# Lesson Explainer: The Electric Potential Difference Provided by Cells Science

In this explainer, we will learn how to calculate the potential difference provided by a cell based on the amount of work it does to separate charge.

Recall the properties of charge. An object or particle can be either positively charged, negatively charged, or neutral. Charge is measured in units of coulombs, C.

Like charges repel each other, and opposite charges attract each other. This means that a positive charge and a negative charge will experience an attractive force between them. The attractive force pulls them toward each other.

If we wish to separate two opposite charges, we must overcome the attractive force between them. This means we must do work on the charges. In order to increase the distance between the charges, we must transfer energy to the charges, so they are able to overcome the attractive force between them.

When we separate the charges, we create an electric potential difference between them. The electric potential difference tells us how much work has been done on the charges in order to separate them.

### Example 1: Recognizing Electric Potential Difference between Separated Charges

The picture shows a positive charge and a negative charge that are near each other. The charges are fixed in place and cannot move.

Complete the following sentence: The separation of the positive and negative charges creates an between them.

1. electric potential difference
2. electric current

The answer is A, electric potential difference.

The picture shows a positive charge and a negative charge, with a distance in between them. Hence, the picture shows a pair of opposite charges, which have been separated.

To separate opposite charges, work must be done to overcome the attractive force between the charges. When work is done to separate charges, an electric potential difference is created between the charges.

An electric current is the flow of charge. We are told that the charges are fixed and cannot move. Hence, there is no electric current in this picture.

Now that we have understood how separating charges creates a potential difference, let us look at how a potential difference is created between two points in a material.

We can create a potential difference between two points in a material, by separating the charges in that material.

Materials are made up of atoms. Atoms contain two types of charged particles. The nucleus of the atom contains protons, which are positively charged. Outside the nucleus, there are electrons, which are negatively charged.

Protons and electrons both have the same-sized charge, but a proton is positively charged, and an electron is negatively charged. In an atom, the number of protons is equal to the number of electrons.

The picture below shows the charges in a piece of material. The blue circles represent electrons. The red circles represent the nuclei of the atoms in the material. In this material, each nucleus contains one proton. This means that the number of positive charges in the material is equal to the number of negative charges.

There is no electric potential difference between the two ends of this material.

Because the material contains equal numbers of positive charges and negative charges, the material is neutral overall. The positive charges and negative charges are both spread evenly throughout the material. This means that the material is neutral everywhere.

This is shown in the following picture of the same material.

If we add up all the charges in the region at the right-hand end of the material, we find that this region contains the same number of negative electrons and positive nuclei. This means that, overall, this region is neutral.

Similarly, the region at the left-hand end is also neutral.

Both the left-hand end and the right-hand end of this material are neutral. So, there is no separation of charge across the material. Hence, there is no electric potential difference between the left-hand end and the right-hand end of the material.

However, we can create a potential difference across this material, by doing work on the charges.

In a solid, the atomic nuclei are fixed in place, according to the structure of the material. Protons are contained within the nuclei of the atoms. This means that the protons in a solid are fixed in place. Hence, the positive charges in a solid cannot move.

Electrons are not contained within the nucleus. This means we can do work on the electrons, in order to move them around within the material.

By doing work on the electrons, we can move them toward one end of the material. This is shown in the following picture.

In this diagram, the electrons have been moved toward the right-hand side of the material. We call this a βbuildup of electronsβ at the right-hand side.

Because the charges in the material are no longer evenly spaced, the two sides of the material have different overall charges.

This is shown in the following picture.

On the right-hand side of the material, there is a buildup of electrons. This means that this region of the material contains more electrons than protons. Hence, the right-hand side of the material is negatively charged.

On the left-hand side of the material, there are more protons than electrons. Hence, the left-hand side of the material is positively charged.

In this material, work has been done to move the electrons. The right-hand side of the material is now negatively charged, and the left-hand side of the material is now positively charged. This means there is a separation of charge across the material. Hence, there is now an electric potential difference between the two sides of the material.

### Example 2: Identifying Charge Separation in a Material

The picture shows the electrons and atomic nuclei in a piece of material. The electrons cannot flow along this material. The blue circles represent the electrons and the red circles represent the atomic nuclei.

1. At which end of the material is there a buildup of electrons?
2. Fill in the blank: The buildup of electrons at one end of the material creates an along the piece of material.
1. electric potential difference
2. electric current

Part 1

There is a buildup of electrons at the right-hand end of the material.

A buildup of electrons occurs at one end of a material, when the electrons in the material move toward that end. This means we get more electrons at that end of the material than we do at the other end.

In this picture, there are more electrons at the right-hand end than at the left-hand end. The electrons have moved toward the right-hand end of the material, so there is a buildup at the right-hand end.

Part 2

The answer is A, electric potential difference.

Because there is a buildup of electrons at the right-hand end of the material, the two ends of the material now have opposite charges.

The right-hand end contains more electrons than protons, so it is negatively charged. The left-hand end contains more protons than electrons, so it is positively charged.

The two ends of the material now have opposite charges, so there is a separation of charges across the material. Hence, there is an electric potential difference between the two ends of the material.

A conductor is a type of material where charge can flow very easily.

In conductors, work can be done to cause a buildup of electrons at one end of the material, as we have already discussed. This means there is a separation of charge, and hence a potential difference across the conductor. But when we stop doing this work, the electrons can flow very easily through the material.

