Calculating Electron Motion in a Uniform Electric Field

[aek]

An electron traveling at $$2.5 \cdot 10^8 m/s$$ of passes through a hole in a screen into a region where there is a uniform electric field strength $$6.5 \cdot 10^4 N/C$$. If the velocity of the electron is in the same direction as that of the electric field, how far does the electron travel before it reverses its direction of motion?

Now this is the question in its entirety, it was a question off my half-yearly examination which i attempted incorrectly. Now ultimately all i know to this question is that it has to meet an opposite charge before it can reverses it's motion...would anyone be nice enough for me to understand how to attempt this question correctly next time. Thanks

 

[Doc Al]

Hint: What force does an electron experience in an electric field? Use energy methods or kinematics to find the distance. (Hint 2: The electron is move at an appreciable fraction of light speed.)

 

[aek]

i know what happens to an electron in an electric field but that hasn't helped me understand. And also i don't think i covered kinematics. Can you elaborate please?

 

[The_Thinker]

Consider a normal electric field...

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our electron enters the field which is normally consider as +ve to -ve ... Hence it enters the +ve side and is sent back in the reverse drection due to the opposing electric field... At least this is what i think is the answer...

 

[aek]

yeah once again, i think that is very much elementary for the question at hand. Doc Al, can you please help.

 

[cepheid]

I think The Thinker's diagram is actually useful because you don't seem to have grasped this point: in what direction does the electric field point, by convention? It points in the direction that a positive test charge would move under the applied field. A positive charge would move away from the positive side, and toward the negative side. Hence the electric field points from +ve to -ve. But we are told that the electron (a negative test charge) is moving in the same direction as the electric field! It is therefore moving away from the positive side! It clearly doesn't "want" to do that does it? It is only doing so because of its initial momentum. But it is actually going against the direction in which the field is trying to push it. Make sure you understand this point: the force on the electron due to the electric field is always in the opposite direction of the field, which is in the opposite direction of its velocity in this case. So there is a force acting to slow it down, to give it a negative acceleration. That's why it will eventually slow to a stop and switch directions. There are at least two methods of figuring out how far it will travel before that happens.

1. Yes, you do know what kinematics is. For surely you must have studied mechanics (the study of motion) of which kinematics is a small part. Kinematics deals with the properties of the motion of bodies. The other part of mechanics (dynamics) deals with the causes of the motion of those bodies, ie forces, Newton's laws etc. So you must have already done all of that if you are already into electricity. The kinematical method would be, knowing the magnitude of this opposing electric force, you know the negative acceleration on the electron. Given that, and its initial velocity, you can calculate how far it will travel before it decelerates to zero.

2. The energy approach works because there is a conservative force acting on the electron, doing negative work on it. Therefore, the particle's initial kinetic energy is being converted to potential energy, and all you need to know is how much work is done for that conversion to be complete. Then you can easily calculate how far it must have traveled for that much work to be done by that force.

 

[Doc Al]

Now this is the question in its entirety, it was a question off my half-yearly examination which i attempted incorrectly.

Why don't you show us your attempted solution? Also, what class are you taking? (Is this for a course in which relativity is covered?)

After you read what cepheid explained, start by answering these questions: (1) what force does the field exert on the electron? (2) What KE does the electron have?

 

[aek]

oryt let me scan it in