I need the form of potential energy for a simple problem

[Brummell]

Homework Statement

A particle of mass "m" and electric charge "q" moves without friction along an ellipse in the horizontal plane, in the presence of a constant electric field of intensity E directed along the large semiaxis of the ellipse.

Write the Lagrange function

Homework Equations

We now, obviously the ellipse equation so we choose as general coordinates:

X1 = a*cos(phi) X2 = b*sin(phi)

The Attempt at a Solution

L = T - U;

T = m/2*(X1'squared + X2' squared)

But U?

 

[Matterwave]

We know that F=qE

How can we get U from F? (notice that there are no dissipative forces here)

 

[Brummell]

We know that F=qE

How can we get U from F? (notice that there are no dissipative forces here)

Hehe. Yes. U = - integral (F - along x direction in our case - dx) because Fx = - dU/dx