I actually have a question related to this.
In my case, the magnetic field is coming out of the page and there is a positively charged particle initially at rest a distance "r" from the axis of the solenoid. Then, the current in the solenoid is flipped the other way instantaneously (all of the conditions are ideal here). The problem wants me to describe the trajectory of the particle. We know the mass, m, and the charge, q, of the particle as well as the current, I, and the magnetic field, B.
As for my attempt at the solution:
I think the particle doesn't initially move because of the magnetic field because the initial velocity is zero. Perhaps the instantaneous flip of current induces some sort of electric field INSIDE the solenoid. I'm not sure about the direction (into the page, out of the page, tangential to a loop of radius r) or nature of the field, but I'm fairly certain that once it starts moving, the positive particle will be redirected by the uniform magnetic field "B" to move in a left-handed helix (of radius r?) about the solenoid axis.
Am I somewhat on the right track? There is very little info about the electric field in a solenoid so any help would be greatly appreciated. Thanks.