If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: MCAT>Unit 9

Lesson 10: Electrostatics

# Electric potential

## How do electric forces work?

Electric forces are responsible for almost every single chemical reaction that occurs in your body. Almost all of biochemistry relies on understanding how these forces cause electrons to move between atoms, and the changes in the structure or composition that occur when electrons move between atoms. But the basic rules for electric forces are surprisingly simple: electrons repel other electrons, but protons and electrons attract each other. Here we’ll talk about where these forces come from, and the different concepts that physicists, chemists, and biologists use to better understand the electric force.

## What is the electric force?

Electric force is the force that pushes apart two like charges, or that pulls together two unlike charges. Just like two magnets that snap together when you point the North end of one magnet towards the South end of the other, two different electric charges (like a negatively-charged electron and a positively-charged proton) always want to join together. The size of this attraction decreases as the distance between them increases.
When you point the North ends of two magnets towards each other (or if you do the same with two South ends), the magnets will repel each other. The same effect happens when you put two electrons near each other (or two protons). But once again, the magnitude of this repulsion gets smaller as the charges get further apart. Unlike magnets, though, which always have a North and a South end, positive and negative charges can be separated and then brought back together.

## What is electric field?

We know that if you have a single positively charged particle, a positively charged particle will be pushed away from it by the electric force.
The electric field is a “force field” around a charged object that illustrates the direction the electric force would push an imaginary positively charged particle if there was one there. It also shows us how hard a push the electric force would give. We don’t have to actually place a positively charged particle near the charged object to find out what the electric field would be, we just have to know what would happen if we did. Once we’ve used the imaginary positive charge to find the electric field, we can use the electric field to determine how any other charged particles would move around the charged object.
Imagine we have a sphere that is negatively charged. The electric field would show that an imaginary positively charged particle is pulled towards the sphere by the electric force. The electric field would always point towards the sphere, because we always use an imaginary positively charged particle to determine the electric field. As we move away from the sphere, the electric field gets weaker and weaker.
Now say we have two flat plates with a space between them. The left one is positively charged and the right-hand one is negatively charged.
The electric field between the plates is going to be strong, because we not only have a negatively charged plate pulling our imaginary positive particle (that we use to measure the electric field, remember) to the right, we also have a positively charged plate pushing it to the right. The plates are working together to make the imaginary particle move toward the right.

## What is electric potential energy?

Electric potential energy is the energy that is needed to move a charge against an electric field. You need more energy to move a charge further in the electric field, but also more energy to move it through a stronger electric field.
Imagine that you have a huge negatively charged plate, with a little positively charged particle stuck to it through the electric force. There’s an electric field around the plate that’s pulling all positively charged objects toward it (while pushing other negatively charged objects away).
You take the positive particle, and start to pull it off the plate, against the pull of the electric field. It’s hard work, because the electric force is pulling them together. If you let the positive particle go, it would snap back to the negative plate, pulled by the electric force. The energy that you used to move the particle away from the plate is stored in the particle as electrical potential energy. It is the potential that the particle has to move when it’s let go.
If you pulled the positive particle further away from the plate, you would have to use more energy, so the charge would have more electrical potential energy stored in it. If we doubled the charge on the plate, again, you would need more energy to move the positive particle. If we doubled the charge on the positive particle, you would need more energy to move it. You get the idea.
Imagine that instead of a negatively charged plate, our plate is positively charged. Our positive particle would be pushed away from the plate since they are both positively charged. This time, we have to put in energy to try to move the particle closer to the plate, instead of to pull it away. The closer we try to move it to the plate, the more energy we have to put in, so the more electrical potential energy the particle would have.

