Coulomb’s law
Why do packing peanuts stick to you, or a cat?
Reading: Mazur 22-­‐4 to 22-­‐6
Charge polarization
Coulomb’s law
Force exerted by distributions of charge carriers
LECTURE 1
1
22.4 Charge polarization / demo
Any separation of charge carriers in an object is called charge polarization, or simply polarization.
Demo: ◦ If we bring a positively charged object next to a metal the electrons in the metal will move towards the charged object.
◦ Likewise, if we bring a negatively charged object next to a metal the electrons in the metal will move away from the charged object.
◦ Due to conservation of charge this must leave a positive charge where the electrons have moved from.
LECTURE 2
2
Question: 22.4-­‐1 (Charge of object) A negatively charged object A attracts object B and repels object C. Which state or states are possible for objects B and C?
A.
B.
C.
D.
E.
F.
Object B is positively charged
Object B is neutral
Object B is negatively charged
Object C is positively charged
Object C is neutral
Object C is negatively charged
LECTURE 2
3
Question: 22.4-­‐1 (Charge of object) answer
A negatively charged object A attracts object B and repels object C. Which state or states are possible for objects B and C?
A.
B.
C.
D.
E.
F.
Object B is positively charged
Object B is neutral
Object B is negatively charged
Object C is positively charged
Object C is neutral
Object C is negatively charged
Like charges repel and opposite charges attract.
If object C is neutral then object A could cause charge polarization such that the positive charge in object C is closer to object A than the equal negative charge, and hence it attracts.
LECTURE 2
4
Demo: Attraction by charge separation
A positively charged rod or a negatively charged rod will attract a neutral metal rod and a wooden rod.
The metal rod is a conductor, so electrons are free to move causing charge polarization.
The wood rod is an insulator, so charge polarization is caused by a small shift in the electron cloud that surrounds the proton.
LECTURE 2
5
Reading quiz (Problem 22.26)
Metal sphere A is hung from the ceiling by a long, thin string and given a positive charge. An identical sphere B is suspended nearby with an identical string and given a negative charge that has the same magnitude as the charge on A . The two spheres are 50 mm apart when in equilibrium.
If an identical sphere C carrying no surplus charge is placed between them, does the distance between A and B increase, decrease, or remain the same?
A.
B.
C.
The distance decreases.
The distance remains the same.
The distance increases.
The charge carriers in C separate and move closer to the two spheres (A and B). This strengthens the interaction.
LECTURE 2
6
So why do packing peanuts stick to you?
The packing peanuts are insulators and can get charged easily.
As these charged packing peanuts get close to objects, they cause charge separation within the object. Since the opposite charge is closer to each other, the attractive force is stronger than the repulsive force between the similar charges.
LECTURE 2
7
Question: 22.4-­‐2 (Touching conducting spheres)
Two identical conducting spheres, one has an initial charge +Q, the other initially uncharged, are brought into contact. While the spheres are in contact, a positively charged rod is moved close to one sphere, causing a redistribution of the charges on the two spheres so the charge on the sphere closest to the rod has a charge of -­‐Q. What is the charge on the other sphere?
A.
B.
C.
D.
E.
-­‐2Q
-­‐Q
zero
+Q
+2Q
LECTURE 2
8
Question: 22.4-­‐2 (Touching conducting spheres) answer
Two identical conducting spheres, one has an initial charge +Q, the other initially uncharged, are brought into contact. While the spheres are in contact, a positively charged rod is moved close to one sphere, causing a redistribution of the charges on the two spheres so the charge on the sphere closest to the rod has a charge of -­‐Q. What is the charge on the other sphere?
A.
B.
C.
D.
E.
-­‐2Q
-­‐Q
zero
+Q
+2Q The initial net charge of both spheres is +Q.
Since the spheres are isolated from everything else the net charge of the two spheres must remain +Q.
One sphere has a charge of –Q so the other must have a charge of +2Q.
LECTURE 2
9
Demo: Charging by induction
LECTURE 2
10
Question: 22.4-­‐3 (Charging an neutral object)
You can use a positively charged object to charge a neutral object by conduction or by induction. Select the charge of the neutral object for each process.
A.
B.
C.
D.
Charging by conduction: The neutral object becomes positively charged.
Charging by conduction: The neutral object becomes negatively charged.
