Can an axisymmetric electric field be created without charges?

In summary, we discussed the idea of a field that accelerates charges in opposite directions on each side of an axis. We also considered the interference of similarly polarized waves traveling in opposite directions and whether there would be a symmetric field or no net field at any point. We concluded that such a field would not be axisymmetric and that the electric force from these waves would not cancel out everywhere. This is an idealization and in a physical stream of waves, the electric force would not cancel out completely.
  • #1
Christofer Br
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That is, a field that accelerates charges in opposite directions on each side of an axis. I was thinking about interference of similarly polarized waves traveling in opposite directions (so that electric field peaks and valleys overlap but magnetic field adds constructively) - would there be an symmetric field or just no net field at any point ? If the latter, are there any other possibilities?
 
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  • #2
Christofer Br said:
That is, a field that accelerates charges in opposite directions on each side of an axis (looking in 2D).
Such a field would not be axisymmeteic. Axisymmetric means that if you rotate it about an axis then there is no change. Having it change directions would not qualify.
 
  • #3
Dale said:
Such a field would not be axisymmeteic. Axisymmetric means that if you rotate it about an axis then there is no change. Having it change directions would not qualify.
If it accelerates charges away from the axis from every side, there's no change upon rotation - hence axial symmetry (by 2D I meant 2D projection, to make it easier to visualize). Anyway, do you now know the answer?
 
  • #4
Christofer Br said:
That is, a field that accelerates charges in opposite directions on each side of an axis. I was thinking about interference of similarly polarized waves traveling in opposite directions (so that electric field peaks and valleys overlap but magnetic field adds constructively) - would there be an symmetric field or just no net field at any point ? If the latter, are there any other possibilities?

Christofer Br said:
If it accelerates charges away from the axis from every side, there's no change upon rotation - hence axial symmetry (by 2D I meant 2D projection, to make it easier to visualize). Anyway, do you now know the answer?

This is not very clear. Are you talking about something having, say, a cylindrical TEM mode symmetry?

Zz.
 
  • #5
Christofer Br said:
If it accelerates charges away from the axis from every side, there's no change upon rotation - hence axial symmetry (by 2D I meant 2D projection, to make it easier to visualize).
Oops, sorry. I misunderstood what you meant by opposite direction. I was thinking opposite directions parallel to the axis.

Christofer Br said:
Anyway, do you now know the answer?
Yes, the field you describe has non zero divergence on the axis, so the charge density is non zero there also.
 
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  • #6
Dale said:
Oops, sorry. I misunderstood what you meant by opposite direction. I was thinking opposite directions parallel to the axis.

Yes, the field you describe has non zero divergence on the axis, so the charge density is non zero there also.
Is the case that we considered only an idealization (of just two waves colliding)? I mean, when you have a real, physical stream of waves, would the electric force from them cancel out (mostly)?
 
  • #7
Christofer Br said:
Is the case that we considered only an idealization (of just two waves colliding)?
You could certainly consider two plane waves colliding. It would not be axisymmetric, but it would have no charge.

Christofer Br said:
would the electric force from them cancel out (mostly)?
If you had one wave with the E field along x and the B field along y then it would propagate along z. The other wave could have the E field along -x and the B field along z so it would propagate along y. There would be regions where the E fields would cancel out, but that would not happen everywhere.

Edit: You could also have the other wave with E along -x and B along y so it would propagate along -z. In that case there would be moments where the E fields would cancel out everywhere, but it would not happen all the time.
 
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1. Can an axisymmetric electric field exist without any charges?

Yes, an axisymmetric electric field can exist without any charges. This type of field is known as a pure electric field, which is created by a changing magnetic field or by varying the electric potential over time.

2. Is it possible to create an axisymmetric electric field without using any external sources?

No, it is not possible to create an axisymmetric electric field without using external sources. The creation of an axisymmetric electric field requires the presence of charges or changing electromagnetic fields, which act as the source of the field.

3. How is an axisymmetric electric field different from a non-axisymmetric electric field?

An axisymmetric electric field has the same magnitude and direction at all points on a symmetrical axis, while a non-axisymmetric electric field does not have this symmetry. Additionally, an axisymmetric field only exists in three-dimensional space, while a non-axisymmetric field can exist in any number of dimensions.

4. Can an axisymmetric electric field be created in a vacuum?

Yes, an axisymmetric electric field can be created in a vacuum. In fact, many experiments involving charged particles in a vacuum use axisymmetric electric fields to manipulate and control the particles.

5. What is the significance of an axisymmetric electric field in practical applications?

An axisymmetric electric field has several practical applications, including in particle accelerators, plasma physics, and medical imaging. It is also used in engineering and design processes for creating symmetrical electric fields for specific purposes.

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