Yes the two electrons will “touch” each other when their centers are at a separation equal to one electron in diameter
We have particle A which is curved to the left-hand side.
Particles B is slowly bent to the right side.
Particle C curves towards the right side.
Particle D is perpendicularly straight.
The particle E bends towards the right side.
Therefore D is showing none deflection then it is the part D which is neutral
This attached image is basically the answer
If there happens to be an electric current flowing in the wire, then the core will become magnetized. Otherwise, nothing will happen.