Where Do Electric Fields Cancel Out Between Two Charged Particles?

[Bashyboy]

Homework Statement

In the figure below, determine the point (other than infinity) at which the electric field is zero. (Let q1 = -2.45 µC and q2 = 6.50 µC.)

Homework Equations

The Attempt at a Solution

Here is a little commentary my author gives on this problem:

Each charged particle produces a field that gets weaker farther away, so the
net field due to both charges approaches zero as the distance goes to infinity in any direction. We are asked for the point at which the nonzero fields of the two particles add to zero as oppositely directed vectors of equal magnitude.

The electric field lines are represented by the curved lines in the diagram. The field of positive charge q2 points radially away from its location. Negative charge q1 creates a field pointing radially toward its location. These two fields are directed along different lines at any point in the plane except for points along the line joining the particles; the two fields cannot add to zero except at some location along this line. To the right of the positive charge on this line, the fields are in opposite directions but the field from the larger magnitude of the positive charge dominates. In between the two particles, the fields are in the same direction and add together. To the left of the negative charge, the fields are in opposite directions and at some point they will add to zero such that E = E₊ + E_{_} = 0.

For the first selection, are they saying that the particles together create one field? How is that so? As for the second selection, I honestly do not know what is it is saying.

Also, I know that the electric force that two particles exert on each other are equal in magnitude and opposite, but the electric fields aren't equal and opposite. So, when I find that the distance between the two particles where the two electrics fields are equal and opposite and they cancel, what is happening physically? What does it mean for electric fields to cancel each other out?

 

[Simon Bridge]

For the first selection, are they saying that the particles together create one field? How is that so?

The field is a description of how objects move in relation to the two charges ... thus it has to made from both particles together. We can break it up into contributions due to each charge to help us do the math.

I know that the electric force that two particles exert on each other are equal in magnitude and opposite, but the electric fields aren't equal and opposite.

Since the electrostatic force on a particle with charge q is given by $\vec{F}=q\vec{E}$, if the forces are equal and opposite then the fields must also be equal and opposite.

These two fields are directed along different lines at any point in the plane except for points along the line joining the particles; the two fields cannot add to zero except at some location along this line

What the section is telling you is that the electric field is a vector - if the contributions from each charge, at a point, do not point in exactly opposite directions, then they cannot cancel. You've seen this in your work on forces.

So, when I find that the distance between the two particles where the two electrics fields are equal and opposite and they cancel, what is happening physically? What does it mean for electric fields to cancel each other out?

It means there is no electric field there - physically, the motion of a point test charge placed at that point is unaffected by the presence of the charges around it.

A real test charge there will have some extent in space - so would experience conflicting forces pulling all around it, resulting in no net change in momentum. Just the same as you are used to when forces all balance.

 

[Bashyboy]

Wow, that was a phenomenal explanation. Thank you!

 

[Simon Bridge]

No worries - we aim to please but shoot to kill.