Electric potential of a dipole moment

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Homework Help Overview

The discussion revolves around calculating the electric potential of a dipole moment, specifically for a water molecule with a known dipole moment value. The problem involves determining the potential at a specified distance from the dipole along its axis.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between dipole moment, charge, and distance, questioning how to derive the electric potential from the given dipole moment. Some suggest starting with the potential of point charges and considering the dipole arrangement.

Discussion Status

There is an ongoing exploration of the problem, with participants sharing different approaches and equations related to electric potential. Some have expressed confusion about the procedure and the necessary values, while others have attempted to clarify the relationships between the variables involved.

Contextual Notes

Participants note the absence of certain values, such as charge and distance, which complicates the calculation. The discussion also touches on the assumptions regarding the dipole's configuration and the relevance of the dipole moment in the context of the problem.

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Homework Statement


The dipole moment of a water molecule is 6.29E-30Cm. What is the electric potential's magnitude 1.43nm from a water molecule along the axis of the dipole?


Homework Equations


p = qr


The Attempt at a Solution


I don't have values for q or r. I just know the magnitude of the dipole moment and the distance away from the molecule in which I have to figure out the electric potential. I don't know where to go from here.

And even if given q, how would I figure out V.
 
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Find the electric potential of two equal and opposite charges d distance apart symbolically, at distance x from the centre of the dipole, and then take into account that x>>d.

ehild
 
That doesn't really help me.
 
You know the formula for the potential of a point charge? A point charge q is at x1=d/2, and an other one is at x2=-d/2. What is the potential at the point with coordinate x?

ehild
 
Has anyone figured out how to do this question? I have it too but I can't find the procedure anywhere online for it.
 
TheExibo said:
Has anyone figured out how to do this question? I have it too but I can't find the procedure anywhere online for it.
Do you know what is the electric potential of a point charge at distance D from it?
You have two charges, arranged along the x axis, both at distance d/2 from the origin. What are their potential at the point P, distance x from the origin?
upload_2017-10-31_5-39-15.png
 

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ehild said:
Do you know what is the electric potential of a point charge at distance D from it?
You have two charges, arranged along the x axis, both at distance d/2 from the origin. What are their potential at the point P, distance x from the origin? View attachment 214070

How do I determine what d/2 is?
 
TheExibo said:
How do I determine what d/2 is?
You do not need to determine it. The dipole momentum is given, and P=qd. At the end, you will find that the potential is proportional to qd, that is, the dipole moment.
 
ehild said:
You do not need to determine it. The dipole momentum is given, and P=qd. At the end, you will find that the potential is proportional to qd, that is, the dipole moment.

So I have P/(2q)=d/2 so far. I have also made the equations V=qk/(r-d/2) and V=qk/(r+d/2) and r is the distance from the origin to the point at which potential is measured.

What is next? I don't understand how to substitute them since d/2, V, and q are unknown.
 
  • #10
Nevermind. I have found that the equation V=kp/r^2 works, although I don't know how this equation was derived.
 
  • #11
TheExibo said:
So I have P/(2q)=d/2 so far. I have also made the equations V=qk/(r-d/2) and V =qk/(r+d/2) and r is the distance from the origin to the point at which potential is measured.

What is next? I don't understand how to substitute them since d/2, V, and q are unknown.
The two charges have opposite signs. The positive charge causes V+=qk/(r-d/2) potential at distance r from the origin, and the negative charge contributes to the potential by V-=qk/(r+d/2). The potential at P is the sum of V+ and V-: ##V(r)=qk\left(\frac{1}{r-d/2}-\frac{1}{r+d/2}\right)##. Bring the fractions to common denominator and use that d/r << 1.
 

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