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The Electric Field

Introducing the concept of the electric field we are adding another layer to our model of charges. This new model, called electric field, not only makes things easier but also explains two things that we did not bother looking into when we talked about forces, especially when we talked about gravity.

These two questions are: When two charges are brought close to another, how does one charge “know” the other charge is there at all? In other words, how to non-contact forces work? The second question is: when two charges interact with one another, why does a charge experience a force immediately after a second charge is brought in? In other words, how can a force act immediate over long distances? 

The concept of a FIELD surrounding the charge at all times and stretching out into space in all directions answers both of these questions. A charge sets up the field around itself that is everywhere. This explain how a non-contact force can exist. The second charge is in “contact” with the field rather than the charge. And it also explains how the force can act immediately, because as soon as the charge enters the field, which is everywhere, it interacts with it and a force is exerted.

These two questions are: When two charges are brought close to another, how does one charge “know” the other charge is there at all? In other words, how to non-contact forces work? The second question is: when two charges interact with one another, why does a charge experience a force immediately after a second charge is brought in? In other words, how can a force act immediate over long distances? 

The concept of a FIELD surrounding the charge at all times and stretching out into space in all directions answers both of these questions. A charge sets up the field around itself that is everywhere. This explain how a non-contact force can exist. The second charge is in “contact” with the field rather than the charge. And it also explains how the force can act immediately, because as soon as the charge enters the field, which is everywhere, it interacts with it and a force is exerted.

 

That means that the force-vector field that we are measuring with the test charge depends on the test charge itself. It’s like saying that the length of the measured table depends on the ruler.

In order to have a field that does not depend on the test charge we need to “divide out” the dependence on the test charge. That simply means dividing the force by the test charge. This ratio of force and test charge, or the force per unit test charge is how the electric field is defined. The electric field is therefore the force per unit test charge.

 

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The model of the electric field makes our life much easier. We can now find the force on a test charge without using superposition even four or more charges set up a very complicated field, like in the picture. Since the electric field is related to the force we can fin the force on a test charge by drawing the tangent line to the electric field. The strength of the force (or the length of the force vector) depends on how string the electric field is at that particular point. We find the strength of the electric field by looking at how dense the lines are around that point. The denser they are the stronger the electric field is.

Below is a sample problem you might solve. Before we introduced the model of the electric field, you would have to find the force on a test charge, both in length and in magnitude. There are four locations that I am interested in, so I would have to put four test charges at these locations. The force on these test charges is always tangent to th eclectic field line, so I would draw a tangent line. Then I will need to find how the forces compare. I do that by comparing the electric field. The density of the field lines tells me where the field is the strongest.

 

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