Calculating Kinetic Energy of a Charge at a Given Distance

AI Thread Summary
To calculate the kinetic energy of a charge in an electric field, the work done on the charge by the field can be used, which equals the change in kinetic energy. In the given problem, a uniform electric field of 2 kN/C acts on a 3 microcoulomb charge, initially at rest, as it moves from x=0 to x=4m. The work done can be calculated using the formula F*d, where F is the force (E*q) and d is the distance moved. Since the electric field is constant, integration is not necessary, simplifying the calculation. The relationship between potential energy and kinetic energy indicates that the work done by the field is equal to the negative change in potential energy.
Aerosion
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Homework Statement



I don't want to sound like I'm asking anyone to do my homework for me, but I really don't know how to find this.

Let me give an example problem: A uniform electric field of 2kN/C is in the x direction. A point charge Q=3 microcoloumbs initially at reast at the origin is released. What is the kinetic energy when it is at x=4m and what is the change in potential energy of the charge from x=0 to x=4m?

Homework Equations





The Attempt at a Solution



I know that the potential energy difference is the negative of the kinetic energy of the charge, and I know how to get the potential energy (integrate the electric field with regard to the increase in x and multiply by the negative of the charge) but I'd rather know exactly how to find the kinetic energy of a charge.
 
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Aerosion said:
...but I'd rather know exactly how to find the kinetic energy of a charge.
Sounds to me like you just described how to find the KE of a charge as it is accelerated in an electric field. So I'm unclear what the problem is. Why don't you show your work for that sample problem and tell us where you get stuck?
 
Well, that's the thing: I don't know how to find the kinetic energy of a charge; as in I'm unclear as to what the formula is. That's why I said that I don't want anyone to think that they're doing homework for me: because I don't know how to get started.

Like, I know that KE=1/2mv^2, but I don't think that's any use in this particular problem. If the formula for KE of a charge is similar to the potential energy difference of a charge, and if I've already found it out (unknowingly), then could someone tell me?
 
Oh oh...and the work I did for PE is...

I used the change in potential energy equation -q=(integrate)E*ds, and subsituated 3microcoloumbs for q, 2kn/C for E, and 0 and 4 for the definite integral, such that it looked like

-3mC*(integrate fr. 0 to 4)2 ds.
 
Realize that the field is constant here, so no real integration is needed. The work done on the charge by the field is just F*d = Eqd. The work done will equal the change in KE of the charge. (Note that the work done by the field is just the negative of the change in PE.)

This might help you: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elewor.html"
 
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