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Conductors and insulators

Conductors and insulators

All atoms are electrically neutral i.e. they have the same amounts of negative and positive charge inside them. By convention, the electrons carry negative charge and the protons carry positive charge. The basic unit of charge, called the elementary charge, e, is the amount of charge carried by one electron.

The charge on a single electron is qe=1,6x10-19Cqe=1,6x10-19C. All other charges in the universe consist of an interger multiple of this charge (i.e. Q=nqeQ=nqe). This is known as charge quantisation.

All the matter and materials on earth are made up of atoms. Some materials allow electrons to move relatively freely through them (e.g. most metals, the human body). These materials are called conductors.

Other materials do not allow the charge carriers, the electrons, to move through them (e.g. plastic, glass). The electrons are bound to the atoms in the material. These materials are called non-conductors or insulators.

If an excess of charge is placed on an insulator, it will stay where it is put and there will be a concentration of charge in that area of the object. However, if an excess of charge is placed on a conductor, the like charges will repel each other and spread out over the outside surface of the object. When two conductors are made to touch, the total charge on them is shared between the two. If the two conductors are identical, then each conductor will be left with half of the total charge.

Note: Electrostatic Force:

The electrostatic force determines the arrangement of charge on the surface of conductors. This is possible because charges can move inside a conductive material. When we place a charge on a spherical conductor the repulsive forces between the individual like charges cause them to spread uniformly over the surface of the sphere. However, for conductors with non-regular shapes, there is a concentration of charge near the point or points of the object. Notice in Figure 1 that we show a concentration of charge with more -- or + signs, while we represent uniformly spread charges with uniformly spaced -- or + signs.

This collection of charge can actually allow charge to leak off the conductor if the point is sharp enough. It is for this reason that buildings often have a lightning rod on the roof to remove any charge the building has collected. This minimises the possibility of the building being struck by lightning. This “spreading out” of charge would not occur if we were to place the charge on an insulator since charge cannot move in insulators.

Aside: Charge and electrons:

The basic unit of charge, namely the elementary charge is carried by the electron (equal to 1.602×10-19×10-19 C!). In a conducting material (e.g. copper), when the atoms bond to form the material, some of the outermost, loosely bound electrons become detached from the individual atoms and so become free to move around. The charge carried by these electrons can move around in the material. In insulators, there are very few, if any, free electrons and so the charge cannot move around in the material.

Note: Interesting fact:

In 1909 Robert Millikan and Harvey Fletcher measured the charge on an electron. This experiment is now known as Millikan's oil drop experiment. Millikan and Fletcher sprayed oil droplets into the space between two charged plates and used what they knew about forces and in particular the electric force to determine the charge on an electron.

Exercise 1: Conducting spheres and movement of charge

I have 2 charged metal conducting spheres which are identical except for having different charge. Sphere A has a charge of -5 nC and sphere B has a charge of -3 nC. I then bring the spheres together so that they touch each other. Afterwards I move the two spheres apart so that they are no longer touching.

1. What happens to the charge on the two spheres?
2. What is the final charge on each sphere?

Solution

1. Step 1. Identify what is known and what question/s we need to answer: :

We have two identical negatively charged conducting spheres which are brought together to touch each other and then taken apart again. We need to explain what happens to the charge on each sphere and what the final charge on each sphere is after they are moved apart.

2. Step 2. What concept is being used? :

We know that the charge carriers in conductors are free to move around and that charge on a conductor spreads itself out on the surface of the conductor.

3. Step 3. Use the concept to find the answer :
1. When the two conducting spheres are brought together to touch, it is as though they become one single big conductor and the total charge of the two spheres spreads out across the whole surface of the touching spheres. When the spheres are moved apart again, each one is left with half of the total original charge.
2. Before the spheres touch, the total charge is: -5 nC + (-3) nC = -8 nC. When they touch they share out the -8 nC across their whole surface. When they are removed from each other, each is left with half of the original charge:
-8 nC 2=-4 nC -8 nC 2=-4 nC
(1)
on each sphere.

In the previous example we worked out what happens when two identical conductors are allowed to touch. We noticed that if we take two identically sized conducting spheres on insulating stands and bring them together so that they touch, each sphere will have the same final charge. If the initial charge on the first sphere is Q1Q1 and the initial charge on the second sphere is Q2Q2, then the final charge on the two spheres after they have been brought into contact is:

Q= Q1+Q22 Q=Q1+Q22
(2)

Exercise 2

Two identical, insulated spheres have different charges. Sphere 1 has a charge of -96×10-18C-96×10-18C. Sphere 2 has 60 excess electrons. If the two spheres are brought into contact and then separated, what charge will each have?

Solution

1. Step 1. Determine what is being asked and what has been given: We need to determine what will happen to the charge when the spheres touch. They are insulators so we know they will NOT allow charge to move freely. When they touch nothing will happen.

