This question is probably either really easy or nonsensical, but I'm not versed in the physics involved.
Suppose we have a beam of positively charged particles firing along the y axis into a static planar electric field with strong negative charges on each side, such that at any point on the y axis the beam particles would experience two equal strong opposing forces summing to zero net force. Were the beam to deviate slightly, it would deflect strongly in the direction of deviation. We crank up the strength of the field as much as we can without observing any deflection in the beam. Now, we reduce beam until only one charged particle is emitted at a time.
Do we still observe that all of the particles went as straight as the original beam, or will quantum effects now ensure that we see a wider spread? In an ideal situation, would we observe a predictable distribution centered around the target point? In a practical situation? Would the width of the spread depend on the strength of the electric field? Are there other interesting phenomena we could observe in a setup like this, or am I just barking up an imaginary tree? Thanks in advance.