- #1

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i am looking for an equation that gives me the potential energy of 2 quadrupole moments and their mutual distance is assumed to be large.

and they have no total charge or dipole moments.

does such an equation exist?

- Thread starter Gavroy
- Start date

- #1

- 235

- 0

i am looking for an equation that gives me the potential energy of 2 quadrupole moments and their mutual distance is assumed to be large.

and they have no total charge or dipole moments.

does such an equation exist?

- #2

Bill_K

Science Advisor

- 4,155

- 199

W = (

where

Ok similarly, the quadrupole moment of an object is described by a symmetric traceless tensor

W = (

Maybe you'd rather see this written out explicitly with all the indices.

Φ = (Q

- #3

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thank you this exactly what i needed!!!p. The electrostatic potential energy between two dipolespandp' a distance r apart is

W = (p.p' -3 (n.p)(n.p'))/r^{3}

wherenis the unit vector pointing from one dipole to the other.

Ok similarly, the quadrupole moment of an object is described by a symmetric traceless tensorQ. The electrostatic potential energy between two quadrupolesQandQ' is given by

W = (Q:Q' -10n.Q.Q'.n+ 35/3 (n.Q.n)(n.Q'.n))/r^{5}

Maybe you'd rather see this written out explicitly with all the indices.

Φ = (Q_{ij}Q'_{ij}- 10 n_{i}Q_{ij}Q'_{jk}n_{k}+ 35/3 n_{i}Q_{ij}n_{j}n_{k}Q'_{kl}n_{l})/r^{5}

- #4

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could you explain to me, why there are 4 indices? i,j,k and l

i thought that this tensor would only use 3 cartesian coordinates?

then why are there 4 different indices?

- #5

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could anyone tell me the dipole-quadrupole energy formula?

I have the dipole moment and explicit quadrupole moment terms but aren't sure how to calculate their interaction energy!

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