Plate Capacitors (Velocity selector)

[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!

 

[dynamicsolo]

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.

 

[Moetasim]

I can provide some insight into this problem and suggest potential approaches to finding a solution. Firstly, it is important to understand the concept of a plate capacitor and how it works. A plate capacitor consists of two parallel plates with opposite charges and a potential difference between them. When a charged particle enters the capacitor, it experiences a force due to the electric field between the plates. This force can be balanced by an equal and opposite force due to a magnetic field, resulting in the particle moving in a straight line without crashing into the plates.

In this problem, we are given the length of the plates, the distances between them, and the velocity of the test charge. We are also told that the magnetic field is being increased from 0 to some maximum value. To find this maximum value, we need to consider the forces acting on the test charge and how they change with the magnetic field.

As you mentioned, the equation qvB = qE is important here. This equation relates the force due to the magnetic field (Fm = qvB) to the force due to the electric field (Fe = qE). In order for the test charge to escape the capacitor without crashing into the plates, the two forces must be equal and opposite. This means that we need to find the value of the magnetic field (B) that will create an equal and opposite force to the electric field (E).

To do this, we can use the geometry of the capacitor. The distance between the plates and the length of the plates can help us determine the strength of the electric field (E = V/d). We also know the charge and mass of the test particle, which can be used to calculate the force due to the magnetic field (Fm = qvB). By setting these two forces equal to each other, we can solve for the maximum value of the magnetic field (B) that will allow the test charge to escape the capacitor without crashing into the plates.

It is also important to note that the trajectory of the test charge will bend as the magnetic field is increased. This is because the force due to the magnetic field will act perpendicular to the motion of the test charge, causing it to move in a circular path. We can use the principles of circular motion to determine the relationship between the magnetic field and the radius of the trajectory, which can help us in our calculations.

In summary, to solve this problem we need to use the equations qvB = q