Can electric dipoles violate Newton's 3rd Law?

[dipole]

Suppose you have an electric dipole centered at the origin and aligned with the z-axis. If you place a test charge somewhere in the x-y plane, you can show that the force on the dipole by the charge cancels to be zero, yet the dipole still seems to exert a force on the charge...

If this is true, then this is a violation of Newton's third law, and this also means that momentum isn't being conserved (at least not the sum of the momentum of the dipole and of the charge).

Is this situation valid, and is this something which can really happen? If so, where is the momentum going - the electric field somehow?

 

[xlines]

Suppose you have an electric dipole centered at the origin and aligned with the z-axis. If you place a test charge somewhere in the x-y plane, you can show that the force on the dipole by the charge cancels to be zero, yet the dipole still seems to exert a force on the charge...
...

Why do you think forces cancel? As far as I see it, they most certainly do not! Let say dipol is oriented to +z and test charge is positive. Repulsive force z component will be negative, and attractive force by negative part of dipol will have z component also negative, so you don't have cancellation.

 

[dipole]

I just realized my error, Newton's 3rd law is safe!