Charging by induction: The neutral object becomes positively charged.
Charging by induction: The neutral object becomes negatively charged.
LECTURE 2
11
Question: 22.4-­‐3 (Charging an neutral object) answer
You can use a positively charged object to charge a neutral object by conduction or by induction. Select the charge of the neutral object for each process.
A.
B.
C.
D.
Charging by conduction: The neutral object becomes positively charged.
Charging by conduction: The neutral object becomes negatively charged.
Charging by induction: The neutral object becomes positively charged.
Charging by induction: The neutral object becomes negatively charged.
Charging by conduction: When the two objects are brought into contact with each other (a necessary condition for conduction), surplus positive charge moves from the charged object to the neutral one. Thus the neutral object acquires the same type of charge as the charged object.
Charging by induction: Because the objects don’t touch during charging by induction, charge carriers of the same type as the charged object escape from the neutral object during grounding.
LECTURE 2
12
22.5 Coulomb’s law
If two charged particles having charges 𝑞" and 𝑞# are separated by a distance 𝑟"# , then the magnitude of the electric force between them is given by Coulomb’s law:
&
𝐹"#
𝑞" 𝑞#
=𝑘
#
𝑟"#
The constant is 𝑘 = 9.0×10. N 1 m# C 4#
Including direction, Coulomb’s law becomes
&
𝐹⃗"#
=𝑘
𝑞" 𝑞#
# 𝑟̂"#
𝑟"#
LECTURE 2
13
22.5 Coulomb’s law -­‐ Charge quantization
All electrical charge comes in whole-­‐number multiples of elementary charge, 𝑒 = 1.6×104". C, which is the magnitude of the electron charge.
For fun: ◦ Search for fractionally charged particles
◦ Quarks have a smaller charge than an electron, but they do not occur as free particles.
◦ An up quark has charge +⅔ e
◦ A down quark has charge -­‐⅓ e
◦ A proton consists of 2 up quarks and 1 down quark, total charge +e
◦ A neutron consists of 1 up quark and 2 down quarks, total charge 0
Number of drops
◦ http://www.slac.stanford.edu/exp/mps/FCS/FCS_rslt.htm
Charge of drop in units of e
LECTURE 1
14
Reading quiz (Problem 22.30)
Two particles carrying charges 𝑞" and 𝑞# are separated by a distance 𝑟 and exert an electric force 𝐹⃗ & on each other.
If 𝑞" is doubled, what change must you make to one of the other variables in order to keep the magnitude 𝐹 & constant? There is more than one answer.
Check all that apply.
9
#
A.
𝑟 should be changed to .
B.
𝑟 should be halved.
C.
𝑞# should be changed to 2𝑞# .
D.
𝑞# should be changed to = .
E.
F.
𝑞# should be doubled.
𝑞# should be halved.
G.
𝑟 should be changed to 2𝑟.
H.
𝑟 should be doubled.
<
#
&
𝐹"#
=𝑘
<> <=
=
9>=
LECTURE 2
15
Question: 22.5-­‐1 (Coulomb force)
Two uniformly charged spheres are firmly fastened to and electrically insulated from frictionless pucks on an air table. The charge on sphere 2 is three times the charge on sphere 1. Which force diagram correctly shows the magnitude and direction of the electrostatic forces?
A.
B.
C.
D.
E.
F.
G.
1
2
3
4
5
6
None of the above
LECTURE 2
16
Question: 22.5-­‐1 (Coulomb force) answer
Two uniformly charged spheres are firmly fastened to and electrically insulated from frictionless pucks on an air table. The charge on sphere 2 is three times the charge on sphere 1. Which force diagram correctly shows the magnitude and direction of the electrostatic forces?
A.
B.
C.
D.
E.
F.
G.
1
2
3
4
5
6
None of the above
This is an interaction pair. The magnitude of the force on the left sphere due to the right sphere must be equal to the magnitude of the force on the right sphere due to the left sphere. Since the spheres have like charges they must repel, so the force is directed away from the other sphere.
LECTURE 2
17
Example: 22.5-­‐1 (Mazur 22.31)
A particle carrying a −4.6-­‐μC charge is located at the origin of an 𝑥𝑦 coordinate system.
What are the components of the electric force exerted on a particle carrying a 1.6-­‐μC charge if that particle is located at 𝑥 = 10 m, 𝑦 = 0?
