Electric Field Lines: Midpoint Between 2 Charges

[lawsonfurther]

I notice from the classic electric field line diagram of two positive charges that there is no field line going along the line segment joining those two charges.
So I wonder whether that is true or it's just a way that you can't show all the field lines in the diagram but it actually exists.
(I know that there is electric field right in between those two charges, maybe except for the midpoint of the line segment, but what I am interested in is the electric field line)
Thanks

 

[ZapperZ]

I notice from the classic electric field line diagram of two positive charges that there is no field line going along the line segment joining those two charges.
So I wonder whether that is true or it's just a way that you can't show all the field lines in the diagram but it actually exists.
(I know that there is electric field right in between those two charges, maybe except for the midpoint of the line segment, but what I am interested in is the electric field line)
Thanks

Try a "parallel" route here. Have you seen the magnetic field lines when a N-pole of a bar magnet faces the N-pole of another bar magnet?

Zz.

 

[Doc Al]

Electric field lines are just a way to help visualize the strength and direction of the electric field. It's the field that exists, not the field lines.

 

[Drakkith]

No, there would be no field line since a field line going directly between the two would end on a positive charge, which cannot happen. Field lines only exit positive charges, they don't end on them.

The field lines allows us to visualize the vector field, and they represent the direction that the vectors in the vector field point to at any location. A single field line is the path through the vector field such that each vector points towards the very next point along the field line (kind of. I'm probably butchering my explanation, and the true explanation requires some knowledge of vector calculus).

For two positive charges, the line directly between the two leads to a point in the very middle where the forces are exactly balanced and completely cancel each other out. Trying to draw a field line would result in the line simply ending at this point, so we can't do it. But we can draw field lines as close to this as we want, so we can always represent the repulsive force with field lines.

So I wonder whether that is true or it's just a way that you can't show all the field lines in the diagram but it actually exists.

There are an infinite number of possible field lines in any diagram, so we have to choose which ones are most convenient for us to draw. Also remember that field lines aren't real. They're like the topographic lines in a topographic map or the latitude and longitude lines on a globe. They only exist on paper and in our heads and are only one of several possible ways of representing the electric field. Another common way is to colorize a diagram so that the intensity of the color represents how much force would be felt by a test charge in the field.

 

[kuruman]

Assume that the two positive charges are identical. How would you draw the field line (there can be only one) on the line joining the charges? At the midpoint the field is zero. To the left of the midpoint the field points to the right and to the right of midpoint the field points to the left. However, if you draw arrows on each side of the midpoint, one pointing to the right and one to the left, there is a problem: the drawing implies that field lines end at the midpoint which is incorrect. Field lines end at negative charges but there is no negative charge at the midpoint. So I repeat, how would you draw the field line? It is best to draw nothing rather than something misleading.

 

[lawsonfurther]

Electric field lines are just a way to help visualize the strength and direction of the electric field. It's the field that exists, not the field lines.

I agree with you.

 

[lawsonfurther]

They only exist on paper and in our heads and are only one of several possible ways of representing the electric field. Another common way is to colorize a diagram so that the intensity of the color represents how much force would be felt by a test charge in the field.

Colorizing a diagram may look like a better way to visualize the electric field.
Right now I am thinking there may be some kind of flaw in the field line diagram, which is that it cannot really show in which direction would a test charge move if it is placed somewhere along the line joining those charges (ignoring it is placed right at the midpoint at this moment). Am I correct?

 

[lawsonfurther]

Try a "parallel" route here. Have you seen the magnetic field lines when a N-pole of a bar magnet faces the N-pole of another bar magnet?

Zz.

Yes. It looks like the electric field lines when two positive charges are placed near each other.
So there you remind me. Is there any magnetic field line that lies along the line which joins those two magnets together?
The answer to it looks like similar to the answer to my question :)

 

[lawsonfurther]

Assume that the two positive charges are identical. How would you draw the field line (there can be only one) on the line joining the charges? At the midpoint the field is zero. To the left of the midpoint the field points to the right and to the right of midpoint the field points to the left. However, if you draw arrows on each side of the midpoint, one pointing to the right and one to the left, there is a problem: the drawing implies that field lines end at the midpoint which is incorrect. Field lines end at negative charges but there is no negative charge at the midpoint. So I repeat, how would you draw the field line? It is best to draw nothing rather than something misleading.

I admit I can't come up with any idea to draw the field line on the line joining the charges, and I won't say the field line is discontinuous right between those charges.
I think you're right. That is a good way to avoid any confusion.

 

[Drakkith]

Colorizing a diagram may look like a better way to visualize the electric field.

It's not any better or worse than drawing field lines. It's just different.

Right now I am thinking there may be some kind of flaw in the field line diagram, which is that it cannot really show in which direction would a test charge move if it is placed somewhere along the line joining those charges (ignoring it is placed right at the midpoint at this moment). Am I correct?

No. The diagram would indeed show which way the charge moves. It would move away from the nearer charge directly towards the other charge. You can tell that this would happen because the field lines coming from the nearer charge are denser near the test charge than the field lines from the charge further away.

