Question

We consider four positive charges Q at the corners of a square of side length a and centered around (0,0), we will assume that the charges are very massive and do not move. An electron of mass m and charge -e is close to the center of the square, with coordinates (x,y).

1. What is the total energy of the electron?

2. Approximate the potential energy by a quadratic expression in x and y

3. Assuming the electron at t=0 has initial conditions (x,y)=(0,ε) and (vx,vy) = (v0,0), determine (x(t),y(t)). Which kind of trajectory is that?

*This is for classical mechanics*

Answer 1