When this happens, the electrons will move, so that they are once again spread evenly throughout the material. This is because electrons have the same charge. Hence, there is a repulsive force between the electrons, pushing them away from each other.

When the charges are spread evenly in the material, there is no charge separation and so no potential difference across the material.

So, when charged particles are allowed to flow in a conductor, the separation between charges can reduce to zero. When this happens, there is no potential difference between any two points in the conductor.

### Example 3: Recognizing Electric Potential Difference in Van de Graaff Generators

The picture shows a Van de Graaff generator.

1. Fill in the blank: When the generator is turned on, charges build up on the large sphere.
1. positive
2. negative
2. The small sphere is connected to the ground by a copper cable. It is brought closer to the large sphere, but no spark jumps between them.
Fill in the blank: The buildup of negative charges on the large sphere creates an between the large sphere and the small sphere.
1. electric current
2. electric potential difference

Part 1

The answer is B, negative.

A Van de Graaff generator is a device that separates charges. Inside the Van de Graaff generator, electrons are removed from a rotating rubber belt and transferred to the large sphere. This causes a buildup of negative charge on the large sphere.

Part 2

The answer is B, electric potential difference.

There is a buildup of electrons on the large sphere, so the large sphere is negatively charged.

The small sphere is grounded by a copper cable. Copper is a conductor, meaning charge can flow easily through the cable. This means that there is no buildup of charge on the small sphere. The small sphere is neutral.

There is an electric potential difference between the large sphere and the small sphere, due to the buildup of charge on the large sphere. This is due to the repulsive forces between the electrons, which all have the same charge.

It is possible to have an electric current between the large sphere and the small sphere. Due to the electric potential difference, electrons can flow from the large sphere to the small sphere. When this happens, the charges moving through the air produce a flash of light and a crackling sound, called a βspark.β

However, in this question, we are told that there is no spark between the spheres. Hence, there must be no current flowing between the spheres.

### Example 4: Identifying Charge Separation in Copper Wire

The picture shows the electrons and atomic nuclei in a section of copper wire. The blue circles represent electrons and the red circles represent atomic nuclei.

At first, there is a buildup of electrons at the right-hand end of the wire. What will happen in the wire over time?

The answer is the following: electrons will move toward the left-hand end of the wire until they are spaced out evenly.

In this material, work has been done to move the electrons toward the right-hand end of the material, causing a buildup of charge. This creates a charge separation between the two ends of the material. Hence, there is an electric potential difference between the two ends of the material.

Copper is a conducting material. This means that it is very easy for charge to flow through copper.

When we stop doing work to move the electrons, the electrons will move, so that they are once again spread evenly throughout the material. This is because electrons have the same charge. Hence, there is a repulsive force between the electrons, pushing them away from each other.

This reduces the charge separation in the material to zero. When the charges are evenly spaced, there is no potential difference between any two points on the wire.

Now, let us consider the electric potential difference across a battery in a circuit.

A battery is a power source in an electric circuit. Batteries contain chemicals, which consist of charged particles. The battery does work in order to separate the oppositely charged particles. This creates an electric potential difference across the battery. The electric potential difference across a battery is called an electromotive force.

The electromotive force of a battery allows charges to flow around a circuit.

Recall that there is an attractive force between separated, opposite charges that pulls negative charges toward positive charges. When a battery is connected to conducting wires, electrons from the negatively charged terminal of the battery flow through the circuit, until they reach the positively charged terminal of the battery.

The electrons flow through the circuit, instead of flowing back through the battery, because the circuit is made of conducting materials. This means it is easier for the electrons to flow through the circuit.

Hence, the electromotive force of a battery can produce a current in an electric circuit.

We can calculate the electric potential difference across a battery, , using the following formula.

### Formula: The Potential Difference across a Battery

The electric potential difference, , between the two terminals of a battery is given by where the amount of work done to separate opposite charges in the battery, and the amount of charge separated.

Electric potential difference is measured in units of volts, V.

The above formula shows us that the voltage across a battery is equal to the work done separating charges, measured in joules, divided by the amount of charge separated, measured in coulombs. Hence, . So, the unit of one volt, V, is equal to one joule per coulomb, J/C.

### Example 5: Calculating the Potential Difference across a Cell

A cell does 10 joules of work to separate 2 coulombs of charge. What potential difference does this create across the terminals of the cell?

The electric potential difference, , between the two terminals of a cell is given by the formula where the amount of work done to separate opposite charges in the battery, and the amount of charge separated.

The cell does 10 joules of work to separate charges. So, . The cell separates 2 coulombs of charge, so .

Using the above formula, we can calculate that

So, the potential difference between the terminals of the cell is 5 V.

Let us now summarize what has been learned in this explainer.

### Key Points

• There is an attractive force between oppositely charged particles, which pulls them toward each other.
• In order to separate opposite charges, we have to do work to overcome the attractive force between the charges.
• Doing work to separate charges creates an electric potential difference between the charges.
• In a conductor, charge can flow very easily. If we separate charges in a conductor and then allow the charges to flow, the separation between charges can return to zero.
• Separating charges in a battery creates a potential difference between the terminals of the battery. This potential difference is called the electromotive force of the battery.
• We can calculate the electromotive force of a battery using the formula .