LECTURE 2
18
Reading quiz (Problem 22.14)
A closed system consists of a neutron and a positron. The neutron eventually decays.
Right after decay, what are the most likely particles in the system and what is the charge in the system? (Use the principle of conservation of charge.)
A.
B.
C.
D.
Proton, electron, and antineutrino. The total charge is zero.
Proton, electron, antineutrino and positron. The total charge is +e.
Proton, positron, and antineutrino. The total charge is +2e.
The particles annihilate leaving nothing but a flash of highly energetic radiation. The total charge is zero.
The initial total charge of the system is +e (0 for neutron and +e for positron), so the final total charge of the system is also +e.
LECTURE 1
19
22.6 Force exerted by distributions of charge carriers
The force exerted by an assembly of objects carrying charges 𝑞# , 𝑞A , 𝑞B . . . on an object 1 carrying charge 𝑞" is the vector sum of all the forces exerted on object 1
&
&
&
𝐹⃗"& = 𝐹⃗#"
+ 𝐹⃗A"
+ 𝐹⃗B"
+⋯
LECTURE 2
20
Reading quiz (Placing Charges Conceptual Question)
Below are free-­‐body diagrams for three electric charges that lie in the same plane. Their relative positions are unknown.
Along which of the lines (A to H) in the figure should charge 2 be placed so that the free-­‐
body diagrams of charge 1 and charge 2 are consistent?
C) There should be an interaction pair
Along which of the lines (A to H) in the figure should charge 3 be placed so that the free-­‐
body diagrams of charge 1, charge 2, and charge 3 are consistent?
D) There should be an interaction pair
LECTURE 2
21
Question 22.6-­‐1 (Compare electric forces)
Consider the two cases shown below. In both cases a central charge 𝑞 has two charges of equal magnitude at equal distances above and below it. In case 1 the signs of the two outer charges is opposite, and in case 2 they are both positive. You are not told the sign of the charge in the center 𝑞.
In which case is the magnitude of the net force on the center charge bigger?
A.
B.
C.
D.
Case 1
Case 2
They are the same
We need more information
LECTURE 2
22
Question 22.6-­‐1 (Compare electric forces) answer
Consider the two cases shown below. In both cases a central charge 𝑞 has two charges of equal magnitude at equal distances above and below it. In case 1 the signs of the two outer charges is opposite, and in case 2 they are both positive. You are not told the sign of the charge in the center 𝑞.
In which case is the magnitude of the net force on the center charge bigger?
A.
B.
C.
D.
Case 1
Case 2
They are the same
We need more information
The arrows show the direction of the force from each charge assuming 𝑞 is positive. If 𝑞 were negative the direction of each arrow would be reversed.
LECTURE 2
23
Question: 22.6-­‐2 (Forces from 4 charges)
A positive charge 𝑄 is placed at the origin. Four other positive charges are placed on a circle in the 𝑥𝑦 plane centered on 𝑄 as shown. The top charge is located on the 𝑦 axis and has a magnitude of 3𝑞. The three bottom charges are symmetric about the 𝑦 axis as shown and each has magnitude 𝑞. Which of the following statements best describes 𝐹G& (the 𝑦 component of the force on the charge at the origin)?
A. 𝐹G& > 0
B. 𝐹G& = 0
C. 𝐹G& < 0
LECTURE 2
24
Question: 22.6-­‐2 (Forces from 4 charges) answer
A positive charge 𝑄 is placed at the origin. Four other positive charges are placed on a circle in the 𝑥𝑦 plane centered on 𝑄 as shown. The top charge is located on the 𝑦 axis and has a magnitude of 3𝑞. The three bottom charges are symmetric about the 𝑦 axis as shown and each has magnitude 𝑞. Which of the following statements best describes 𝐹G& (the 𝑦 component of the force the 𝑦 component of the force on the charge at the origin)?
A. 𝐹G& > 0
B. 𝐹G& = 0
C. 𝐹G& < 0
The magnitude of the force on 𝑄 from the 3𝑞 charge is three times that from each of the 𝑞 charges. The charges that are not on the 𝑦 axis only have a fraction of the total force along the 𝑦
direction. So the downward force from the 3𝑞 charge is bigger.
LECTURE 2
25