1. Observations
Place one nylon rod on a rotating stand, and bring another nylon rod close to the first rod, without allowing the rods to touch.

2. Observations
Place one nylon rod on a rotating stand, and bring another nylon rod close to the first rod, without allowing the rods to touch.
Nothing happens.
Repeat after rubbing both rods with a piece of silk.

3. Observations
Place one nylon rod on a rotating stand, and bring another nylon rod close to the first rod, without allowing the rods to touch.
Nothing happens.
Repeat after rubbing both rods with a piece of silk.
Now the rods repel one another. How can we explain this?

4. Observations
Place one nylon rod on a rotating stand, and bring another nylon rod close to the first rod, without allowing the rods to touch.
Nothing happens.
Repeat after rubbing both rods with a piece of silk.
Now the rods repel one another. How can we explain this?
Rubbing a nylon rod with silk transfers electrons from one to the other, giving the rod a net charge. Both rods have a net charge of the same sign, and like charges repel.

5. Observations
When we go through a similar process with rubber rods, using felt or fur, we also observe that the rods repel one another, after they are rubbed with the felt or fur.
What happens when a rubber rod, after being rubbed with felt or fur, is brought close to a nylon rod that has been rubbed with silk?

6. Observations
When we go through a similar process with rubber rods, using felt or fur, we also observe that the rods repel one another, after they are rubbed with the felt or fur.
What happens when a rubber rod, after being rubbed with felt or fur, is brought close to a nylon rod that has been rubbed with silk?
The rods attract, although nothing in our previous observations would allow us to predict that would be the case. This tells us that the signs of the net charges on the rods are opposite, because unlike charges attract.

7. Charging an object
An object can acquire a net charge by touching another material. Which material acquires electrons is determined by where the materials fit in the triboelectric series.
MORE POSITIVE
rabbit's fur
glass
nylon
cat's fur
silk
polyethylene
rubber balloon
MORE NEGATIVE
When materials are rubbed together, the one higher up the list gives electrons to the one further down the list.
Nylon is higher up than silk, so nylon gives up electrons, becoming positive, when rubbed with silk.
Rubber is lower than fur (or felt), so rubber acquires electrons and a negative charge.

8. Our basic model of electric charge
There are two kinds of electric charge, positive and negative.
Objects are generally charged by either acquiring extra electrons (a net negative charge), or giving up electrons (a net positive charge).
Forces between charged objects can be very large. Such forces are really what stop us from falling through the floor. In other words, what we called the normal force is really associated with repulsive forces between electrons.
Our symbol for charge is Q or q.
The unit is the coulomb (C).

9. Four charged objects
The picture shows four charged objects, and the net force that each of the objects experiences because of the other three objects.
How many of these objects are positive?
Two atoms walk into a bar.
Atom 1: I just lost an electron!
Atom 2: Are you sure?
Atom 1: Yes, I’m positive.

10. Four charged objects How many of the objects have a positive charge?
One of them
Two of them
Three of them
Four of them
One or three of them, we can’t tell.

11. Calculating charges
In solving a problem, you calculate the charges on three objects to be:
Q1 = 5 × C; Q2 = 5 × C; Q3 = 5 × C
Are any of these results clearly incorrect?
They’re all wrong
Q1 and Q3 are wrong
Q2 and Q3 are wrong
Q3 is wrong
No - all three of these answers are possible.

12. Calculating charges Q3 = 5 × 10-23 C is definitely a problem.
The issue is that charge is quantized – in general, charge comes in integer multiples of e, the magnitude of the charge on the electron.
e = 1.60 × C
An electron has a charge of –e; a proton has a charge of +e.
Q2 is probably 3e, 4.8 × C.
What is another example of something that is quantized?

13. Calculating charges Q3 = 5 × 10-23 C is definitely a problem.
The issue is that charge is quantized – in general, charge comes in integer multiples of e, the magnitude of the charge on the electron.
e = 1.60 × C
An electron has a charge of –e; a proton has a charge of +e.
Q2 is probably 3e, 4.8 × C.
What is another example of something that is quantized?
Money. The smallest increment, in the American system, is the penny.

