Dipole moment, electric potential

[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)

Homework Equations

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

 

[haruspex]

I got 5x10^-12 in the x direction

What happened to the 3/2?

 

[Cocoleia]

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?

 

[haruspex]

And for the potential?

Assuming a certain definition of θ, yes.

 

[Cocoleia]

Assuming a certain definition of θ, yes.

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

 

[haruspex]

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 $\vec r$?

 

[Cocoleia]

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

 

[haruspex]

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.

 

[Cocoleia]

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?

 

[haruspex]

So the dot product of p and r?

Yes. Can you write the whole expression?

 

[Cocoleia]

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]

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.

See the equation for φ(R) in the fourth line of "bold" equations at https://en.wikipedia.org/wiki/Electric_dipole_moment#Potential_and_field_of_an_electric_dipole.

 

[Cocoleia]

See the equation for φ(R) in the fourth line of "bold" equations at https://en.wikipedia.org/wiki/Electric_dipole_moment#Potential_and_field_of_an_electric_dipole.

So I will use this?

 

[haruspex]

So I will use this?
View attachment 112276

Yes.

 

[Cocoleia]

Yes.

What will the r hat be ?

 

[haruspex]

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 $\vec x$, $\hat x=\frac{\vec x}{|\vec x|}$

 

[Cocoleia]

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"

 

[haruspex]

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.