effect where it is. (Only psychological value) Fields allow us to talk about forces due to many charges that we don t know how to specify or where they are. Since all matter has lots of charge we can t specify where each charge is. Summing over them all would be impossible. Talking about what fields they produce allows us to sum the effect of many charges. (This is a real practical value) 2/17/17 Physics

15 Foothold idea: Fields Test particle We pay attention to what force it feels. We assume it has no effect on the source particles. Source particles We pay attention to the forces they exert and assume they do not move. Physical field We consider what force a test particle would feel if it were at a particular point in space and divide by its coupling strength to the force. This gives a vector at each point in space. g = 1 m 1 W E m E = q F all charges q V = 1 q U elec all charges q 2/17/17 Physics

16 Units Gravitational field units of g = Newtons/kg Electric field units of E = Newtons/C (also Volts/m) Electric potential units of V = Joules/C = Volts Energy = qv, so eδv = the energy gained by an electron (charge e = 1.6 x C) in moving through a change of ΔV volts. 1 ev = 1.6 x J A very useful and natural unit when dealing with individual atoms and molecules! 2/17/17 Physics

17 Reading question Are electric fields and gravitational fields the same regarding the acceleration that results from them? For example, in free fall all objects accelerate toward the center of Earth with the same magnitude regardless of mass. In an electric field, do source charges accelerate toward test charges with the same magnitude regardless of charge? What do you think? 2/17/17 Physics

18 The electric field at a particular point in space 1. Depends only on the magnitude of the test charge used to measure it. 2. Depends only on the sign of the test charge used to measure it. 3. Depends on both the sign and magnitude of the test charge used to measure it. 4. Does not depend on the test charge used to measure it. 5. None of the above.

19 A test charge, q, is a distance d from a charge Q as shown. It feels an electric field, E 0. If q were replaced by a charge 3q, the electric field on it would 1. Change to -3E 0 2. Change to -E 0 /3 3. Not change 4. Change to 3E 0 5. Change to E 0 /3 6. Something else

20 A test charge, q, is a distance d from a charge Q as shown. It feels an electric force, F 0. If q were replaced by a charge -3q, the electric force on it would 1. Change to -3F 0 2. Change to -F 0 /3 3. Not change 4. Change to 3F 0 5. Change to F 0 /3 6. Something else

21 Explore the field near a point charge 2/17/17 21 Physics 132