# B Is the total electric field of two opposite charges 0?

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1. Sep 19, 2016

Let's say you have two particles that are the same in magnitude but have opposite charges like the equation down below:

E1 = -q*k/r^2
E2 = q*k/r^2

ETotal = q*k/r^2 + -q*k/r^2 = 0

Does this mean that the electric field of both these charges cancel out each other? Then what is the electric field if they ever come into contact since opposite attracts?

2. Sep 19, 2016

### Staff: Mentor

Only if the two charges are right on top of each other. In general, the field at any point will be the vector sum of the fields from each charge.

3. Sep 19, 2016

So it's like the picture down below where at any point (position) in that picture the electric field = 0 just as long as those two charges are either 0, 90, 180, and 270 degrees from each other? Anything that does not make their magnitude different from one another. In that case 45 degrees, the magnitude and the Electric field will be 0 as well? As a result, the negative charge can is all to pull all the electric field that the positive charge has to give out?

4. Sep 19, 2016

### Staff: Mentor

I don't understand what you mean by "0, 90, 180, and 270 degrees from each other". Where do you think the field is zero?

5. Sep 19, 2016

### sophiecentaur

The field at a distance of one single charge will be reduced by the presence of a second, opposite charge. (An Electric Dipole).
The cancellation is never complete but the field will drop off quicker than the Inverse Square Law for a single charge. See this link.

6. Sep 19, 2016

I think that the electric field is zero everywhere within the bottom picture since they share the same axis.

7. Sep 19, 2016

### Staff: Mentor

The electric field at any point is the vector sum of the fields from the two charges. See this diagram for an example:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/mulpoi.html#c2

This example is for two positive charges, not for one positive and one negative. However, if you make one of the charges negative, you simply "flip" its electric field vector around the point in question so it points in the opposite direction (directly towards the negative charge). This changes the resultant (total) electric field vector, but does not make it zero.

For your situation, two charges that are equal in magnitude but opposite in sign, there is no point where the total electric field is zero.

8. Sep 19, 2016

### Staff: Mentor

It is not. In fact, the red arrows indicate the direction of the electric field at each point in the diagram, and there is nowhere where it is zero.

It would be a good exercise to try calculating the field at a few points, just to see how it never comes out zero. You can do this for points on the line through the two charges with just elementary arithmetic; you'll need some trigonometry to do it for points off that line.

9. Sep 19, 2016

### Staff: Mentor

Realize that the two charges would 'share the same axis' no matter where they are. (You'd just rotate the diagram as needed.)

Please read the posts above (by jtbell and Nugatory) to understand why the field is not zero anywhere.

10. Sep 20, 2016

### CWatters

If the charges were the same then there would be one point where the field is zero.

11. Sep 20, 2016

### A.T.

If they merge, the resulting charge and thus the field is zero. Otherwise see the other answers.

12. Sep 20, 2016

### pixel

You have to be careful when using equations. In particular, how are you defining "r?" If it's the distance from the first charge (located therefore at the origin where r=0), then you can't use the second equation unless the second charge is also at the origin.