So there you remind me. Is there any magnetic field line that lies along the line which joins those two magnets together?
The answer to it looks like similar to the answer to my question :)

There is not.

 

[lawsonfurther]

It's not any better or worse than drawing field lines. It's just different.
No. The diagram would indeed show which way the charge moves. It would move away from the nearer charge directly towards the other charge. You can tell that this would happen because the field lines coming from the nearer charge are denser near the test charge than the field lines from the charge further away.
There is not.

However, we are talking about the test charge which does not occupy any space, i.e. it is a point charge. So in the perspective of a test charge, there is no meaning of dense or sparse electric field lines. Only whether an electric field line passes through that charge and (if so) how a field line indicates the physical behavior of that test charge are meaningful to discuss. (Again, I agree that there is an electric field(or to be precise, a net electric field) everywhere around and between the charges, except for the midpoint of the line segment connecting those charges together. And that is what a test charge will actually experience.)

Generally speaking, if the direction of the electric field line shows the direction of the acceleration of a positive test charge when it is placed inside the field, and now that a test charge does accelerate when it is placed between two positive charges, shouldn't there be an electric field line along the line which connects those charges?

(Please forgive me if I mess up the relationship between the direction of the electric field line and the one of the acceleration experienced by the test charge)

 

[kuruman]

Generally speaking, if the direction of the electric field line shows the direction of the acceleration of a positive test charge when it is placed inside the field, and now that a test charge does accelerate when it is placed between two positive charges, shouldn't there be an electric field line along the line which connects those charges?

You seem to think that there is. Please make a drawing and post it. Be sure to use arrowheads to indicate the direction of the electric field at representative points.

 

[lawsonfurther]

You seem to think that there is. Please make a drawing and post it. Be sure to use arrowheads to indicate the direction of the electric field at representative points.

It is just part of my assumption. I said it before, if there isn't, please give me a logical explanation on the relationship between those two directions. I haven't been fully convinced by both opinions yet.

 

[kuruman]

Electric field lines, as has been said before, are an artifact to help us visualize forces on charges placed in a region where there is an electric field. They exist and are drawn following the rule that they must start at positive charges (or at infinity) and end at negative charges (or at infinity.) If you have two positive charges, as is the case here, any field line that you draw starting at either one of the charges, must end at infinity because there are no negative charges anywhere. Connecting the two charges you have a line segment. If you start at the charge on the left, say, and draw a field line on the segment and keep going along the segment, what happens when you reach the midpoint? You can't keep going past the midpoint because the force on a test charge changes direction. Your only choice is to veer up or down at a right angle and continue out to infinity along the perpendicular bisector. So if you insist on drawing a field line, along the segment, at the midpoint you would have to draw a 90° cross with two arrows going in horizontally and two arrows coming out vertically and continuing out to infinity. They are the asymptotes of the field lines that you see in textbooks when you have two positive charges.

 

[Drakkith]

However, we are talking about the test charge which does not occupy any space, i.e. it is a point charge. So in the perspective of a test charge, there is no meaning of dense or sparse electric field lines. Only whether an electric field line passes through that charge and (if so) how a field line indicates the physical behavior of that test charge are meaningful to discuss.

That is incorrect. The density of the field lines around a point gives you an indication of what the field is doing and you can use this knowledge to predict what will happen to a point-like test charge. The fact that the horizontal components of the field lines around a point all point right means that a test charge will feel a force that pushes it to the right. The fact that the density of the field lines is higher to the left of the point than the right means that the force weakens as the test charge moves from left to right.

Even though we can't draw a field line straight through the middle doesn't mean the field vectors aren't there. The field vectors along the line all point towards the a point exactly halfway along the line connecting the charges.

Generally speaking, if the direction of the electric field line shows the direction of the acceleration of a positive test charge when it is placed inside the field, and now that a test charge does accelerate when it is placed between two positive charges, shouldn't there be an electric field line along the line which connects those charges?

No.

 

[lawsonfurther]

That is incorrect. The density of the field lines around a point gives you an indication of what the field is doing and you can use this knowledge to predict what will happen to a point-like test charge. The fact that the horizontal components of the field lines around a point all point right means that a test charge will feel a force that pushes it to the right. The fact that the density of the field lines is higher to the left of the point than the right means that the force weakens as the test charge moves from left to right.

Even though we can't draw a field line straight through the middle doesn't mean the field vectors aren't there. The field vectors along the line all point towards the a point exactly halfway along the line connecting the charges.
No.

So electric field lines don't need to cover all the vicinity of two like charges (while they indeed cover when only a single charge is present). There are somewhere (to be exact, the perpendicular bisector and the line connecting the charges) where the direction of the acceleration of a test charge cannot be shown directly by the direction of the field lines, simply because the field line doesn't exist in the diagram. Therefore not all the field vectors can be covered by specific field lines in this scenario. Am I correct?

