- #1

user1139

- 72

- 8

- Homework Statement
- Clarification on electric quadrupole moment definition

- Relevant Equations
- The equations are as given below

I have encountered two (?) definitions of the electric quadrupole moment. They are:

$$Q_{ij}=\frac{1}{2}\int \rho(\vec{x}')x'_i x'_j\,\mathrm{d}^3x'$$

and

$$Q_{ij}=\int (3x'_i x'_j-\delta_{ij}x'^2)\rho(\vec{x}')\,\mathrm{d}^3x'$$

I am trying to study radiation arising from the electric quadrupole. I am confused since sometimes the first definition is used while other times, the second. As such, which definition should be used and why?

$$Q_{ij}=\frac{1}{2}\int \rho(\vec{x}')x'_i x'_j\,\mathrm{d}^3x'$$

and

$$Q_{ij}=\int (3x'_i x'_j-\delta_{ij}x'^2)\rho(\vec{x}')\,\mathrm{d}^3x'$$

I am trying to study radiation arising from the electric quadrupole. I am confused since sometimes the first definition is used while other times, the second. As such, which definition should be used and why?