# Force and electric field relationship

### Electric Field Intensity

Very definition of electric field is the region of space at every point of which electric force is exerted on charge. The field strength or electric field intensity at any point in the field is defined as the force on unit positive charge placed at that point. The flux per unit. If the idea of force "acting at a distance" in Coulomb's Law seems troublesome, perhaps the idea of force caused by an electric field eases your discomfort. Like gravitational fields, electric fields are a field of force that act from a distance, where the force here is Therefore, the relationship can be expressed as.

Of course if you don't think at all - ever - nothing really bothers you.

### A-level Physics/Forces, Fields and Energy/Electric fields - Wikibooks, open books for an open world

After all, the quantity of charge on the test charge q is in the equation for electric field. So how could electric field strength not be dependent upon q if q is in the equation? But if you think about it a little while longer, you will be able to answer your own question. Ignorance might be bliss.

But with a little extra thinking you might achieve insight, a state much better than bliss. Increasing the quantity of charge on the test charge - say, by a factor of 2 - would increase the denominator of the equation by a factor of 2.

But according to Coulomb's lawmore charge also means more electric force F. In fact, a twofold increase in q would be accompanied by a twofold increase in F.

So as the denominator in the equation increases by a factor of two or three or fourthe numerator increases by the same factor. These two changes offset each other such that one can safely say that the electric field strength is not dependent upon the quantity of charge on the test charge. So regardless of what test charge is used, the electric field strength at any given location around the source charge Q will be measured to be the same.

Another Electric Field Strength Formula The above discussion pertained to defining electric field strength in terms of how it is measured. Now we will investigate a new equation that defines electric field strength in terms of the variables that affect the electric field strength. To do so, we will have to revisit the Coulomb's law equation. Coulomb's law states that the electric force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between their centers.

Note that the derivation above shows that the test charge q was canceled from both numerator and denominator of the equation. The new formula for electric field strength shown inside the box expresses the field strength in terms of the two variables that affect it.

The electric field strength is dependent upon the quantity of charge on the source charge Q and the distance of separation d from the source charge.

### electrostatics - Relation between Electric field and potential - Physics Stack Exchange

An Inverse Square Law Like all formulas in physics, the formulas for electric field strength can be used to algebraically solve physics word problems. And like all formulas, these electric field strength formulas can also be used to guide our thinking about how an alteration of one variable might or might not affect another variable. One feature of this electric field strength formula is that it illustrates an inverse square relationship between electric field strength and distance.

The strength of an electric field as created by source charge Q is inversely related to square of the distance from the source. This is known as an inverse square law. Electric field strength is location dependent, and its magnitude decreases as the distance from a location to the source increases.

And by whatever factor the distance is changed, the electric field strength will change inversely by the square of that factor. Use this principle of the inverse square relationship between electric field strength and distance to answer the first three questions in the Check Your Understanding section below. The Stinky Field Analogy Revisited In the previous section of Lesson 4, a somewhat crude yet instructive analogy was presented - the stinky field analogy.

The analogy compares the concept of an electric field surrounding a source charge to the stinky field that surrounds an infant's stinky diaper. Just as every stinky diaper creates a stinky field, every electric charge creates an electric field.

And if you want to know the strength of the stinky field, you simply use a stinky detector - a nose that as far as I have experienced always responds in a repulsive manner to the stinky source. That first charge feels the force. So conceptually that's how this electric field works and that's how it does. So at this point you might not be impressed. You might be like, "Are we just making up a story "to make ourselves feel better here? Mathematically in terms of physics, talking about the electric field makes describing the physics way easier.

In fact it makes it so that you don't even have to know about the charge creating that field at all. If you have a way of knowing the field even if you don't know what charge is creating that fied, you could figure out what the force is gonna be on any charge in that field without even knowing the charge that created that field and that turns out to happen a lot.

So knowing the electric field is extremely useful. It lets you determine the electric force on a charge even if you don't know what charge is exerting that force. So up to this point, I've been trying to motivate why we would want this idea of the electric field, why physicists would come up with this idea.

But I wouldn't blame you if at this point you aren't thinking, I still don't know what electric field is.

## A-level Physics/Forces, Fields and Energy/Electric fields

I know what it isn't. Electric field is not electric force but what exactly is the electric field. So let me give the electric field a proper definition here. The electric field E at a point in space is defined to be the amount of electric force per charge exerted at that point in space.

So this is what the electric field is. It's the force per charge. The way physicists usually think about this is imagine throwing a test charge in here. We call this a test charge.

We'd like to imagine that this charge is really little so that it doesn't completely likes swamped and overwhelmed. The other charge is creating this field. Otherwise if you threw some huge charge in here, all the other charge would scatter and it would change the whole situation. So let's say we put a really small test charge in here.

**Electric Charge and Electric Fields**

If I want to know what the electric field is at a point in space, I'd just bring my test charge over here, measure the amount of electric force on that test charge and then I just divide by how much was there in that test charge.

What was the charge of that test charge? I'll call this charge two. If I take the force on charge two, divide it by charge two, that would be the value of the electric field at that point in space. So this is how we define the electric field. The definition of electric field is the amount of force per charge. In other words, let's put some numbers in here. Let's say Q two was two coulombs. This is actually an enormous amount of charge. This is kind of unrealistic example but it will make the numbers come out nice and conceptually it's the same thing.

So a positive two coulombs was placed here. That's the value of Q two. Let's say when we measure the force on Q two, we're getting 10 newtons of force.

In that case, we can just say, "All right, then the electric field, "in that region of that vicinity "is gonna be 10 newtons of force per two coulombs of charge "and we get an electric field of five.

If you put more coulombs at that point in space, there'd be a greater force. This number is telling you the number of newtons you would get per coulomb. Since we had two coulombs at this point in space and there was five newtons per coulomb, the force was 10 newtons. So this number five newtons per coulomb is important because it's the same for any charge you put there. This is why the electric field is useful. At this point in space right here, if the electric field is five, it's five newtons per coulomb no matter what charge you put there.

So if I put a four coulombs charge at that point, since there's five newtons for every coulomb, there'd be a 20 newton force there because there's five newtons for every coulomb.

If there's four coulombs, there'd be five times four newtons which is 20 newtons. So you can imagine rearranging this formula another way. You could just multiply those sides by Q and you get that the electric force on a charge is equal to the value of that charge at that point in space multiplied by the value of the electric field at that point in space.

But it's important to note this electric field is not created by this charge Q two. This was created by some other charge or collection of charges. Remember this charge Q one is creating this electric field E one and that electric field is causing this electric force on Q two.

Q two did not create the electric field E one that it interacted with. Q one created that electric field E one. So people get mixed up. They see this formula. They start to think maybe this Q two is creating this electric field. This electric field is causing the electric force on that charge, not the other way around. This Q two is not creating this field. This field is causing the force on that charge.

So this formula is extremely useful. In other words, the electric field intensity is constant for all points. The electric field lines are represented by parallel lines. The source consists of charges that are at rest. A static uniform electric field can be established at points very close to a charged sheet. For example, a parallel plate capacitor offers a static uniform electric field in the dielectric medium present in between its plates. The field curves outwards slightly on the edges of the plates, and it is important that you draw it like that.

These are conservative fields.