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## End of chapter exercises

What are the two types of charge called?

Positive charge and negative charge

Provide evidence for the existence of two types of charge.

When rubbing certain materials against each other, we observe that some of the materials are able to attract or repulse other objects.

Fill in the blanks: The electrostatic force between like charges is ____________________ while the electrostatic force between opposite charges is ____________________ .

The electrostatic force between like charges is repulsive while the electrostatic force between opposite charges is attractive.

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?

Repulsive

The repulsive force will increase by a factor of 4.

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.

d.

swing away from each other due to the repulsive electrostatic force between them

Describe how objects (insulators) can be charged by contact or rubbing.

When rubbing certain materials against each other, electrons can be transferred from the one material to the other, thereby giving the materials nett charge.

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?

• The ruler can be charged by rubbing it with the piece of cloth

• Due to the rubbing, electrons are transferred from the cloth to the ruler, giving it a nett negative charge. The cloth will therefore now have a nett positive charge.

• The charged ruler will attract small pieces of paper through the process of polarisation. When the ruler is brought close to a piece of paper, the positive nuclei in the paper will move slightly close to the ruler and the electrons in the paper will move slightly away from the ruler. The piece of paper will then be slightly positively charged closest to the ruler and feel an attractive force.

(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.

d.

It is evenly distributed over the outer surface of the hollow sphere

What is the process called where molecules in an uncharged object are caused to align in a particular direction due to an external charge?

Polarisation

Explain how an uncharged object can be attracted to a charged object. You should use diagrams to illustrate your answer.

When a charged object is brought close to an uncharged object, the uncharged object will be given a slight nett charge, opposite to the charge of the charged object. This process is called polarisation, see drawing below.  Because the side of the uncharged object which is closest to the charged object  has a nett charge due to polarisation, it will feel an attractive force to the charged object.

Explain how a stream of water can be attracted to a charged rod.

Water molecules are polar, meaning they have positively and negatively charged sides. When a charged object is brought close to a stream of water, the molecules will feel an electrostatic force, causing the stream to be deflected.

An object has an excess charge of $-8,6×10 -18 C$. How many excess electrons does it have?

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 -1.6×10â»19C.

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:

 $N=\frac{-8,6×{10}^{-18}}{-1,6×{10}^{-19}}$ $=60electrons$

An object has an excess of 235 electrons. What is the charge on the object?

Step 1: Determine what is being asked and what has been given.

We are asked to determine the charge given a number of electrons. We know that charge is quantized and that electrons carry the base unit of charge which is $-1,6×{10}^{â}»19\text{C}$.

Step 2: Apply charge quantization.

As each electron carries the same charge the total charge must be the sum of all the individual electron charges. We just need to multiply the base charge by the number of electrons:

 $Q=235×-1.6×{10}^{-19}$ $=-376×{10}^{-17}C$

An object has an excess of 235 protons. What is the charge on the object?

Step 1: Determine what is being asked and what has been given.

We are asked to determine the charge given a number of electrons. We know that charge is quantized and that protons are positive and carry the base unit of charge which is +1.6×10â»19C.

Step 2: Apply charge quantization.

As each proton carries the same charge the total charge must be the sum of all the individual proton charges. We just need to multiply the base charge by the number of protons:

 $Q=235×1.6×{10}^{-19}$ $=376×{10}^{-17}C$

Two identical, metal spheres have different charges. Sphere 1 has a charge of $-4,8×10 -18 C$. 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?

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.

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 $-1,6×{10}^{â}»19C$ . The total charge will therefore be:

 ${Q}_{2}=60×-1,6×{10}^{-19}C$ $=9,6×{10}^{-18}C$

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;

 $Q=\frac{{Q}_{1}+{Q}_{2}}{2}$ $=\frac{-9,6×{10}^{-18}±4,8×{10}^{-18}}{2}$ $=7,2×{10}^{-18}C$

So each sphere now has $7.2×{10}^{-18}C$ of charge.

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 $-1,6×{10}^{â}»19C$.

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:

 $N=\frac{-7,2×{10}^{-18}}{-1,6×{10}^{-19}}$ $=45electrons$

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

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.

Two identical, metal spheres have different charges. Sphere 1 has a charge of $-4,8×10 -18 C$. 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?

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.

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 $+1,6×{10}^{â}»19C$ . The total charge will therefore be:

 ${Q}_{2}=30×1,6×{10}^{-19}C$ $=4,8×{10}^{-18}C$

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;

 $Q=\frac{{Q}_{1}+{Q}_{2}}{2}$ $=\frac{4,8×{10}^{-18}±4,8×{10}^{-18}}{2}$ $=0C$

So each sphere is now neutral.

Step 4: Determine how many electrons this is.

No net charge means that there is no excess of electrons or protons.