## What is electric potential?

The electric potential, or voltage, is the difference in potential energy per unit charge between two locations in an electric field. When we talked about electric field, we chose a location and then asked what the electric force would do to an imaginary positively charged particle if we put one there. To find the electrical potential at a chosen spot, we ask how much the electrical potential energy of an imaginary positively charged particle would change if we moved it there. Just like when we talked about electric field, we don’t actually have to place a positively charged particle at our chosen spot to know how much electrical potential energy it would have.
We know that the amount of charge we are pushing or pulling (and whether it is positive or negative) makes a difference to the electrical potential energy if we move the particle to a chosen spot. That’s why physicists use a single positive charge as our imaginary charge to test out the electrical potential at any given point. That way we only have to worry about the amount of charge on the plate, or whatever charged object we’re studying.
Let’s say we have a negatively charged plate. We know that a positively charged particle will be pulled towards it. That means we know that if we choose a spot near the plate to place our imaginary positively charged particle, it would have a little bit of electrical potential energy, and if we choose a spot further away, our imaginary positively charged particle would have more electrical potential energy. So we can say that near the negative plate the electrical potential is low, and further from the negative plate the electrical potential is high.
What if our plate was positively charged? A positively charged particle would be pushed away from the plate. This is the exact opposite of the last case. Near the plate the electrical potential is high and far from the plate the electrical potential is low.
If we have two plates, as before, where one is positive and one negative with a space between them, the electrical potentials of the positive and negative plates combine, so we know that near the negative plate and far from the positive plate, the electrical potential is very low, but far from the negative plate and near the positive plate that electrical potential is very high.

## Consider the following… cell membranes

The membranes that surround your cells are comprised of thin layers of molecules that stick together to form a continuous, two-dimensional sheet. The sheet is held together because the molecules that form the membrane have special distributions of electric charges that allow them to stick together without dissolving in the water surrounding the cell.
Because the membrane is held together by the attraction of opposite charges, it is possible to overcome this attraction by applying a large electric potential across the membrane. In some cells, applied electric potentials are used to open and close the cell membrane in order to allow nutrients and waste to enter and exit the cell. In nerve cells, the electric potential across the membrane can be easily changed, allowing the cells to carry messages encoded in their membrane potential.

## Want to join the conversation?

• For the (last diagram) combined electric fields of the positive and negative plates, isn't the direction of the electric field supposed to be pointing toward the negative plate? Because if we use a positive test charge wouldn't it be repelled away from the positive plate and attracted towards the negative plate? Someone please clarify for me.
-Thanks
• the conductors have free electrons which can align themselves when external magnetic or electric fields are applied. these free electrons align themselves in the proximity of positive plate and positive charges in proximity of negative plate. this makes the direction of electric field point towards the positive plate. this is due to net charge in the system to become zero . <you will study this in gauss law>
• is it true that electric potential is the work done on a unit positive charge to bring it from infinity to conducting body ?
• In the last Paragraph, how a large electric potential is applied through the cell membrane?
• how do you think increasing the size of the point charge would affect the potential at a certain distance away from the center of the charge
• The word " size " , if u mean by size as " charge" , even then it wouldn't affect the electric potential energy of a test charge in a charged electric field .
(1 vote)
• May I know how is electric potential related in terms of electrode potential? I meant in an electrode which are the two points where one has high electric potential energy and the other has less potential energy? This might be a silly question but I could not figure it out exactly.
• "so we know that near the negative plate and far from the positive plate, the electrical potential is very low, but far from the negative plate and near the positive plate that electrical potential is very high."

Based on what? It says electrical potential is very low if far from positive plate and close to negative plate, are they basing this electrical potential on an "imaginary positive charge"? If so, they need to disclose this because that was very confusing.
• Yes, they are basing this on an "imaginary positive charge". Quote:". When we talked about electric field, we chose a location and then asked what the electric force would do to an imaginary positively charged particle if we put one there. To find the electrical potential at a chosen spot, we ask how much the electrical potential energy of an imaginary positively charged particle would change if we moved it there. Just like when we talked about electric field, we don’t actually have to place a positively charged particle at our chosen spot to know how much electrical potential energy it would have."