Exercise 3

Two identical, metal spheres have different charges. Sphere 1 has a charge of -9,6×10-18C-9,6×10-18C. Sphere 2 has 60 excess protons. If the two spheres are brought into contact and then separated, what charge will each have? How many electrons or protons does this correspond to?

Solution

1. Step 1. Determine what is being asked and what has been given: We need to determine what will happen to the charge when the spheres touch. They are metal spheres so we know they will be conductors. This means that the charge is able to move so when they touch it is possible for the charge on each sphere to change. We know that charge will redistribute evenly across the two spheres because of the forces between the charges. We need to know the charge on each sphere, we have been given one.
2. Step 2. Determine the charge on sphere 2: This problem is similar to the earlier worked example. This time we have to determine the total charge given a certain number of protons. We know that charge is quantized and that protons carry the base unit of charge and are positive so it is +1,6×10-19C+1,6×10-19C. The total charge will therefore be:
Q2=60×1,6×10(19)Cx=9,6×1018CQ2=60×1,6×10(19)Cx=9,6×1018C
3. Step 3. Determine the redistributed charge: As the spheres are identical in material, size and shape the charge will redistribute across the two spheres so that it is shared evenly. Each sphere will have half of the total charge:
Q=Q1+Q22x=9,6×1018+(9,6×1018)2x=0CQ=Q1+Q22x=9,6×1018+(9,6×1018)2x=0C.
So each sphere is now neutral.
4. Step 4. Determine how many electrons this is:
No net charge means that there is no excess of electrons or protons.

The electroscope

The electroscope is a very sensitive instrument which can be used to detect electric charge. A diagram of a gold leaf electroscope is shown the figure below. The electroscope consists of a glass container with a metal rod inside which has 2 thin pieces of gold foil attached. The other end of the metal rod has a metal plate attached to it outside the glass container.

The electroscope detects charge in the following way: A charged object, like the positively charged rod in the picture, is brought close to (but not touching) the neutral metal plate of the electroscope. This causes negative charge in the gold foil, metal rod, and metal plate, to be attracted to the positive rod. Because the metal (gold is a metal too!) is a conductor, the charge can move freely from the foil up the metal rod and onto the metal plate. There is now more negative charge on the plate and more positive charge on the gold foil leaves. This is called inducing a charge on the metal plate. It is important to remember that the electroscope is still neutral (the total positive and negative charges are the same), the charges have just been induced to move to different parts of the instrument! The induced positive charge on the gold leaves forces them apart since like charges repel! This is how we can tell that the rod is charged. If the rod is now moved away from the metal plate, the charge in the electroscope will spread itself out evenly again and the leaves will fall down because there will no longer be an induced charge on them.

Grounding

If you were to bring the charged rod close to the uncharged electroscope, and then you touched the metal plate with your finger at the same time, this would cause charge to flow up from the ground (the earth), through your body onto the metal plate. Connecting to the earth so charge flows is called grounding. The charge flowing onto the plate is opposite to the charge on the rod, since it is attracted to the charge on the rod. Therefore, for our picture, the charge flowing onto the plate would be negative. Now that charge has been added to the electroscope, it is no longer neutral, but has an excess of negative charge. Now if we move the rod away, the leaves will remain apart because they have an excess of negative charge and they repel each other. If we ground the electroscope again (this time without the charged rod nearby), the excess charge will flow back into the earth, leaving it neutral.

Quantisation of Charge

Unit of Charge

Charge is measured in units called coulombs (C). A coulomb of charge is a very large charge. In electrostatics we therefore often work with charge in microcoulombs (1μC=1×10-6C1μC=1×10-6C) and nanocoulombs (1nC=1×10-9C1nC=1×10-9C).

Exercise 4: Charge quantization

An object has an excess charge of -1,92×10-17C-1,92×10-17C. How many excess electrons does it have?

Solution

1. Step 1. Determine what is being asked and what has been given: We are asked to determine a number of electrons based on a total charge. We know that charge is quantized and that electrons carry the base unit of charge which is -1,6×10-19C-1,6×10-19C.
2. Step 2. Apply charge quantization: As each electron carries the same charge the total charge must be made up of a certain number of electrons. To determine how many electrons we divide the total charge by the charge on a single electron:
N=1,92×10171,6×1019x=120electronsN=1,92×10171,6×1019x=120electrons
(3)

Exercise 5: Conservation of charge - 1

Two identical, metal spheres have different charges. Sphere 1 has a charge of -9,6×10-18C-9,6×10-18C. Sphere 2 has 30 excess electrons. If the two spheres are brought into contact and then separated, what charge will each have? How many electrons does this correspond to?

