Ions passing through a parallel plate capacitor with a varying voltage

[LuisP]

Consider the scenario

• Two parallel plates
• One ion particle (mass 1, charge +1) traveling parallel to the plates through the middle. Voltage of the plates is the same.
  
• As the ion travels between the plates the voltage on the plates ramps up, and the electric field between the plates remains constant and equal to zero.
• Ion exits with the same KE (KE1= KE0) as it enters
• Electric potential of the ion that exits is higher than when it entered. (V1 > V0)
  
• Total energy on the particle (U= KE + qV) is therefore higher, U1 = U0 + q(V1-V0).

This seems to be against the paradigm that the total energy of the ions should remain constant unless there are collision.
This appears to be violating conservation of energy.

How to explain this

 

[berkeman]

Welcome to the PF.

As the ion travels between the plates the voltage on the plates ramps up, and the electric field between the plates remains constant and equal to zero.

I'm guessing that you mean the voltage of both plates together is ramped up with respect to some other conductor, like the electron gun in a CRT with respect to the anode faceplate...?

Ion exits with the same KE (KE1= KE0) as it enters

No, it is accelerated just like the electrons are in the CRT electron gun. The E-field has to go somewhere, and it goes to the other conductor that the two plates are being charged up with respect to. So if the E-field lines are going out of the plates toward that conductor, and the ion travels that way, it is accelerated...

If you could Upload a sketch, that would help. Be sure to include the conductor that you are charging up both plates with respect to...

http://electriciantraining.tpub.com/14188/img/14188_180_1.jpg

 

[anorlunda]

This seems to be against the paradigm that the total energy of the ions should remain constant unless there are collision.

Why can't an ion exchange energy with the plates?

 

[slow]

Let's try to remember some details that can guide us.

1. The ion is a good example of an electrically charged particle.

2. In the case presented, gravity does not intervene. Then the electromagnetic interaction is the only way to cause changes in the ion energy.

3. Before approaching the zone of influence of the plates, the velocity vector of the ion is parallel to the plates. When it approaches, the deflection begins and that vector becomes oblique with respect to the plates. Then the Lorentz force has a component other than zero in the direction of the velocity vector and the modulus of the velocity changes. This means that the dependent energies of the velocity modulus, ie, the kinetic energy and the energy of the magnetic field, are modified.

 

[LuisP]

It seems that there has been some confusion. I attach a sketch of the problem.
I change the notation slightly so that T = Kinetic energy

The electric field between the plates (probably is best assuming it's a cylinder) is constant.

I suppose the only explanation for the increase in energy is that the outer electrode V(t) raises the potential energy of the particle.

 

[LuisP]

I found the answer to this.
The total energy of the ion does increase while traveling within electrodes plates/cylinder. In fact particle accelerators such as Linear Particle Accelerator (linac) work using this principle.
https://en.wikipedia.org/wiki/Linear_particle_accelerator

 

[DrClaude]

It seems that there has been some confusion. I attach a sketch of the problem.

I found the answer to this.
The total energy of the ion does increase while traveling within electrodes plates/cylinder. In fact particle accelerators such as Linear Particle Accelerator (linac) work using this principle.

Note that in your case, there is no change in the velocity of the ion while it is between the plates. The linear accelerator is based on the fact that there is a potential gradient in the direction of motion.

 

[ZapperZ]

I found the answer to this.
The total energy of the ion does increase while traveling within electrodes plates/cylinder. In fact particle accelerators such as Linear Particle Accelerator (linac) work using this principle.
https://en.wikipedia.org/wiki/Linear_particle_accelerator

I had to re-read your scenario at least a couple of times, JUST to make sure that I understand that BOTH plates are at the SAME potential here. So this is not the same case as a typical parallel plate capacitor.

Because it has no potential gradient, there is no electric field, and thus, the particle experiences no net force and acceleration while inside the parallel plate. This is DIFFERENT than a particle accelerator (an area that I work in). A linac is typically a RF structure, and you definitely have a potential gradient inside the structure, resulting in an axial force that accelerates the particle. In a DC gun, there is a potential difference between the electron or ion source and the end plate to accelerate the charge particles.

This means that a particle accelerator is different than the scenario that you are describing. So I'm not sure why you are finding similarities here.

Zz.

 

[willem2]

There's no electric field while the ion is between the plates, so the ion gains no kinetic energy between the plates but potential energy. When the ion leaves the plates there will be a field and all of the potential energy of the ion will be converted to kinetic as the ion flies off. The potential energy comes from the energy source that was used to charge the plates. It's harder to give the plates a positive charge when there is another positive charge nearby, and if you then let this positive charge fly off, the extra energy you used to charge the plates will be gone.
This is indeed rather like a linear accelerator. To accelerate a positive charge, you use a tube with negatively charged rings around it, and you flip the charge on a ring to positive just as the positive charge passes through it.