Electric Dipole Moment: Mechanics Counterpart Explained

[KFC]

I know the definition of the electric dipole moment is given by $$\mu = -e x$$, where e is the charge of electron and x is the displacement. I am thinking a mechanics counterpart of the dipole moment. We note that in mechanics, the moment is defined as the force cross the position vector. Consider 1D problem, the force of electric field is given by

$$F = -e E$$
where E is the electric field. So the moment should be

$$\mu = Fx = -eE x$$

but why this is different from the one in text ($$\mu=-ex$$) ? What's wrong in my reasoning?

 

[tiny-tim]

Hi KFC!

Because a moment is of something … in the example you gave, it's the moment of a force, so obviously the force is part of it.

Electric dipole moment, however, is a moment of charge … force doesn't come into it.

(As for the cross product , I think dipole moment uses the geometric meaning of moment, without cross product, as in moment of inertia, moment of area, etc.

For the first moment, you multiply by one coordinate: M_i = (something) times x_i

For the second moment (like an electric quadrupole moment), you multiply by two coordinates: M_ij = (something) times x_ix_j

and so on.)