Lorentz force law and capacitor problem

[music_lover12]

An electron is moving with a speed of V when it enters an electric field generated by two equally but oppositely charged parallel plates. The electron passes through the field without being deflected. How can this be?



I was thinking that the electrons electric field would cancel out with the parallel plates, causing it to move through them without anything happening to it. Am I right?

 

[chroot]

The Lorentz force law says that a particle with charge q feels a force:

\vec F = q \vec E

If it experiences no deflection, then the force vector must be aligned with its velocity vector. (It will change speed though, just not direction.) What does this then tell you about the electric field vector?

- Warren

 

[music_lover12]

What is an electric force vector?

 

[chroot]

I didn't say "electric force vector," I said electric field vector.

- Warren

 

[music_lover12]

Oh. Oops. Sorry. So is the force vector and the velocity vector equal in magnitude?

 

[chroot]

No -- as the equation above states, their magnitudes of F and E are related by the charge, q.

All you need to know is that the electron's direction of motion didn't change. This means the force imparted on it by the field must have been in the same direction it was already moving, thus speeding it up (or in the exact opposite direction, thus slowing it down). If the force is in the same direction as its motion, then so is the electric field.

- Warren

 

[music_lover12]

Well in a capacitor, the electric field moves from positive to negative. Both plates of the capacitor are horizontal and parallel to each other, so the field would be moving down. Now this confuses me because the the electron is moving through the middle of the plates and is not feeling a deflecting force, even though there is a force acting on it.

 

[chroot]

What if the electron is moving parallel to the lines of the electric field? What kind of force does it feel then? I don't see anything in the question that requires the electron to come into the gap between the plates from the side, do you?

- Warren

 

[music_lover12]

Well it is the problem I was given. The electron was already moving a certain speed, and it just happened to come across two oppositely charged parallel plates.

 

[chroot]

What if the electron is intially on one plate? It has some initial thermal velocity, and leaves the plate, headed directly across the gap to the other.

- Warren

 

[music_lover12]

Well it's not. It just entered the electric filed that the plates created, and some how, it did not experience a defecting force.

 

[chroot]

The question says nothing at all about how the electron entered the gap. All it says is that it enters the gap with some initial velocity V, and doesn't change direction. This doesn't preclude the electron from entering the gap after leaving one of the plates.

The bottom line is that there is no way at all for the electron to enter the gap with any sideways velocity without feeling a deflection force.

- Warren

 

[music_lover12]

It makes no sense that the electron wouldn't feel a deflecting force, but there must be an answer because I was given this problem to find out why this is.

 

[chroot]

I've given you the answer several times now! The electron is initially moving in the direction of the electric field, and thus never feels any deflecting force.

What don't you like about the answer? It is the only possible answer.

- Warren

 

[music_lover12]

It doesn't make sense to me because the electric field is not moving in the same direction as the the electron. The plates are horizontal and parallel to one another, so the direction of the electric field is down, not right (which is the direction the electron is traveling).

 

[chroot]

WHAT MAKES YOU THINK THE ELECTRON MUST BE TRAVELLING TO THE RIGHT?

- Warren

 

[music_lover12]

I HAVE A PICTURE OF IT! The electron is traveling to the right through the middle of the parallel plates.

 

[chroot]

Well Jesus H. Christ, do you think you could have presented the ENTIRE PROBLEM here before asking for help?!

The electron will necessarily be deflected by the electric field between the plates, but the amount of deflection can be made arbitrarily close to zero by increasing the electron's speed. If it's going very, very quickly, the amount of deflection can be made very, very small. It can never be made zero, however.

- Warren

 

[music_lover12]

Well sorrrrry. I did not realize I left that little detail out.


So the deflecting force is not strong enough to have any effect on the electron?

 

[chroot]

Like I said, you cannot make the deflection zero -- but you can make it as close to zero as you want. As it is worded, I believe the question has no answer, since it refers to zero deflection. (Unless you're omitting some other part of the question.)

- Warren