# Dipole moment, electric potential

• Cocoleia
In summary: The potential is necessarily a function of position. You cannot say what it is "everywhere" without involving a variable to specify position.In summary, the conversation discusses finding the total dipole moment of a system with two given electric charges, and then using that to find the electric potential at any point in space. The formula for calculating dipole moment is mentioned, as well as the formula for electric potential due to a net dipole moment. The conversation ends with a clarification on the notation for the unit vector in a certain direction.
Cocoleia

## Homework Statement

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)

p=qd

## 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:
Cocoleia said:
I got 5x10^-12 in the x direction
What happened to the 3/2?

haruspex said:
What happened to the 3/2?
What is the direction of a dipole moment vector?
Ok, so 7.5x10^-12 in the x direction. And for the potential?

Cocoleia said:
And for the potential?
Assuming a certain definition of θ, yes.

haruspex said:
Assuming a certain definition of θ, yes.
I'm not quite sure what θ would be in this case

Cocoleia said:
I'm not quite sure what θ would be in this case
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##?

haruspex said:
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##?
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

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

haruspex said:
That makes for not terribly useful notes!
It arises from the dot product of the two vectors.
So the dot product of p and r?

Cocoleia said:
So the dot product of p and r?
Yes. Can you write the whole expression?

haruspex said:
Yes. Can you write the whole expression?
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.

haruspex said:
Yes.
What will the r hat be ?

Cocoleia said:
What will the r hat be ?
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|}##

haruspex said:
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|}##
Here they don't specify a length or direction for r, it just says "everywhere"

Cocoleia said:
Here they don't specify a length or direction for r, it just says "everywhere"
The potential is necessarily a function of position. You cannot say what it is "everywhere" without involving a variable to specify position.

## 1. What is a dipole moment?

A dipole moment is a measure of the separation of positive and negative charges in a system. It is a vector quantity, meaning it has both magnitude and direction.

## 2. How is dipole moment calculated?

Dipole moment is calculated by multiplying the magnitude of the charge by the distance between the charges and the angle between the dipole vector and an external electric field.

## 3. What is the significance of dipole moment?

Dipole moment is significant in understanding the polarity and strength of electric fields in molecules. It also helps to explain the behavior of molecules in electric fields.

## 4. How does dipole moment affect electric potential?

Dipole moment affects electric potential by creating an electric field that can interact with other charged particles. This can lead to changes in the electric potential energy of a system.

## 5. Can dipole moment be zero?

Yes, dipole moment can be zero if the magnitude of the positive and negative charges are equal and the distance between them is zero. This creates a symmetrical distribution of charges, resulting in a net dipole moment of zero.

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