How do you calculate the electric dipole moment of a complex system?

[tsang]

Hi,can anyone tell me how to calculute magnitude and direction of the electric dipole moment of a system? If the system is a bit complicated? What kind of formula I suppose to use? $$\vec{p}=q\vec{d}$$?

 

[G01]

For a general charge distribution, $\rho(\vec{x})$, the electric dipole moment is defined as follows:

$$\int \rho(\vec{x})\,\vec{x}\,d^3x$$

 

[tsang]

For a general charge distribution, $\rho(\vec{x})$, the electric dipole moment is defined as follows:

$$\int \rho(\vec{x})\,\vec{x}\,d^3x$$

Hi friend, may I ask you to explain details please? I never seen this formula before, and I have no idea how to use it. Could you please give me a simple example? For example, I saw a question talks about the dipole moment for three metal balls which are connected on three coners of a equalateral triangle. How to use that formula to solve this question? Thanks a lot.

 

[G01]

OK. You're dealing with a much simpler situation than I thought. The above relation still applies, but you'll want to use the discrete form:

$$\vec{p}=\sum_i q_i \vec{x_i}=q_1\vec{x_1}+q_2\vec{x_2}+q_3\vec{x_3}+...$$

Here, $\vec{x_i}$ is the distance vector vector the ith charge from the origin.

Thus you need to compute the distances of each charge from your chosen origin, and then compute the above vector sum.

Beyond this, you'll need to show some work for more help, as this is sounding like a homework question.