# Direction of a dipole moment

1. Nov 1, 2009

### ananthu

1. The problem statement, all variables and given/known data

Can any one explain why the direction of the dipole moment of an electric dipole is always taken as "from -q to +q" but not "from +q to -q"? In fact when we draw the electric lines of force we are only drawing in such a way that they start from +q and terminate at -q.Then why this contradiction? What is the correct explanation for this convention?

2. Relevant equations

3. The attempt at a solution

2. Nov 1, 2009

### Staff: Mentor

It's just a convention.
What does that have to do with the definition of dipole moment? There's no contradiction.

3. Nov 1, 2009

### tiny-tim

But why is the convention for a dipole the opposite to the other convention?

4. Nov 1, 2009

### Staff: Mentor

Ah... now I understand the question. The "natural" definition of dipole moment (the first moment of the charge distribution) is:

$$\vec{p} = q_1\vec{r}_1 + q_2\vec{r}_2$$

That will give the direction of the dipole moment as minus to plus.

5. Nov 1, 2009

### rl.bhat

When you keep a dipole in an electric field, it acquires the stable equilibrium position with positive charge toward the electric field. Potential energy for a dipole is given by
U = - p.E
It has minimum value = -pE at the stable equilibrium position. It is possible only when p is parallel to E, i.e. p is from -q to +q.

6. Nov 1, 2009

### Staff: Mentor

But if you defined the dipole moment with the opposite convention, U = p.E. And the minimum value would be when p is anti-parallel to E. The physics wouldn't change. (Not that I'm suggesting one flout convention. )

7. Nov 2, 2009

### ananthu

Will you please elaborate this point?

8. Nov 2, 2009

### Staff: Mentor

I'll try. Let q1 = +q and q2 = -q, then:

$$\vec{p} = q_1\vec{r}_1 + q_2\vec{r}_2 = q\vec{r}_1 - q\vec{r}_2 = q(\vec{r}_1 - \vec{r}_2)$$

The vectors r1 and r2 are the position vectors of +q and -q. Thus the vector r1 - r2 points from -q to +q.

9. Nov 3, 2009

### ananthu

Thank you. Now it is clear.