# Dipole moment, electric potential

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1. Jan 29, 2017

### Cocoleia

1. The problem statement, all variables and given/known data
I am given this picture

and I know that |q1|=2nC, |q2|=5nC, d=1mm
I need to first find the total dipole moment of the system. Then I need to find an equation that represents the electric potential due to this net dipole moment for all (everywhere)

2. Relevant equations
p=qd

3. The attempt at a solution
I saw a formula which was p=qd (vectors)
so I thought I would separate it into two different dipole moments, one for q1 and one for q2, and then add them together. For p1 I got 2x10^-12 in the y direction, and for p2 I got 5x10^-12 in the x direction. Would this be correct?

Also, would I be using this formula for the potential?
V = kpcosθ/r^2

Last edited: Jan 29, 2017
2. Jan 29, 2017

### haruspex

What happened to the 3/2?

3. Jan 29, 2017

### Cocoleia

Ok, so 7.5x10^-12 in the x direction. And for the potential?

4. Jan 29, 2017

### haruspex

Assuming a certain definition of θ, yes.

5. Jan 29, 2017

### Cocoleia

I'm not quite sure what θ would be in this case

6. Jan 29, 2017

### haruspex

Maybe better to put the answer in vector form. If $\vec p$ is the dipole at the origin and $\vec r$ is a point in space, what is the potential at $\vec r$?

7. Jan 29, 2017

### Cocoleia

I don't know what the formula for potential would be,except I had V=kpcosθ/r^2 in my notes but I don't know when to use it

8. Jan 29, 2017

### haruspex

That makes for not terribly useful notes!
It arises from the dot product of the two vectors.

9. Jan 29, 2017

### Cocoleia

So the dot product of p and r?

10. Jan 29, 2017

### haruspex

Yes. Can you write the whole expression?

11. Jan 29, 2017

### Cocoleia

I'm not really sure what you want, I assume r will have an x and y component, so r cosθ and r sinθ
so then
(7.5x10^-12)(rcosθ)+(2x10^-12)(rsinθ)

Sorry I don't really have any idea what I am doing because I have no notes/ teaching on this stuff.

12. Jan 29, 2017

### haruspex

13. Jan 29, 2017

### Cocoleia

14. Jan 29, 2017

### haruspex

15. Jan 29, 2017

### Cocoleia

What will the r hat be ?

16. Jan 29, 2017

### haruspex

Putting a hat on a vector is a standard notation meaning the unit vector in that direction. So for any vector $\vec x$, $\hat x=\frac{\vec x}{|\vec x|}$

17. Jan 29, 2017

### Cocoleia

Here they don't specify a length or direction for r, it just says "everywhere"

18. Jan 29, 2017

### haruspex

The potential is necessarily a function of position. You cannot say what it is "everywhere" without involving a variable to specify position.