# Finding the Electric Potential Difference Between Two Points

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• 0:01 What Is Electric…
• 2:19 Uniform Electric Field
• 3:11 Example
• 4:01 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you will be able to explain what electric potential difference is and calculate the electric potential difference between two points in a uniform electric field. A short quiz will follow.

## What is Electric Potential Difference?

The electric potential at a particular point in space is the work done in moving a positive charge from infinity to that point. The electric potential at infinity is defined as zero. It is related to the electric potential energy in that electric potential is the electric potential energy per unit charge.

So, if a four coulomb charge has 4,000 Joules of electric potential energy due to its position in an electric field, that would mean that the electric potential at that point in the field is 1,000 Joules per coulomb - each coulomb has a thousand Joules of electric potential energy. Whereas electric potential energy is specific to a particular charge, electric potential is defined only by a position inside a field. This makes it a much more useful quantity.

To understand how a point can have potential at all, think about dropping a mass in a gravitational field. If you drop a ball, it falls to the ground. This is because it had gravitational potential energy relative to the ground, and this energy was released when you let go of the ball. Gravitational potential (instead of electric potential) would be the energy per unit mass (instead of energy per unit charge), and would describe the point in space where you let go of the ball.

Let's imagine we have two parallel plates: one with a positive charge and one with a negative charge. In electromagnetism, we use a positive charge to define electric fields. So we'll focus on what happens to a positive charge inside the plates. If you release a positive charge on the negative plate, it won't go anywhere because opposites attract. But, if you release it on the positive plate, it will follow the field lines and 'fall' to the negative plate. So when we talk about electric fields, we say that the field lines point in the direction of decreasing electric potential.

And now, finally, that brings us to electric potential difference. Electric potential difference is the difference in electric potential between two points in space. That's really all it is. It is also measured in Joules per coulomb, but this is usually shortened to a different unit: volts. The electric potential difference between two sides of a battery is what makes electricity flow around a circuit. A 12V battery, for example, has a difference in potential of 12 Joules per coulomb on the two sides of the battery.

## Uniform Electric Field

In a uniform electric field, the equation to calculate the electric potential difference is super easy: V = Ed. In this equation, V is the potential difference in volts (or Joules per coulomb), E is the electric field strength in the area (in newtons per coulomb), and d is the distance between the two plates (in meters).

The parallel plates situation I mentioned earlier is an example of a uniform electric field. Between the plates the field lines are equally spaced, so the field has the same strength everywhere - it's uniform. If we wanted to figure out the potential difference between the plates, we could take the electric field between the plates, E, and just multiply it by the distance between the plates. Strictly speaking, this distance, d, should always be in the direction of the field lines (if you move left and right on this diagram, the electric potential doesn't actually change at all).

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