Calculating Equilibrium Distance for HCl Electric Dipole and Electron

[K29]

Homework Statement

Calculate the equilibrium distance between an electron and the HCl molecule. Assume the HCl molecule constitutes an electric dipole with an electric dipole moment of 6.3 * 10^-28 Cm (Coulomb metre) and that the dipole and atom are near the Earth's surface.
The mass of the electron is 9.1 * 10^-31 kg. Assume that the distance between the H and Cl atom is much smaller than the distance between the electron and the Hcl molecule, (Hint:calculate the electric field due to the dipole first)

My problem is just getting started

Homework Equations

E = kp/(z^3) wherek is the electrostatic constant, p is the electric dipole moment, and z is the distance from the centre of the dipole to a distant point from the dipole

The Attempt at a Solution

My problem is just getting started. But here are my thoughts
First I am thinking I should use the above equation, however is z that which I should be solving(this equilibrium distance)?
I am a bit confused as to how this system functions. The H and Cl atoms must be of opposite charge to create the dipole. But is the electron in question the one giving the Cl the negative charge, (because it 'hangs around' the Cl more)? And as for this 'equilibrium distance': does the electron weave between the H and Cl in a figure-8 motion? Or does it spin around them in a circle, which would lead me to believe that gravitational forces are going to play a role here too.
Or does Heisenburg's uncertainty principle suggest I should ignore the specific motion of the electron and focus on somehow calculating z, by simply putting the electron at a point in line with the dipoles axis. If gravity is involved here should I not have been given the mass of the HCl molecule? What is keeping the electron in {orbit??} around the atom anyway?
If I do need to calculate z then I will need another equation... :?

I would appreciate any help in understanding and solving the problem
Thanks in advance.

edit: ok well I've done a bit of research, and I know exactly how the electron is held by the electric field. But still unsure how to get thid equilibrium distance. Would the distance not change as the electron approaches the opposite side of the dipole? The direction of the electric field caused by the dipole is equal to the direction of the electric diople moment. Which means at the positive side of the dipole the electron would be attracted, and on the negative side it would be repelled..

 

[NateD]

Also, I'm not sure if I'm allowed to use the electric field equation to calculate this distance - would it not be a dynamic equation? As the electron moves around, the distance will change.