# Electric & magnetic dipole moment

1. Jul 5, 2010

### Grufey

Hello, I have doubts with this problem, I'm not sure, if my solutión is right, so, here we go

Let's two equal charges with the same charge but opposite signs, positive and negative, in a circle, such a distance between them is constant and equal to diametre of the circle. Both charges, turn around the center of the circle with angular speed w. Calculate, the electric dipole moment, and the magnetic dipole moment.

the electric dipole moment, is define as, $$\vec{p}=q\vec{d}$$, with $$\vec{d}$$ the vector that go from the positive charge to negative charge.

The system turn around the center, so we have to applicate a rotational matrix to $$\vec{d}$$, and so, we have calculated the electric dipole moment

The magnetic dipole moment, must be zero, because the charges have opposite signs, and the problem is equivalent to two spirals with circulating intensites in opposite directions.

I think that my solution is too simple, for this reason I mistrust it

Thank's

2. Jul 5, 2010

### Dickfore

Electric dipole moment of a system:

$$\vec{d} = \sum_{a}{q_{a} \, \vec{r}_{a}}$$

where $q_{a}$ is the charge of the ath particle and $\vec{r}_{a}$ is its position vector. The summation goes over all the particles of the system.

Magnetic dipole moment:

$$\vec{m} = \frac{1}{2} \, \sum_{a}{q_{a} \, (\vec{r}_{a} \times \vec{v}_{a})}$$

where $\vec{v}_{a} = d\vec{r}_{a}/dt$ is the velocity of the ath particle and $\times$ stands for the vector product between the two vectors.

3. Jul 5, 2010

### Grufey

I am glad to have it well. If we calcule the moment, with your definition, we recover, my result.

So, Thank you again

4. Jul 5, 2010

### Dickfore

actually, no. The electric dipole moment of two opposite charges is always directed from the negative towards the positive one.

5. Jul 5, 2010

### Grufey

I agree, sorry. I was wrong.

Thank's

6. Jul 5, 2010

### Dickfore

You are right about the magnetic moment though. It is zero. The simplest way to look at it is, to ask yourself what the current carried by two opposite charges moving along a circle with the same frequency is. It is zero, and no current implies no magnetic moment.

7. Jul 5, 2010

### Grufey

I think that the problem is similar to two magnetics domains with opposite spin, the resultant moment is zero, or two electrons, spirals...

8. Jul 5, 2010

### Dickfore

No. If two electrons were orbiting around a common center, then the magnetic moment would not be zero, but the electric dipole moment would have been. This is more like the positronium atom, where an electron and a positron orbit around a common center of mass. Also, we have to neglect the spin of the charges, since there is no classical analogue to spin.

9. Jul 5, 2010

### Grufey

Then, two electrons were orbiting around a common center, have magnetic moment, iff, turn around in the same direction.?

I understood the positronium's example, thank's

10. Jul 5, 2010

### Dickfore

oh, did you mean two electron orbiting in opposite directions? Yes, that is also a viable option.