Calculating Electric Potential from Charge Densities

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Calculating Electric Forces, Fields & Potential

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:04 Electrical Potential
  • 0:54 Formula
  • 1:51 Sample Equation
  • 2:44 Electrical Potential…
  • 4:29 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

In this lesson, we'll learn about the electric potential from charge densities and how to calculate the electric potential. We'll also learn how the electric potential, potential energy, and electric fields are related.

Electric Potential

If you were holding a ball out of the window of a tall skyscraper, then that ball has a potential energy based on the pull of gravity. Now, imagine that this ball has an electric charge. Instead of gravity acting as the energy pulling on the ball, there's an electric (or magnetic) field pulling on the ball. This ball still has a potential energy, but instead of being based on gravity, it's based on the energy of the electric field. This potential energy can also be called the electric field strength.

Electric potential is the potential energy per unit of charge of a charged density in an electric field. In our example, the charged density is the ball, or the point of charge in which we are interested. This electric potential is responsible for the voltage in batteries.


The formula for electric potential is:

Electric potential formula

Here, Q is the charge of the charge density. The formula for potential energy (or electric field energy) is:

Potential energy

Notice that in the equation for potential energy, we multiply by Q, and in the equation for electric potential, we divide by Q. Since we are dividing Q by Q, which equals 1, the variable cancels out in the final equation:

Insert potential energy formula

The 'k' is Coulomb's constant, which is equal to:

coulombs constant

The 'q' in the formula for electric potential is the charge on the source of the electric field. And the 'r' refers to the distance from the source of the electric field.

Sample Equation

Let's look at an example:

Let's say that we have a charged density with a charge of 3 coulombs, which is 2.5 meters away from a charge of 7 coulombs. Looking at our formula, here's what we know:

  • k = 8.99 * 109
  • r = 2.5 meters
  • q = 7 coulombs

We use the charge of the source charge - not the charged density - because we want to know the potential energy at the point of the charged density, not the source charge.


The electric potential at this point is 2.52 * 10 10 N*m/C. Notice that N*m is equal to Joules (J), so it is equal to 2.52 * 10 10 J/C. This is our energy per charge.

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account