# Question on electromagnetism

let's say a hypothetical particle with a positive charge interacts with a negative particle with the same amount of charge, what will happen to their electromagnetic field? will it get neutralized?

thank you...

That's an interesting question.
Which is the relative position of these two particles ?
The geometry is an important point when thinking about electromagnetic fields.
For instance, let us suppose the two particles are in fixed positions, separated by a distance a.
Could you visualize the resultant electrical field ?
Where would the field get the value zero ? Everywhere ?
Remember the dependence of the intensity of electric field with the distance.

ZapperZ
Staff Emeritus

let's say a hypothetical particle with a positive charge interacts with a negative particle with the same amount of charge, what will happen to their electromagnetic field? will it get neutralized?

thank you...

I'm not sure what is stopping you from solving this yourself. For example, put a +q at x=a, and put another charge -q at x=-a. Solve for the E-field everywhere! If you find that too difficult for any r (i.e. you don't know how to use Green's method), then solve it along the axis of symmetry for simplicity sake.

For a approaching zero, you get the solution to the electric dipole problem.

Zz.

Guys...i m really not familiar with green's method or axis of symmetry...

let's say the two particles are mixed (the distance between them is zero), then what happens to the e-m field? does it get neutralized?

i just want to know the result and some proof is also welcomed...

My two cents: the keyword that describes your problem is "electric point dipole".
Put that into google to find the result/proof.

can anyone be more specific?

ZapperZ
Staff Emeritus
can anyone be more specific?

What about YOU being more specific? What is it exactly that you are having trouble here?

Are you able to, say find the E-field of a point charge, located at a location?

Are you also able to google the phrase "electric dipole"? Have you checked that at, say, the Hyperphysics website?

So where exactly are you still having a problem here? The request to be clear and specific goes both ways!

Zz.

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Redbelly98
Staff Emeritus
Homework Helper
the distance between them is zero
In that case the electric field is zero. However, it's a lot more interesting to think about if the distance between them is "very small", but not zero.

In that case the electric field is zero. However, it's a lot more interesting to think about if the distance between them is "very small", but not zero.

In this case i believe the electric field will also be very small but not zero

Right?

Right.

In your original question, the field would disappear. But reality is a little more complicated and wants to conserve energy. The charges will either destroy each other releasing their energy as outgoing fields or other forces will intervene to prevent the charges from coinciding (ex hydrogen atom).

Also, is the coulomb's law useful here in calculating the electromagnetic field between two particles?

Redbelly98
Staff Emeritus
Homework Helper
Not Coulomb's Law per se, since you are not calculating a force. But an equation similar to Coulomb's Law is used to calculate the E-field of a point charge:

$$E = k \frac{q}{r^2} \ ,$$

pointing away from the charge if it is positive, or towards the charge if it is negative.

The best way to learn this is to look at any introductory physics textbook, and go to the section on electric field lines. Also read the material leading up to that discussion, if this is really new to you. Here is a really quick overview of the electric dipole field:

For the electric field of two charges, you need to take the vector sum of the fields due to each charge (E1 and E2 in this figure):

http://www.cavehill.uwi.edu/fpas/cmp/online/p10d/Hunte/Electric%20fields_files/image032.jpg​

And the field you get looks something like this:

http://www.cavehill.uwi.edu/fpas/cmp/online/p10d/Hunte/Electric%20fields_files/image046.gif​

(Images are from http://www.cavehill.uwi.edu/fpas/cmp/online/p10d/Hunte/Electric fields.htm )

vanhees71
Gold Member
It's better to write the fundamental laws in vector form right away. The electric field of a point charge at rest (in the origin of the coordinate system) reads (in Heaviside-Lorentz units)

$$\vec{E}(\vec{x})=\frac{q}{4 \pi} \frac{\vec{x}}{|\vec{x}|^3}.$$

Redbelly98
Staff Emeritus
Homework Helper
It's better to write the fundamental laws in vector form right away.
What's better or best depends on the level of understanding of the person you are addressing.

In that case the electric field is zero. However, it's a lot more interesting to think about if the distance between them is "very small", but not zero.

Are there any real life scenarios where the electromagnetic field is observed as zero?

Also, if any particle's em field is zero (or very small) then does it still have the ability to excite or ionize other particles (let's say in a reactor)?