Finding the Trajectory of a Test Charge in an Electric Field

[tickle_monste]

Let's say I were to place a test charge, q0, in a standard electric field E = k*q1/(r^2).
How would I find the trajectory of the charge? I have been trying the method used for finding the trajectory in a gravitational field, but I believe the problem is that that formula (Gm1m2/(r^2)) assumes a uniform field, whereas in this smaller scale problem, no such approximation can be made. I'm not sure whether I should be looking for a differential equation or something like Newton's method or what.

 

[sweet springs]

Hello

Test charges would keep still on the points during observation of electric fields by measuring the applied force/charge. In this sense trajectory of test charge does not make good sense to me. If you are interested in motion of charges, two body problem under square inverse law with parameters e1,e2,m1,m2, should be your case. I believe scale problem does not matter in square inverse law.

Regards.

 

[mikelepore]

I think you're talking about a point charge placed into a field generated by another point charge. The direction of the resulting force is along the line connecting the two point charges, therefore the resulting acceleration is along that line.

Gm1m2/r^2 is not for a uniform gravitational field. It's for the force between two point masses, which is a radial set of directions for field lines.

 

[tickle_monste]

Well the problem I get when I don't assume a uniform field is that the amount of acceleration is a function of position. But the position is a function of acceleration which is a function of position etc.

*EDIT* so yea, I realize now that I'm looking at a differential equation