Why Does Positive Charge Exert Elec. Field Beyond Neg. Charge?

[Callmelucky]

Homework Statement

I wonder how is possible that positive charge can exert el. field beyond negative charge?

Relevant Equations

E=(k*Q)/r^2

I wonder how it is possible that a positive charge can exert el. field beyond negative charge?
Shouldn't they "connect" and therefore positive charge should stop to have el. field beyond neg. charge? I mean, I am obviously wrong about that, but can someone please explain why/how el. field from positive charge continues beyond negative charge?

Red arrows represent the direction of el. field of positive charge(pic below). Also here is the link to YT video( ).

In this case, they are of different value, but would positive charge exert el. field beyond negative charge if they were of same value?

Thank you

 

[BvU]

The fields simply add up (as vectors). If the charges have the same but opposite value, the field strength from the charge that is further away can't outdo the field from the closer one.

Draw plots of the horizontal component of $\vec E$ on the horizontal axis to convince yourself.

$\$

 

[Callmelucky]

So, that means that field from the positive charge continues to go through the negative charge?
Like this(pic below)?

 

[PeroK]

Homework Statement:: I wonder how is possible that positive charge can exert el. field beyond negative charge?
Relevant Equations:: E=(k*Q)/r^2

I wonder how it is possible that a positive charge can exert el. field beyond negative charge?
Shouldn't they "connect" and therefore positive charge should stop to have el. field beyond neg. charge? I mean, I am obviously wrong about that, but can someone please explain why/how el. field from positive charge continues beyond negative charge?

Red arrows represent the direction of el. field of positive charge(pic below). Also here is the link to YT video( ).

In this case, they are of different value, but would positive charge exert el. field beyond negative charge if they were of same value?

Thank you

I think it's a good question. The theory of classical EM tells you to add fields due to point charges regardless of whether there are other charges in the way, as it were. If you say that's physically unrealistic, then I might agree with you. But, that's the mathematical model that underpins classical EM.

Classical Newtonian gravity is physically unrealistic too. And Newton himself was the first to point this out.

If you dig deeper then classical EM is replaced by QED (quantum electrodynamics) and things are explained very differently. But, that theory to many people is even less physically realistic.

 

[Callmelucky]

I think it's a good question. The theory of classical EM tells you to add fields due to point charges regardless of whether there are other charges in the way, as it were. If you say that's physically unrealistic, then I might agree with you. But, that's the mathematical model that underpins classical EM.

Classical Newtonian gravity is physically unrealistic too. And Newton himself was the first to point this out.

If you dig deeper then classical EM is replaced by QED (quantum electrodynamics) and things are explained very differently. But, that theory to many people is even less physically realistic.

Thank you very much. I also wonder why textbook authors didn't mention that in the textbook, if you didn't answer so fast God knows how long would I have been looking for an explanation.

 

[Callmelucky]

I think it's a good question. The theory of classical EM tells you to add fields due to point charges regardless of whether there are other charges in the way, as it were. If you say that's physically unrealistic, then I might agree with you. But, that's the mathematical model that underpins classical EM.

Classical Newtonian gravity is physically unrealistic too. And Newton himself was the first to point this out.

If you dig deeper then classical EM is replaced by QED (quantum electrodynamics) and things are explained very differently. But, that theory to many people is even less physically realistic.

And I forgot to ask, what is meant when they say that el. fields cancel each other out? I don't get that. If you open the link of the video I posted in the opening post and go to the end of the video, you will hear that guy from the video(I guess his name is Michael Van Biezen) says that at 5.45 meters on the x-axis charges cancel out and that el. field is 0 at that point. How can el. field be 0 if el. field has no end? It can only become weaker and weaker with distance but can't disappear.

EDIT: I understand what is meant when it's said that same charges cancel out right in the middle(so that there is no el. field at that one point), but how can opposite charges cancel out?

 

[PeroK]

EDIT: I understand what is meant when it's said that same charges cancel out right in the middle(so that there is no el. field at that one point), but how can opposite charges cancel out?

Positive plus negative can be zero. In this case, by symmetry, it can't be anything but zero.

 

[BvU]

How can el. field be 0 if el. field has no end? It can only become weaker and weaker with distance but can't disappear.

