# Strange question about cancelling electric fields

Summary:
I am curious about the case where two electric or magnetic fields cancel each other out. If a charged particle travels through the region where the cancellation exists, does that area still have electric field energy density?
I am curious about the case where two electric or magnetic fields cancel each other out (I'm assuming this is possible). If a charged particle travels through the region where the cancellation exists, I am assuming the particle behaves as if no field exists. Does that area still have electric field energy density? Should it be understood that there is *no* electric field or is there twice as much energy density, but the two fields are fighting for control of the charged particle and the net force cancels out?

## Answers and Replies

Mister T
Science Advisor
Gold Member
There is no electric field there. The fields you describe as cancelling don't exist. They are just artifacts of the technique used to calculate the value of the field.

There is no electric field there. The fields you describe as cancelling don't exist. They are just artifacts of the technique used to calculate the value of the field.
I am curious then, what happens to the energy that was required to create the two cancelling fields? I was under the impression that the energy was 'stored' in the field itself. Take an extreme example, where the energy to create these fields had a measurable gravitational contribution to the overall system (I know this is a bit unrealistic). But shouldn't the total system gravitate as if there are two large opposing electric fields and not an absence of any field?

Mister T
Science Advisor
Gold Member
That energy never existed. The same reasoning applies.

• Herbascious J
DaveE
Science Advisor
Gold Member
I would vote for the following interpretation:
Every charged particle in the universe creates an EM field which spans the entire universe. At any given point a charged particle reacts to the sum of these fields. If that effect is zero, then people may say that the fields cancel, but I think they are incorrect, the EM field is larger than a single point. In general, fields don't cancel everywhere. To cancel the EM field from an electron, you would need to have a positive particle at the same place with the same velocity, etc.

I would vote for the following interpretation:
Every charged particle in the universe creates an EM field which spans the entire universe. At any given point a charged particle reacts to the sum of these fields. If that effect is zero, then people may say that the fields cancel, but I think they are incorrect, the EM field is larger than a single point. In general, fields don't cancel everywhere. To cancel the EM field from an electron, you would need to have a positive particle at the same place with the same velocity, etc.
If I may propose a hypothetical. Imagine two electrons existing in a void, spatially separated by a distance but in proximity. Each electron's electric field (due to their charge) wants to repel the other electron. Bringing them together required a small amount of energy to over come this repulsion. So now the the over all system is gravitating due to the total mass/energy of each particle (including their inherent fields' energy density I'm assuming) and the additional energy put into the sytem to bring them in proximity of one another. I imagine this energy is stored in the electric field created by bringing them together. My point is that it seems like there is MORE net energy contained within the gravitational field of the system. If I pass a charged particle exactly between them, the field at that location should be canceled. Are not both particles' fields overlapping at that point and in fact have a field energy density at that point? My question is basically, are the two fields fighting for the particle and the particle 'feels' two opposing forces which have energy density, or is the field empty of energy? I am thinking that somehow the energy density is dependent on the geometry of how the fields are laid out and the energy is re-distributed to another part of the field.

Mister T
Science Advisor
Gold Member
Each electron's electric field (due to their charge) wants to repel the other electron. Bringing them together required a small amount of energy to over come this repulsion.

That energy is part of the two-particle system. It cannot be assigned to either particle separately.

In the situations you described above, at a point midway between the particles the fields "cancel" only because of the scheme used to calculate the value of the field. The scheme goes like this. First we calculate the field due to one of the particles alone, then we calculate the field due to the other alone. But both of these calculations are based on a fiction. Those particles are not alone!

That energy is part of the two-particle system. It cannot be assigned to either particle separately.

In the situations you described above, at a point midway between the particles the fields "cancel" only because of the scheme used to calculate the value of the field. The scheme goes like this. First we calculate the field due to one of the particles alone, then we calculate the field due to the other alone. But both of these calculations are based on a fiction. Those particles are not alone!
The energy from bringing them together is like a potential energy, right? Much like raising a weight in a gravitational field. If I 'release' the particles they will fly apart. Does that stored potential energy, that is part of the two particle system, have some physical position in the system where it can be identified and shown to contribute to the increase in gravitational field? I know I'm going out on a ledge here, but I don't fully have my head around this yet. Thanks for the inputs, it's much appreciated.

Mister T
Science Advisor
Gold Member
Does that stored potential energy, that is part of the two particle system, have some physical position in the system where it can be identified and shown to contribute to the [...]

mass of the system. I don't understand the requirement of a physical position. Certainly you you can model the system as though all of its mass is located at the center of momentum.

DaveE
Science Advisor
Gold Member
Are not both particles' fields overlapping at that point and in fact have a field energy density at that point?
I'm not sure that it makes any sense to talk about field energy at a point. The field is larger than a point. You can talk about field energy, or you can talk about the forces that result from a field at a point. But I'm no expert in this regard. The subject is vulnerable to semantics and philosophy. Ultimately what matters is what happens to the stuff you can measure.