Variation of velocity against distance, in an electric field

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Homework Statement

Right, the problem is of course to sketch a graph of velocity against distance in an electric field.

the second part, drawing the grapgh with an electric field opposing the motion of the electron.

The Attempt at a Solution

Right, assume we have an electron. We know that the electrical field strengh/intensity would be uniform.

So we know that Electric field strength=force/charge. Since the electric field strength is constant, an electron will experience constant force throught the electric field.
So since, f=ma, the acceleration is constant.

So the graph of velocity against distance will be a straight line.

Please explain to me whether my reasoning is correct.

Now, the second part.

The electrical field lines are opposing the motion of the electron.

The electron will experience a constant opposing force. But it takes time for these two forces to balance. (the motion of the electron) against the opposing force because of the electric field.

So now the graph should look similar to a terminal velocity graph or underoot x graph.

 

[berkeman]

You are correct in saying that the constant field (regardless of direction) will give you a constant force, and therefore a constant acceleration. So the kinematic equation for the velocity is

V = Vo + a t

So a plot of velocity versus time will be a straight line as you say. What can you say about the slope of the line versus whether the force is aiding the motion or opposing the motion?

 

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Since the electric field lines are opposing the motion of the electron, the force would be resisting it.

So the acceleration would decrease until becoming constant.
The graph would be similar like the terminal velocity graph

 

[berkeman]

Since the electric field lines are opposing the motion of the electron, the force would be resisting it.

So the acceleration would decrease until becoming constant.
The graph would be similar like the terminal velocity graph

No, I don't think that's correct. Consider the analogy of a ball in a gravitational field. If you're standing at the edge of a cliff (in a vacuum) and throw the ball straight down at some Vo, then its velocity keeps increasing as it falls down. If you instead throw the ball up with Vo, then what happens?

 

[fffff]

Ok, the velocity would decrease until becoming zero at maximum height,
Similarly, in an electric field, instead of gravational force opposing the object. The force from the electric field is opposing it. So the graph would be

So the graph would look like this.

Pic of graph is in the attachment

 

[berkeman]

If you plot position versus time, you should get a parabola. If you plot velocity versus time, you should get a straight line like in the equation for V that I posted earlier.

 

[fffff]

so what would the graph look like :(
I mean a graph of velocity against distance should be ??

The velocity would take some time to accelerate, since there is a resisting force the gradient of acceleration should be decreasing. That means velocity is decreasing not constantly against distance because the acceleration is decreasing.

this is the problem, the electron is released from A. The electric field lines are opposing the motion of the electron. Thus the object should be decelerating

!----<----!
!----<----!
A !----<----! B
!----<----!
!----<----!

 

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http://enpub.fulton.asu.edu/nsfreu/Raymond/Image188.gif

the graph would look like that i mean.