Dipole-dipole interaction

1. Feb 5, 2005

secret2

Could anyone please provide (or start off) the proof of (2.4) of the following document?

http://www-its.chem.uva.nl/research/complex_fluids/Teaching/LectureNotes%202004%20vdWaals%202.pdf [Broken]

Many thanks

Last edited by a moderator: May 1, 2017
2. Feb 6, 2005

clive

The scalar potential from a electric dipole is given by
$$\phi=\frac{\vec{p}\cdot \vec{r}}{4\pi \epsilon_0 r^3}$$
Then
$$\vec{E}=-\bigtriangledown \phi$$
and with
$$U=-\vec{p}\cdot \vec{E}$$

you'll get exactly Eq. (2.4)!

3. Feb 8, 2005

secret2

I don't think I get the 3 in the numerator, nor the p dot p term.

4. Feb 8, 2005

clive

You don't think you get it OR you didn't get it?

$$\partial_x (x^2+y^2+z^2)^{-3/2}=-\frac{3}{(x^2+y^2+z^2)^{5/2}}$$

Right?

5. Feb 9, 2005

secret2

Oh....I was working with spherical coordinates.

6. Nov 17, 2009