What is a dipole moment in classical electromagnetisim?

In summary, a dipole moment is a measure of the separation of opposite charges in a body. It is induced when a charged object is brought close to a neutral object, causing a redistribution of charges on the neutral object. The term "moment" refers to the spatial distribution of charges or mass in an object, and can also be seen in rotational motion through the concept of torque.
  • #1
hanson
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I am rather confused about "dipole moment" in classical electromagnetisim. Since I have no previous background in this field of physics, I find it hard to understand the Maxwell's equations and other equations that involve the concept of dipole moment. Could anyone explain this to me in plain terms please?

Please kindly help.
 
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  • #2
Consider a body that has no charge. Now we bring a second body of negative charge close to any point on the first body. Although the first body has no charge, it has an equally distributed amount of both positve and negative charges that cancel out.

Because opposites attract, some of the distributed positive charge will move to the surface at the location of the second body (due to the attracted forces that draw them there). But because the overall charge of the first body is zero, there has to be a loss of positive charges on the other end of the body - it now has a negative charge.

The result is that we have induced a dipole on the body of no charge by bringing the negatively charged body close to it. One side now has a (small) net positive charge, and the other a net negative charge.

So an electric dipole moment of this scenario would be p=qd

where p is the moment created by the charges separated by a distance d. (on each end of the first body). It's an induced dipole moment.
 
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  • #3
hanson said:
I am rather confused about "dipole moment" in classical electromagnetisim. Since I have no previous background in this field of physics, I find it hard to understand the Maxwell's equations and other equations that involve the concept of dipole moment. Could anyone explain this to me in plain terms please?

Please kindly help.

The long answer involves Legendre polynomials (q.v.) which are an orthogonal set involving monopole, dipole, quadripole, etc moments.

The short answer would consider a bar magnet. The dipole moment would be pole strength times pole separation.
 
  • #4
Think about the electric field created by two point charges +q and and -q, separated by a (small) distance d.

If you reduce the distance and increase the charge so that qd remains constant, the field stays approximately the same, except for the region close to the charges.

A dipole is the limiting case of this, as d goes to zero and q goes to infinity but qd remains finite.
 
  • #5
But the term "moment" gives me a feeling of "rotation", as in mechanics...
Is it essetially relevant to any rotational motion?
 
  • #6
hanson said:
But the term "moment" gives me a feeling of "rotation", as in mechanics...
Is it essetially relevant to any rotational motion?

I agree, that's what it suggests to me as well. I'd be interested in understanding a connection between the two as well!
 
  • #7
hanson said:
But the term "moment" gives me a feeling of "rotation", as in mechanics...
Is it essetially relevant to any rotational motion?

Put (say) an electric dipole (with dipole moment [itex]\vec p[/itex]) in an external electric field [itex]\vec E[/itex]. If the dipole moment is not aligned with the field, the dipole experiences a torque [itex]\vec \tau = \vec p \times \vec E[/itex] which tends to rotate it towards alignment.

A more practical example: a magnetic compass needle is a magnetic dipole, which rotates towards alignment in an external magnetic field (such as the Earth's).
 
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  • #8
hanson said:
But the term "moment" gives me a feeling of "rotation", as in mechanics...
Is it essetially relevant to any rotational motion?

The term 'moment' can imply rotation: moment arm, for example. 'Moment' is taken to mean something like 'distribution'.

Take a macroscopic object. Newton's approach is to replace the extended body with a mass-point located at the center of mass. Similarly with a charged sphere- the electric field outside the body behaves as if the total charge is located at the center of the body.

However, we can distribute the mass or charge any way we would like, in real-life. The spatial distribution of mass and charge can then be represented mathematically as a series:

Total = monopole + dipole + quadrupole + octupole +...

Where the dipole moment, quadrupole moment, octupole moment, etc are all idealized geometries- in electrostatics, a dipole is two charged points separated by a certain distance. The quadrupole is four points, octupole 8 points, etc. In terms of mass, it's a little more complex but the mathematics is the same.

In mechanics, Euler introduced the term "moment of inertia" back in 1730, so the origin of the term 'moment' goes back at least that far. But again, the term is used as a way to describe the spatial distribution of mass of an extended body.
 

FAQ: What is a dipole moment in classical electromagnetisim?

1. What is a dipole moment in classical electromagnetism?

A dipole moment in classical electromagnetism is a measure of the separation between positive and negative charges in a system. It describes the strength and direction of the electric dipole created by these charges and is a fundamental concept in understanding the behavior of electric fields.

2. How is a dipole moment calculated?

The dipole moment is calculated by multiplying the magnitude of the charges by the distance between them. The direction of the dipole moment is from the negative charge to the positive charge.

3. What is the significance of a dipole moment in classical electromagnetism?

The dipole moment is a crucial concept in classical electromagnetism because it helps explain the behavior of electric fields. It is also used to describe the interactions between molecules in chemistry and the behavior of materials in an electric field.

4. How is a dipole moment related to electric potential energy?

The electric potential energy of a system with a dipole moment is affected by the orientation of the dipole moment in an external electric field. When the dipole moment is aligned with the electric field, the potential energy is at a minimum. When the dipole moment is perpendicular to the electric field, the potential energy is at a maximum.

5. Can a system have a dipole moment if it does not have charges?

No, a dipole moment is a result of the separation of positive and negative charges. If a system does not have any charges, it cannot have a dipole moment. However, a system can have a net dipole moment even if it has equal and opposite charges, as long as they are not evenly distributed.

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