How is direction of an electric field determined

How does the electric force between two charged objects change? How does electric force affect an atom? How can electric forces be measured? How are electric forces and gravity similar? How are electric forces and distance related? How are electric forces and charge related? See all questions in Electric Force. These cross-sections represent regions of space closer to and further from the source charge.

The field lines are closer together in the regions of space closest to the charge; and they are spread further apart in the regions of space furthest from the charge. Based on the convention concerning line density, one would reason that the electric field is greatest at locations closest to the surface of the charge and least at locations further from the surface of the charge.

Line density in an electric field line pattern reveals information about the strength or magnitude of an electric field. A second rule for drawing electric field lines involves drawing the lines of force perpendicular to the surfaces of objects at the locations where the lines connect to object's surfaces.

At the surface of both symmetrically shaped and irregularly shaped objects, there is never a component of electric force that is directed parallel to the surface. The electric force, and thus the electric field, is always directed perpendicular to the surface of an object. If there were ever any component of force parallel to the surface, then any excess charge residing upon the surface of a source charge would begin to accelerate.

This would lead to the occurrence of an electric current within the object; this is never observed in static electricity. Once a line of force leaves the surface of an object, it will often alter its direction.

This occurs when drawing electric field lines for configurations of two or more charges as discussed in the section below. A final rule for drawing electric field lines involves the intersection of lines. Electric field lines should never cross. This is particularly important and tempting to break when drawing electric field lines for situations involving a configuration of charges as in the section below. If electric field lines were ever allowed to cross each other at a given location, then you might be able to imagine the results.

Electric field lines reveal information about the direction and the strength of an electric field within a region of space. If the lines cross each other at a given location, then there must be two distinctly different values of electric field with their own individual direction at that given location.

This could never be the case. Every single location in space has its own electric field strength and direction associated with it. Consequently, the lines representing the field cannot cross each other at any given location in space. In the examples above, we've seen electric field lines for the space surrounding single point charges. But what if a region of space contains more than one point charge? How can the electric field in the space surrounding a configuration of two or more charges be described by electric field lines?

To answer this question, we will first return to our original method of drawing electric field vectors. Each charge creates its own electric field. The results of these calculations are illustrated in the diagram below with electric field vectors E A and E B drawn at a variety of locations. The strength of the field is represented by the length of the arrow and the direction of the field is represented by the direction of the arrow. Since electric field is a vector, the usual operations that apply to vectors can be applied to electric field.

That is, they can be added in head-to-tail fashion to determine the resultant or net electric field vector at each location. This is shown in the diagram below. The diagram above shows that the magnitude and direction of the electric field at each location is simply the vector sum of the electric field vectors for each individual charge.

If more locations are selected and the process of drawing E A , E B and E net is repeated, then the electric field strength and direction at a multitude of locations will be known.

This is not done since it is a highly time intensive task. Ultimately, the electric field lines surrounding the configuration of our two charges would begin to emerge.

For the limited number of points selected in this location, the beginnings of the electric field line pattern can be seen. This is depicted in the diagram below. Note that for each location, the electric field vectors point tangent to the direction of the electric field lines at any given point.

The construction of electric field lines in this manner is a tedious and cumbersome task. The use of a field plotting computer software program or a lab procedure produces similar results in less time and with more phun. We keep doing this. I can move this somewhere else. I can move this positive charge down here. The charges repel so the electric force would point downward. And that means the electric field would also point down. If you keep doing this, if you keep mapping what's the direction of the electric force on a positive test charge?

Eventually, you realize oh, it's always just gonna point radially out away from this other positive charge. And so we know the electric field from a positive charge is just gonna point radially outward, that's why we drew it like this.

Because this positive charge would push some positive test charge radially away from it since it would be repelling it. Positive charges create electric fields that point radially away from them. Now what if the charge creating the field were a negative charge? So, let's try to figure that one out, let me get rid of this.

Let's say the charge creating the electric field were negative, a big negative charge, how do we determine the electric field direction around this negative charge? We're gonna do the same thing, we're gonna take our positive test charge and we're gonna keep our test charge positive, that way we know that the direction of the electric force on this positive test charge is gonna be the same direction as the electric field in that region.

In other words, the positivity of this test charge will just make it so that the electric field and electric force point in the same direction. And if we do that, I'll move this around. We'll just put it at this point here, we'll move this test charge here. Which way is the force on that test charge? This time it's getting attracted to this negative charge.

Opposite charges attract so the electric force would point this way and since it's a positive test charge and it preserve the direction in this equation, that means the electric field also points in that leftward direction. And we can keep mapping the field we'll move the test charge over to here.

The electric force this time is gonna point up because this positive test charges is attracted to this negative charge. And if the electric force points up, that means the electric field also points up in that region. And you'd realize the electric force is always gonna pull a positive test charge toward this negative creating the field around it. And because of that, the electric field created by a negative charge points radially inward toward that negative charge. This is different. Positive charge created a field that pointed radially away from because it always repelled the positive test charge.

But a negative charge creates an electric field that points radially into because it's always attracting a positive test charge.

Basically what I'm saying is that if we got rid of all these, clean this up, the electric field from a positive charge points radially outward but if it were a negative charge, you'd have to erase all these arrowheads and put them on the other end.

Because the electric field from a negative charge points radially inward toward that negative charge. In other words, the electric field created by a negative charge at some point in space around it is gonna point toward that negative charge creating that electric field. And so, that's how you could determine the direction of the electric field created by a charge.

If it's a positive charge you know the electric field points radially out from that positive. And if it's a negative charge, you know the field points radially inward toward that negative charge. Okay, so that was number one here. We found the direction of the electric field created by a charge.

Check, we've done this. Now we should get good at finding the direction of the electric force exerted on a charge in a field. What does that mean? Let's say you had a region of space with electric field pointing to the right. What's creating this electric field? I don't know. It doesn't even really matter. This is why the electric field is a cool idea. I don't really need to know what created this electric field. I mean, it could be positive charges over here creating fields that point radially away from them.

But it could also be negative charges over here creating fields that point radially toward them or both, we don't really know. It doesn't really matter. As long as I now have an electric field that points to the right, I can figure out the direction of the electric force on a charge in that field.

Let's put a charge in this field. We'll just start with a positive charge. We'll put this charge in here. Since the electric field is equal to the electric force on a charge divided by that charge, if this is a positive charge and this charge we put down here is positive, then the electric force points in the same direction as the electric field and vice versa.

The electric field and electric force would point the same direction if the charge feeling that force is a positive charge. This is just a long way of saying that the electric force on a positive charge is gonna point in the same direction as the electric field in that region. If there's an electric field that points to the right like we have in here then the electric force on a positive charge in that region is also gonna point to the right.