14. Charge and mass
A charged rod is touched to a neutral object. When the rod is removed, the object is found to have acquired a charge of +1 C (this is actually an extremely large charge). Is the object heavier or lighter than when it was neutral?
1. Heavier by a significant amount
2. Heavier by just a small amount
3. The mass is unchanged
4. Lighter by just a small amount
5. Lighter by a significant amount

15. Charge and mass
Charging an object almost always involves transferring electrons. In this case, the object must have lost 6.25 x 1018 electrons, making it lighter.
The charge-to-mass ratio of the electron is:
We really want the inverse of this, which is:

16. Two spheres
Two identical metal spheres are charged. Sphere A has a net charge of +7Q. Sphere B has a net charge of -3Q. The spheres are brought together, allowed to touch, and then separated. What is the net charge on each sphere now?

17. Two spheres
Two identical metal spheres are charged. Sphere A has a net charge of +7Q. Sphere B has a net charge of -3Q. The spheres are brought together, allowed to touch, and then separated. What is the net charge on each sphere now?
1. Each sphere has a net charge of +4Q
2. Each sphere has a net charge of +2Q
3. Sphere A has +4Q, Sphere B has no net charge
4. Sphere A has +7Q, Sphere B has -3Q
5. Sphere A has -3Q, Sphere B has +7Q

18. Two spheres
As long as we allow the spheres to touch in a way that no charge is transferred in or out of the system, we can use the idea that charge is conserved – the net charge in the system must be constant at all times.
In this case, the net charge is +7Q -3Q = +4Q. Because the spheres are metal, charge (or, at least, electrons) can move around easily on the spheres. The spheres are identical, so the net charge of +4Q divides evenly between the spheres, giving each sphere a charge of +2Q.

19. Classifying materials
We can classify materials into three broad categories, based on how easily charge flows through them.
Conductors: charge flows easily (e.g., metals).
Semi-conductors: charge flows, but not easily.
Insulators: very little charge flow.
Application: a power cord you plug into a wall socket has two conducting wires to carry electricity to your cell phone and back, but the wires are wrapped with a rubber coating so you do not get a shock.

20. An electroscope neutral charged
An electroscope is a device that indicates the presence of charge. An electroscope is made from metal, which is a conductor. If you put charge at a particular point, the charge will distribute itself over the surface of the conductor.
neutral
charged

21. An electroscope neutral charged
When the electroscope is uncharged, its rotating arm is vertical. When the electroscope is charged, the arm moves away from vertical. This is true as long as there are no charged objects nearby - in a few minutes we'll discuss what happens when there are charged objects nearby.
neutral
charged

22. Charging an electroscope
Let's charge an electroscope by touching it with a charged insulating rod at one spot. Is there a more effective way to charge the electroscope?
1. Rubbing the rod over the electroscope is better
2. Touching and rubbing are equivalent
3. It depends on whether the insulating rod has + charge or - charge

23. Charging an electroscope
If the charged object is an insulator, touching it to the conductor transfers charge only at the few points of contact.
Rubbing the insulator over the conductor is much more effective at transferring charge.
It makes no difference whether the rod has a positive charge or a negative charge.
The conductor acquires charge of the same sign as the charged object brought into contact with it.

24. Playing with an electroscope
We've given an electroscope a positive charge. We then bring a positively charged rod close to, but not touching, the electroscope. What does the indicator arm do?
1. Nothing
2. The arm deflects even more
3. The arm deflects less

25. Playing with an electroscope
The arm deflects more. Bringing a positively charged rod close to the top of the electroscope means electrons are attracted from the arms of the electroscope to the top. With even more positive charge on the arms than before, the repulsive force is stronger.
Bringing a negatively charged rod close to the positively charged electroscope makes the arm deflect less.
Thus, a charged electroscope can distinguish between positively charge objects and negatively charged objects.

