Trapping Supercooled Atoms with Light Trap Optics

[Hamal_Arietis]

Homework Statement

Scientists want to trap the supercooled atoms (atoms have low thermal energy). They create an electric field by the interference of some laser beams. In the center of the trap, the electric field has fomula:
$$\vec{E(x)}=E_0(1-\frac{x^2}{x_0^2})\vec{e_z}$$
With values: $$E_0=5000V/m;x_0=5\mu m$$
At t=0, a Rubidi atom $$^{87}_{37} Rb$$ moves along x-axis with velocity $$v=0.1mm/s$$
When atom goes to coordinates x=0, the trap is turned on. Consider architecture of Rb that a balloon has a nuclear which is covered by electron cloud (Rutherford's model). Supposed that in electric field, electron cloud isn't transfigured, but nuclear and central point of electron cloud are moved. So that dipole moment isn't equal 0.
With R=2.5A and these values, describe the motion of Rb. Find the maxcimum velocity of atom that it is trapped when the trap is turned on.

Homework Equations

F=qE

The Attempt at a Solution

I don't have any attempt in this problem because there are any force along x-axis, the force just appears along z-axis. And I don't understand this phenomenon. At first, I think the atom will oscillate but it is wrong!

Sorry because my English isn't good. I will pleasure if you check my mistake.

 

[James R]

Are you sure the field is supposed to be in the z direction and not in the x direction?

 

[Hamal_Arietis]

Why it appear in x-axis? Because E equation direct along z axis

 

[James R]

Why it appear in x-axis? Because E equation direct along z axis

I am suggesting that the $\vec{e_z}$ in the expression for the electric field is a mistake in the question, and it should be $\vec{e_x}$.

In any case, perhaps a good place to start with this problem would be to consider the potential energy of a dipole in an electric field. Can you write an expression for the potential energy of this atom in the given electric field?

Once you know the potential energy, what is the relationship between that potential energy and the force on the dipole?

One other question: I don't know what $R=2.5A$ refers to in your statement of the problem.

 

[Hamal_Arietis]

No $\vec{E}$ directs z-axis because there have 3 questions. First, find the dielectric polarization. Second, estimate the radius of Rb. Then the final question, We have R=2.5A, find the maximum velocity (the started question). I finished 2 question and can't solve the last quétion.

 

[James R]

I don't think I can help with this. If it is true that the electric field is in the z direction, then it seems to me that an atom traveling in the x direction will not be trapped. Any net force on the dipole will be in the z direction, not the x direction.

It is possible that I've missed something and this is incorrect.