# Electric dipole moment

1. Sep 16, 2010

### 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? $$\vec{p}=q\vec{d}$$?

2. Sep 16, 2010

### G01

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

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

3. Sep 16, 2010

### tsang

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.

4. Sep 16, 2010

### 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.