# Strength of an Electric Field & Coulomb's Law

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• 0:01 What Is a Field?
• 1:16 Electric Field Strength
• 3:04 Example Calculation
• 5:05 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 lesson, you will be able to explain what an electric field is, distinguish between scalar and vector fields and use two electric field equations to solve problems. A short quiz will follow.

## What Is a Field?

Imagine for a moment that you are walking around an actual field. It's a beautiful, green, farmer's field... warm, with a light breeze. You take lots of lovely deep breaths. And… assuming you're still awake, you also take a few temperature readings. You measure the temperature at lots of locations, because you just love science and want truly reliable data. Finally, you make a map of the field, and write down the temperature at different locations on the map. Without realizing it, you have just drawn a temperature field.

A field in physics is really just a map of a quantity over an area of space. That quantity could be a scalar quantity (like temperature) or a vector (like wind speed). A scalar field just contains a map of numbers, like the temperature at different places. A vector field contains vector quantities - numbers with a direction. Wind speed is a vector quantity because it not only has a number (the speed), but also a direction. And an electric field is another such vector field. An electric field is a map of the electric force over a particular area.

## Electric Field Strength

Electric field strength is defined as the force a +1 coulomb test charge would feel at a particular location, measured in newtons per coulomb (N/C). So, instead of taking your temperature sensor around the farmer's field, to draw an electric field map, you'll have to take a +1 coulomb charge. Or another way of putting it is that it's the force felt per 1 coulomb of charge. For example, if the electric field strength is 3 N/C, that means a 1 coulomb charge would feel a 3 newton force, but a 2 coulomb charge would feel a 6 newton force, and so on. A -1 coulomb charge would feel the same force in the opposite direction: remember, opposites charges attract, and similar charges repel.

If we write this electric field strength as an equation, we would say that electric field strength E, is equal to the force felt, F, divided by the size of the charge, q.

Now, as it happens, we already have an equation for the electric force between two point charges. In another lesson, we introduced Coulomb's Law, which said that the force, F, in newtons, is equal to the electrostatic constant, k, multiplied by the sizes of the two charges in coulombs, divided by the distance they are apart in meters, squared.

If we plug that into the electric field strength equation and cancel out one of the qs, we find that electric field strength in a particular location is equal to the electrostatic constant, k, multiplied by the size of the charge creating the electric field, divided by the distance you are from that charge, squared.

Or in other words, the size of the electric field is independent of (not affected by) the size of the test charge you move around the field. The size of the field only depends on the size of the charge that is creating the field.

## Example Calculation

Let's do an example. Imagine that you have a +4 coulomb charge at the origin (coordinates 0,0), which is actually pretty huge. Even 1 coulomb is a lot in the real world. The question asks you to calculate the electric field at coordinates (0,3). You can assume it's a meter grid.

Well, first of all, let's write out what we know. We have the charge of 4 coulombs, so q = 4. You don't need to plot the points to see that (0,3) is 3 meters away from (0,0) so the distance, d, is 3. And the electrostatic constant, k, is always 9 * 10^9. Plug all of that into the equation and solve for the electric field, and you get 4 * 10^9 newtons per coulomb.

But hold on! We're not done. Electric field is a vector quantity, so we need a direction, too. Since it's a +4 coulomb charge, and since we use a positive test charge as our definition of electric field, those two charges will repel each other. Opposites attract, but similar charges repel. So, that means the field at (0,3) will point directly away from the origin - to the right on a standard axis.

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