In the figure, an electron of mass m, charge − e, and low (negligible) speed enters the region between two plates of potential difference V and plate separation d, initially headed directly toward the top plate. A uniform magnetic field of magnitude B is normal to the plane of the figure. Find the minimum value of B such that the electron will not strike the top plate.
The Attempt at a Solution
Assuming that the electric field accelerates the electron towards the top plate, as the electron accelerates, v will increase so the magnetic force acting on it increases, which acts on the electron in the direction according to the RH rule.
I'm not sure how to incorporate all these equations together, as v is not constant and neither is the direction which the magnetic force acts on the electron, neither is the path circular or the acceleration constant.
Do I need to form some sort of integral regarding the change in v with d and integrate, or how else do i attack this problem? Or am I missing some fundamental concept?
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