# Plate Capacitors (Velocity selector)

• yahoo32
In summary, the problem is to find the largest magnetic field that allows a charged test particle to escape a plate capacitor without crashing into the plates. The capacitor is grounded on the bottom and held at a potential V which is then set to 0. The length of the plates and the distance between them are given, along with the charge and mass of the test particle and its initial velocity. As the magnetic field increases, the trajectory of the test particle will bend. The solution may involve geometry and balancing the equation qvB = qE. However, some conditions in the problem are not clearly stated, such as the voltage and electric field across the capacitor. It is also unclear if the problem is simply asking for the size of the magnetic field

#### yahoo32

You have a plate capacitor which is grounded on the bottom and is held at a potential V which is then set to 0. You are given the length of the plates and the distances between them. A test charge is brought in with the charge and mass given along with its velocity. For a vanishing magnetic field the test charge just moves to the right on a straight line and escapes the capacitor. If you increase the magenetic field the trajectory will bend. The problem is to find the largest magnetic field (increasing the value from 0) such that the test still escapes the capacitor without crashing into the plates.

I am totally clue less on this problem but I think perhaps you must do soem geometry with the radius, the length of the plates and the distances between them and maybe some how incorporate the fact the qvB = qE (and balance that equation) ? But this is all I have been able to come up with, any help would be greatly appreciated!

I think this problem is being ignored because some of the conditions don't seem to be stated very clearly. Are you saying that there is zero voltage across the capacitor? (Why is it even mentioned that one plate is grounded and the other is first set to some potential, but then to zero?) Is it the case that there is no electric field there? (In that case, what difference does it make that this is even a capacitor?)

Are you simply being asked to find the size of the magnetic field acting alone? Are you supposed to assume that the charged particle enters at mid-height between the plates? It seems that maybe this is just a geometry problem: if the plates have length L and separation s, and the particle starts out at a distance s/2 "above" one of the plates, you need to find the circular arc that will just miss the "far end" of the "lower" plate. The geometry of a circle will then tell you the minimum radius the circle may have, which in turn will let you find the stronger magnetic field that can be permitted for a particle of charge q and mass m.