The two electrostatic forces cancel at that point only. The x component of the field changes sign at that point, that's all. On one side the nearest charge wins, on the other side the stronger charge wins.

Draw plots of the horizontal component of $\vec E$ on the horizontal axis to convince yourself.

(i.e. of the two contributions separately, and of the sum)

$\$

 

[Callmelucky]

Thank you @BvU @PeroK

 

[Mister T]

I wonder how it is possible that a positive charge can exert el. field beyond negative charge?
Shouldn't they "connect" and therefore positive charge should stop to have el. field beyond neg. charge? I mean, I am obviously wrong about that, but can someone please explain why/how el. field from positive charge continues beyond negative charge?

The charge is not moving, so it doesn't make sense to say it stops at some place. What you are doing is calculating the value of the electric field due to the positive charge, while ignoring the presence of the negative charge. Likewise, you can find the value of the electric field due to the negative charge, while ignoring the presence of the positive charge. Then finally, you add the two electric field vectors together to get the actual electric field at that point. It's a scheme that people invented, and they use it because it works.

In general, it's called the superposition principle. To get the effect of several causes you calculate the effect of each cause separately, then add them together to get the actual effect.

Now, suppose that when you went to add those two electric field vectors, and they happen to be equal in magnitude but opposite in direction. When you add them you get zero. This is what is meant when people say they "cancel out". They simply mean that they add to zero.

 

[haruspex]

how can opposite charges cancel out?

Don't confuse field cancellation and potential cancellation.
As others have noted, both fields and potentials add, but fields have direction, potentials don’t.
The potential due to opposite charges always tend to cancel, and when at equal distance from equal and opposite charges the potentials cancel completely.
The fields due to opposite charges tend to cancel at a point (i.e. produce a smaller magnitude field than the larger by itself would) if the charges are on the same side of the point; if they are on opposite sides, the fields will reinforce since they act in the same direction, and the fields of like charges tend to cancel in the space between them.

Going back to your original diagram, you may be mixing up two views of field lines. When you draw the field lines of the combined field from two equal and opposite charges, each field line originates at the positive charge and terminates at the negative. This may have given you the impression that they "stop" each others' fields. But it is equally valid to think of the two fields operating independently and unaffected by the other charge.

 

[kuruman]

To @Callmelucky:
A related statement about field lines is "Field lines never cross." Can you figure out the explanation why?

 

[Callmelucky]

To @Callmelucky:
A related statement about field lines is "Field lines never cross." Can you figure out the explanation why?

Thank you for asking. It's because, when adding vector field lines the results in another vector. Like on pic below. Right?

 

[kuruman]

Thank you for asking. It's because, when adding vector field lines the results in another vector. Like on pic below. Right?

Right. That is superposition and answers your original question. With two point charges the electric field at any point in space is, as you said, a single vector. So if you have two point charges, q₁, q₂ and arbitrary point P in space

1. Draw an electric field vector due to q₁ at point P as if q₂ were not there;
2. Draw an electric field vector due to q₂ at point P as if q₁ were not there;
3. Add the two vectors to get the electric field at point due to the two charges. That is superposition.

Do you see how this answers your initial question?

 

[Mark Harder]

Homework Statement:: I wonder how is possible that positive charge can exert el. field beyond negative charge?
Relevant Equations:: E=(k*Q)/r^2

I wonder how it is possible that a positive charge can exert el. field beyond negative charge?
Shouldn't they "connect" and therefore positive charge should stop to have el. field beyond neg. charge? I mean, I am obviously wrong about that, but can someone please explain why/how el. field from positive charge continues beyond negative charge?

Lucky,
By placing opposite charges near each other you have created an electric dipole. It's field will look similar to that of a magnetic dipole. It will extend throughout space, but its strength will fall off as a higher power with distance than 1/r^2. 1/r^6? I forget what power exactly.
In any event, yes the positive field contribution will extend beyond the negative charge and then double back toward it from its backside. Wikipedia has some nice diagrams and simulated motions of the charges.

 

[tech99]

It is interesting that for a chunk of metal, say copper, the charges of the electrons and protons are enormous, yet the external fields cancel due to superposition.

 

[PeroK]

It is interesting that for a chunk of metal, say copper, the charges of the electrons and protons are enormous, yet the external fields cancel due to superposition.

Or a chunk of anything!