Because if you know about vector equations, look at this electric fields vector, this electric forces vector. This electric field is just gonna adopt the same direction as the electric force as long as this Q is positive. If this Q were negative it would flip the sign of this electric force and then the E would point the opposite direction. But if we keep our test charge positive then we know, okay, the electric field's just gonna point the same direction as the electrical force on that positive test charge.
Here's what I mean. We take our positive test charge. We move it around. If I wanna know the electric field at this spot right here, I just ask myself, which way does the electrical force point on that test charge? The electric force would point to the right since it's being repelled by this other positive charge over here. I know that the electric force points to the right, these charges repel each other. And since the electric force points to the right, that means the electric field in this region also points to the right.
It might not have the same magnitude. The electric force might be 20 newtons and the electric field might be 10 newtons per coulomb but they have the same direction.
And I can move this charge somewhere else, let's say I move it over here. Which way would the electric force point? Well, these positive charges are still repelling. I'd still have an electric force to the right. That electric force would be smaller but it would still point to the right and that means the electric field also still points to the right, it would be smaller as well but it would still point to the right.
And if we wanna determine the electric field elsewhere, we can move our positive test charge, I'll move it over to here. I'll ask which way is the electric force on this positive test charge? That would be in this direction since these positive charges are repelling each other, they're pushing each other away so this positive always gets pushed away from this other positive charge.
And so, that also means that the electric field is pointing in that direction as well. 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.
If a positive test charge is placed at point P. Similarly, force due to -Q charge on the test charge would be attractive. Draw two vectors at point P of equal magnitude and directions as discussed above.
The resultant of these two vectors will point in a direction as shown in the figure below. Direction of electric field? See picture. Jun 22, The presence of a few lines around a charge is typically sufficient to convey the nature of the electric field in the space surrounding the lines. There are a variety of conventions and rules to drawing such patterns of electric field lines. The conventions are simply established in order that electric field line patterns communicate the greatest amount of information about the nature of the electric field surrounding a charged object.
One common convention is to surround more charged objects by more lines. Objects with greater charge create stronger electric fields. By surrounding a highly charged object with more lines, one can communicate the strength of an electric field in the space surrounding a charged object by the line density. This convention is depicted in the diagram below. Not only does the density of lines surrounding any given object reveal information about the quantity of charge on the source charge, the density of lines at a specific location in space reveals information about the strength of the field at that location.
Consider the object shown at the right. Two different circular cross-sections are drawn at different distances from the source charge. 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.
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