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UExcel Physics: Study Guide & Test Prep18 chapters | 201 lessons | 13 flashcard sets

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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.

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. Andâ€¦ 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** 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 *q*s, 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.

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.

So the full answer is that the electric field at (0,3) is 4 * 10^9 newtons per coulomb to the right. And now... we're done.

The fact that an electric field is a vector can cause these problems to get very complicated if you're not careful. If you start adding multiple charges, you can calculate the total field by adding up the electric field vectors. And when you have more than two charges, you can very easily bring angles into it. Next thing you know, you're breaking the electric field into *x* and *y* components and figuring out the total *x* and total *y*. The principles of vectors discussed in other lessons apply to any vector quantity, including electric field. But the first step is to understand the basics, and understand that the electric field strength is independent of the size of the charge you use to measure it.

A **field** is really just a map of a quantity over an area of space. That could be a scalar (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** is defined as the force a +1 coulomb test charge would feel at a particular location, measured in newton's per coulomb. 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 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*.

We can combine this equation with Coulomb's Law to get an equation for the electric field produced by a point charge. It looks like this, and says that the electric field strength, *E*, is equal to the electrostatic constant, *k*, that is just 9 * 10^9, 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 (not affected) by the size of the test charge you use - the charge you use to measure the field. The size of the field only depends on the size of the charge that is creating the field.

Pursue these objectives as you work through the lesson:

- Identify and describe different types of fields
- State the electric field strength equation
- Calculate the strength and direction of an electric field

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UExcel Physics: Study Guide & Test Prep18 chapters | 201 lessons | 13 flashcard sets

- Go to Vectors

- Go to Kinematics

- Electric Charge and Force: Definition, Repulsion & Attraction 6:48
- Electric Force Fields and the Significance of Arrow Direction & Spacing 5:56
- Coulomb's Law: Variables Affecting the Force Between Two Charged Particles 8:04
- Strength of an Electric Field & Coulomb's Law 6:46
- What is Capacitance? - Definition, Equation & Examples 4:29
- Capacitance: Units & Formula 6:00
- Go to Electrostatics

- Go to Relativity

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