# Multipole expansion

1. Jul 10, 2008

### BiBByLin

In multipole, the electric quadrupople interaction with incident electric field:

V(2)=-[$$\stackrel{\leftrightarrow}{Q}$$$$\nabla$$]$$\cdot$$Einc(0)

$$\stackrel{\leftrightarrow}{Q}$$ is a tensor of rank two.
$$\stackrel{\leftrightarrow}{Q}$$=$$\frac{1}{2}$$$$\sum$$qnrnrn

However, $$\nabla$$$$\cdot$$E=0.

So, what is the detail expression of this tensor and how to operate it if I denote in Cartesian coordinate.

Thank you!