 

[Drakkith]

So electric field lines don't need to cover all the vicinity of two like charges (while they indeed cover when only a single charge is present). There are somewhere (to be exact, the perpendicular bisector and the line connecting the charges) where the direction of the acceleration of a test charge cannot be shown directly by the direction of the field lines, simply because the field line doesn't exist in the diagram. Therefore not all the field vectors can be covered by specific field lines in this scenario. Am I correct?

There are an infinite number of possible field lines we could label on any diagram. But if we labeled them all the diagram would just be a big dark splotch, so we have to choose a convenient number of them to label. Usually you can find a field line to place your test charge on, but not always, as this example shows. So yes, you are correct in that not all of the field vectors can be covered by field lines in this example.

 

[lawsonfurther]

There are an infinite number of possible field lines we could label on any diagram. But if we labeled them all the diagram would just be a big dark splotch, so we have to choose a convenient number of them to label. Usually you can find a field line to place your test charge on, but not always, as this example shows. So yes, you are correct in that not all of the field vectors can be covered by field lines in this example.

I think we can say for any point inside the field but not along the perpendicular bisector or the line connecting the charges, we can always find an electric field line that passes through that point. And the field lines are shown to us upon our request .
But hold on. Suppose you are asked (though unrealistically) to label all the field lines on the diagram, would it be a big dark splotch as you said or a big dark splotch with one finite white line segment and one white line being perpendicular and bisecting the line segment?

But still. I appreciate your answer to my question.

 

[Drakkith]

Suppose you are asked (though unrealistically) to label all the field lines on the diagram, would it be a big dark splotch as you said or a big dark splotch with one finite white line segment and one white line being perpendicular and bisecting the line segment?

I suppose that depends on how you go about drawing your diagram.

 

[ZapperZ]

I think we can say for any point inside the field but not along the perpendicular bisector or the line connecting the charges, we can always find an electric field line that passes through that point. And the field lines are shown to us upon our request .
But hold on. Suppose you are asked (though unrealistically) to label all the field lines on the diagram, would it be a big dark splotch as you said or a big dark splotch with one finite white line segment and one white line being perpendicular and bisecting the line segment?

First of all, you need to play with this PhET applet

https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.html

Secondly, you are putting WAY too much emphasis on these "lines", when the whole POINT of the visualization is the superposition of electric field vectors at a particular location in space. In other words, pick a point in space, and then ask "What is the electric field vector here?". When you ask that, the insistence on these continuous lines representing "electric field lines" has no bearing on what you need.

These electric field lines, if you still want to use them, represent the gradient of the electric potential field, i.e. E = -∇V. In our intro lab, we ask students to map an equipotential field, and THEN, as a consequence of that potential field, to draw these lines that run perpendicular to the equipotential lines.

In the end, there is nothing to stop you from setting up to positive charges, and then solve for the electric field for both charges at ALL points in space. Map out and sketch the electric field and see for yourself what you get. If this is helpful to you, then you should do it.

Zz.

 

[lawsonfurther]

First of all, you need to play with this PhET applet

https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.html

Secondly, you are putting WAY too much emphasis on these "lines", when the whole POINT of the visualization is the superposition of electric field vectors at a particular location in space. In other words, pick a point in space, and then ask "What is the electric field vector here?". When you ask that, the insistence on these continuous lines representing "electric field lines" has no bearing on what you need.

These electric field lines, if you still want to use them, represent the gradient of the electric potential field, i.e. E = -∇V. In our intro lab, we ask students to map an equipotential field, and THEN, as a consequence of that potential field, to draw these lines that run perpendicular to the equipotential lines.

In the end, there is nothing to stop you from setting up to positive charges, and then solve for the electric field for both charges at ALL points in space. Map out and sketch the electric field and see for yourself what you get. If this is helpful to you, then you should do it.

Zz.

To be honest, I have already played with this simulation program before I posted my question on this forum, and it is the diagram there that makes me think about whether or not there is an electric field line right between two positive charges. I think we can all agree on my last conclusion: not all of the field vectors can be covered by specific field lines in this example.

 

[ZapperZ]

not all of the field vectors can be covered by specific field lines in this example.

What does that mean?

There is nothing to prevent me from calculating the electric field at a midpoint between two equal charges. The value may be zero, but it doesn't mean Coulomb's law doesn't cover that region.

Again, the net field is the superposition of ALL the sources involved. The electric field "lines" are a visualization tool that we use to indicate the vector direction of the coulomb force if a positive test charge is placed at that location, i.e. F = qE. It appears that you are trying to make it more than that.

Zz.

 

[lawsonfurther]

Maybe you are too picky on my statement. What I mean is that the field vector of a positive test charge when it is placed at some point can be shown as the tangent vector (not sure I word it correctly) of the field line at that point if there exists a field line passing through that point. And since we agree on there is no field line in between the charges and yet there indeed exists field vectors between them, we can say that not all of the field vectors can be covered by field lines.

 

[A.T.]

we can say that not all of the field vectors can be covered by field lines.

A zero vector is obviously not the tangent vector of any line.