Solution

1. Step 1. Determine what is being asked and what has been given:
We need to determine what will happen to the charge when the spheres touch. They are metal spheres so we know they will be conductors. This means that the charge is able to move so when they touch it is possible for the charge on each sphere to change. We know that charge will redistribute evenly across the two spheres because of the forces between the charges. We need to know the charge on each sphere, we have been given one.
2. Step 2. Determine the charge on sphere 2:
This problem is similar to the earlier worked example. This time we have to determine the total charge given a certain number of electrons. We know that charge is quantized and that electrons carry the base unit of charge which is -1,6×10-19C-1,6×10-19C. The total charge will therefore be:
Q2=30×1,6×1019Cx=4,8×1018CQ2=30×1,6×1019Cx=4,8×1018C
(4)
3. Step 3. Determine the redistributed charge:
As the spheres are identical in material, size and shape the charge will redistribute across the two spheres so that it is shared evenly. Each sphere will have half of the total charge:
Q=Q1+Q22x=9.6×1018+(4,8×1018)2x=7,2×1018CQ=Q1+Q22x=9.6×1018+(4,8×1018)2x=7,2×1018C
(5)
So each sphere now has:
7,2×1018C7,2×1018C
(6)
of charge.
4. Step 4. Determine how many electrons this is:
We know that charge is quantized and that electrons carry the base unit of charge which is -1,6×10-19C-1,6×10-19C.
5. Step 5. Apply charge quantization:
As each electron carries the same charge the total charge must be made up of a certain number of electrons. To determine how many electrons we divide the total charge by the charge on a single electron:
N=7,2×10181,6×1019x=45electronsN=7,2×10181,6×1019x=45electrons
(7)

Summary

1. Objects can be positively charged, negatively charged or neutral.
2. Objects that are neutral have equal numbers of positive and negative charge.
3. Unlike charges are attracted to each other and like charges are repelled from each other.
4. Charge is neither created nor destroyed, it can only be transferred.
5. Charge is measured in coulombs (C).
6. Conductors allow charge to move through them easily.
7. Insulators do not allow charge to move through them easily.

The following presentation is a summary of the work covered in this chapter. Note that the last two slides are not needed for exam purposes, but are included for general interest.

End of chapter exercise

1. What are the two types of charge called?
2. Provide evidence for the existence of two types of charge.
3. Fill in the blanks: The electrostatic force between like charges is

while the electrostatic force between opposite charges is

.
4. I have two positively charged metal balls placed 2 m apart.
1. Is the electrostatic force between the balls attractive or repulsive?
2. If I now move the balls so that they are 1 m apart, what happens to the strength of the electrostatic force between them?

5. I have 2 charged spheres each hanging from string as shown in the picture below. Choose the correct answer from the options below: The spheres will
1. swing towards each other due to the attractive electrostatic force between them.
2. swing away from each other due to the attractive electrostatic force between them.
3. swing towards each other due to the repulsive electrostatic force between them.
4. swing away from each other due to the repulsive electrostatic force between them.

6. Describe how objects (insulators) can be charged by contact or rubbing.
7. You are given a perspex ruler and a piece of cloth.
1. How would you charge the perspex ruler?
2. Explain how the ruler becomes charged in terms of charge.
3. How does the charged ruler attract small pieces of paper?

8. [IEB 2005/11 HG] An uncharged hollow metal sphere is placed on an insulating stand. A positively charged rod is brought up to touch the hollow metal sphere at P as shown in the diagram below. It is then moved away from the sphere. Where is the excess charge distributed on the sphere after the rod has been removed?
1. It is still located at point P where the rod touched the sphere.
2. It is evenly distributed over the outer surface of the hollow sphere.
3. It is evenly distributed over the outer and inner surfaces of the hollow sphere.
4. No charge remains on the hollow sphere.

9. What is the process called where molecules in an uncharged object are caused to align in a particular direction due to an external charge?
10. Explain how an uncharged object can be attracted to a charged object. You should use diagrams to illustrate your answer.
11. Explain how a stream of water can be attracted to a charged rod.
12. An object has an excess charge of 8,6×1018C8,6×1018C. How many excess electrons does it have?
13. An object has an excess of 235 electrons. What is the charge on the object?
14. An object has an excess of 235 protons. What is the charge on the object?
15. Two identical, metal spheres have different charges. Sphere 1 has a charge of 4,8×1018C4,8×1018C. Sphere 2 has 60 excess electrons. If the two spheres are brought into contact and then separated, what charge will each have? How many electrons does this correspond to?
16. Two identical, insulated spheres have different charges. Sphere 1 has a charge of 96×1018C96×1018C. Sphere 2 has 60 excess electrons. If the two spheres are brought into contact and then separated, what charge will each have?
17. Two identical, metal spheres have different charges. Sphere 1 has a charge of 4,8×1018C4,8×1018C. Sphere 2 has 30 excess protons. If the two spheres are brought into contact and then separated, what charge will each have? How many electrons or protons does this correspond to?

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