26. A soda can
A soda can is an excellent charge detector. If we bring a positively charged nylon rod close to the can, the can is attracted to the rod.
What happens when a negatively charged rubber rod is brought close to the can instead?
1. nothing
2. the can is attracted to the rod
3. the can is repelled by the rod

27. A soda can
In both cases, the soda can is attracted to the charged rod.
What’s the explanation for this?

28. A soda can
In both cases, the soda can is attracted to the charged rod.
Whether the rod is positive or negative, the rod polarizes the can (the can acts like a huge polar molecule) so the side of the can closest to the rod has a charge opposite to the charge on the rod. This leads to a net attractive force between the can and the rod.

29. Try this at home
A thin stream of water is another excellent charge detector.
Amaze your students by charging an object by rubbing it, and then attracting the stream of water toward the charged object.

30. The force between electric charges
Two charged objects, of charge q and Q, separated by a distance r, exert a force on one another. The magnitude of this force is given by:
where k is a constant:
The direction of the force is toward the second object if the objects have opposite signs, and away from the second object if the signs are the same.
What does Coulomb’s Law remind us of?
Coulomb’s Law:

31. The force between electric charges
Two charged objects, of charge q and Q, separated by a distance r, exert a force on one another. The magnitude of this force is given by:
where k is a constant:
The direction of the force is toward the second object if the objects have opposite signs, and away from the second object if the signs are the same.
What does Coulomb’s Law remind us of? Gravity.
Coulomb’s Law:

32. Comparing gravity and the interaction between charges
In general, the force of gravity is much weaker than electrostatic interactions.
Gravity is always attractive, while the force between charges can be attractive or repulsive.
The equations have similar forms, giving rise to similar behavior.

33. The magnitude of the force
Two equal charges Q are placed a certain distance apart. They exert equal-and-opposite forces F on one another. Now one of the charges is doubled in magnitude to 2Q. What happens to the magnitude of the force each charge experiences?

34. The magnitude of the force
Two equal charges Q are placed a certain distance apart. They exert equal-and-opposite forces F on one another. Now one of the charges is doubled in magnitude to 2Q. What happens to the magnitude of the force each charge experiences?
1. Both charges experience forces of magnitude 2F.
2. The Q charge experiences a force of 2F; the 2Q charge experiences a force F.
3. The Q charge experiences a force of F; the 2Q charge experiences a force 2F.
4. None of the above.

35. The magnitude of the force
Let’s examine this question from two perspectives.
Newton’s Third Law – can one object experience a larger force than the other?
2. Coulomb’s Law – if we double one charge, what happens to the force?

36. The magnitude of the force
Let’s examine this question from two perspectives.
Newton’s Third Law – can one object experience a larger force than the other?
No – the objects experience
equal-and-opposite forces.
2. Coulomb’s Law – if we double one charge, what happens to the force?

37. What 1/r2 looks like
The graph shows the force experienced by charge 1 as a function of the position of charge 2.

38. Superposition If an object experiences multiple forces, we can use:
The principle of superposition - the net force acting on an object is the vector sum of the individual forces acting on that object.

39. Worksheet – a one-dimensional situation
Ball A, with a mass 4m, is placed on the x-axis at x = 0. Ball B, which has a mass m, is placed on the x-axis at x = +4a. Where would you place ball C, which also has a mass m, so that ball A feels no net force because of the other balls? Is this even possible?

40. Worksheet – a one-dimensional situation
Ball A, with a mass 4m, is placed on the x-axis at x = 0. Ball B, which has a mass m, is placed on the x-axis at x = +4a. Where would you place ball C, which also has a mass m, so that ball A feels no net force because of the other balls? Is this even possible?

41. Worksheet – a one-dimensional situation
Ball A, with a mass 4m, is placed on the x-axis at x = 0. Ball B, which has a mass m, is placed on the x-axis at x = +4a. Could you re-position ball C, which also has a mass m, so that ball B feels no net force because of the other balls?

42. Worksheet – a one-dimensional situation
Ball A, with a mass 4m, is placed on the x-axis at x = 0. Ball B, which has a mass m, is placed on the x-axis at x = +4a. Could you re-position ball C, which also has a mass m, so that ball B feels no net force because of the other balls?

