Calculating Electric Potential from Charge Densities

Calculating Electric Potential from Charge Densities
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  • 0:04 Electrical Potential
  • 0:54 Formula
  • 1:51 Sample Equation
  • 2:44 Electrical Potential…
  • 4:29 Lesson Summary
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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.

Formula

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.


Calculation


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.

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