# Derivation of dipole-dipole interaction energy

• schattenjaeger
In summary, the conversation discusses the energy of a dipole in an external field and the expression for the energy in terms of the dipole's radial and angular components. The final answer is given as Udd=1/(4pi*epsilon*R^3)*[p1*p2 - 3(p1*R)(p2*R)]. The conversation also mentions finding the electric field of a dipole in a coordinate-free form and using the formula U = - \vec{p}.\vec{E}.
schattenjaeger
if you have 2 point dipoles p1 and p2 located at r1 and r2 respectively(all four are vectors)

what's the energy of p2 in the field of p1?

I know the general expression for the energy of a dipole in an external field Eo is U=-p * Eo but from there I get confused

I can express the electric field of the dipole in terms of its radial and angular components, but I'm not sure how to express p2 in those same terms.

FYI the answer is Udd=1/(4pi*epsilon*R^3)*[p1*p2 - 3(p1*R)(p2*R)]

both those bold Rs are unit vectors, * is dot product if it's between two vectors

Can you find the electric field of a dipole in a coordinate free form?

Use that and $$U = - \vec{p}.\vec{E}$$

Substitute E_0 for a dipole in vector notation:
E_0=3(p.r)r/r^5-p/r^3.

## 1. What is the dipole-dipole interaction energy?

The dipole-dipole interaction energy is the electrostatic potential energy between two polar molecules or atoms. It arises from the interaction between the partial charges of the dipoles, with opposite charges attracting each other and like charges repelling each other.

## 2. How is the dipole-dipole interaction energy calculated?

The dipole-dipole interaction energy can be calculated using the equation: E = -μ1μ2/r^3, where μ1 and μ2 are the electric dipole moments of the two molecules or atoms and r is the distance between them.

## 3. What factors affect the dipole-dipole interaction energy?

The dipole-dipole interaction energy is affected by the magnitude of the dipoles, the distance between them, and the relative orientation of the dipoles. The energy will be stronger if the dipoles are larger, closer together, and have a favorable orientation towards each other.

## 4. How does the dipole-dipole interaction energy contribute to intermolecular forces?

The dipole-dipole interaction energy is one of the main contributors to intermolecular forces, along with London dispersion forces and hydrogen bonding. It is responsible for the attraction between polar molecules, which can lead to the formation of liquids and solids at low temperatures.

## 5. Can the dipole-dipole interaction energy be zero?

No, the dipole-dipole interaction energy cannot be zero as long as there are polar molecules or atoms present. However, the magnitude of the energy can be very small if the dipoles are weak or if they are far apart or have unfavorable orientations.

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