43. Worksheet – a one-dimensional situation
Ball A, with a charge +4q, is placed on the x-axis at x = 0. Ball B, which has a charge –q, is placed on the x-axis at x = +4a. Where would you place ball C, which has a charge of magnitude q, and could be positive or negative, so that ball A feels no net force because of the other balls?

44. Worksheet – a one-dimensional situation
Ball A, with a charge +4q, is placed on the x-axis at x = 0. Ball B, which has a charge –q, is placed on the x-axis at x = +4a. Where would you place ball C, which has a charge of magnitude q, and could be positive or negative, so that ball A feels no net force because of the other balls?

45. Worksheet – a one-dimensional situation
Ball A, with a charge +4q, is placed on the x-axis at x = 0. Ball B, which has a charge –q, is placed on the x-axis at x = +4a. Where would you place ball C, which has a charge of magnitude q, and could be positive or negative, so that ball A feels no net force because of the other balls?

46. Worksheet – a one-dimensional situation
Ball A, with a charge +4q, is placed on the x-axis at x = 0. Ball B, which has a charge –q, is placed on the x-axis at x = +4a. Could you re-position ball C, which has a charge of magnitude q, and could be positive or negative, so that ball B is the one feeling no net force?

47. Worksheet – a one-dimensional situation
Ball A, with a charge +4q, is placed on the x-axis at x = 0. Ball B, which has a charge –q, is placed on the x-axis at x = +4a. Could you re-position ball C, which has a charge of magnitude q, and could be positive or negative, so that ball B is the one feeling no net force?

48. Worksheet – a one-dimensional situation
Ball A, with a charge +4q, is placed on the x-axis at x = 0. Ball B, which has a charge –q, is placed on the x-axis at x = +4a. Could you re-position ball C, which has a charge of magnitude q, and could be positive or negative, so that ball B is the one feeling no net force?

49. A two-dimensional situation
Case 1: There is an object with a charge of +Q at the center of a square. Can you place a charged object at each corner of the square so the net force acting on the charge in the center is directed toward the top right corner of the square? Each charge has a magnitude of Q, but you get to choose whether it is + or – .

50. Case 1 – let me count the ways.
There is an object with a charge of +Q at the center of a square. Can you place a charged object at each corner of the square so the net force acting on the charge in the center is directed toward the top right corner of the square? Each charge has a magnitude of Q, but you get to choose whether it is + or – .
How many possible configurations can you come up with that will produce the required force?
1. 1
2. 2
3. 3
4. 4
5. either 0 or more than 4

51. A two-dimensional situation
Case 1: There are two ways to make this happen.

52. A two-dimensional situation
Case 2: The net force on the positive center charge is straight down. What are the signs of the equal-magnitude charges occupying each corner? How many possible configurations can you come up with that will produce the desired force?

53. Case 2 – let me count the ways.
There is an object with a charge of +Q at the center of a square. Can you place a charged object at each corner of the square so the net force acting on the charge in the center is directed straight down? Each charge has a magnitude of Q, but you get to choose whether it is + or – .
How many possible configurations can you come up with that will produce the required force?
1. 1
2. 2
3. 3
4. 4
5. either 0 or more than 4

54. A two-dimensional situation
Case 2: This is the only way to produce the desired force.

55. A two-dimensional situation
Case 3: There is no net net force on the positive charge in the center. What are the signs of the equal-magnitude charges occupying each corner? How many possible configurations can you come up with that will produce no net force?

56. Case 3 – let me count the ways.
There is an object with a charge of +Q at the center of a square. Can you place a charged object at each corner of the square so there is no net force acting on the charge in the center? Each charge has a magnitude of Q, but you get to choose whether it is + or – .
How many possible configurations can you come up with that will produce no net force?
1. 1
2. 2
3. 3
4. 4
5. either 0 or more than 4

57. A two-dimensional situation
Case 3: There are four ways to do this. All we need to do is to get the forces from opposite corners to cancel out, which means that opposite corners must be like charges.