Can an axisymmetric electric field be created without charges?

[Christofer Br]

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?

 

[Dale]

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.

 

[Christofer Br]

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?

 

[ZapperZ]

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?

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.

 

[Dale]

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.

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.

 

[Christofer Br]

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)?

 

[Dale]

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.

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.