Potential created by two magnetic monopoles

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Homework Help Overview

The discussion revolves around determining the expression for the potential created by two magnetic monopoles, one positive and one negative, positioned equidistant from Earth's center along the rotation axis. Participants are exploring the implications of the inclination of the line joining the monopoles in relation to Earth's rotation.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are attempting to clarify the type of potential being discussed and the implications of the inclination of the line joining the monopoles. Questions are raised about the definition of the inclination and its relation to different axes.

Discussion Status

There is an ongoing exploration of the relationship between the magnetic monopoles and the potential they create, with some guidance on comparing this potential to that of a magnetic dipole. Multiple interpretations regarding the axes involved and their effects on the potential are being discussed.

Contextual Notes

Participants are considering the angle formed by the Earth's rotation axis with respect to a vertical axis, as well as the implications of defining different axes for analysis. The discussion reflects on the assumptions regarding the orientation of the equatorial plane and its perpendicularity to the rotation axis.

Carmen_8
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Homework Statement


Determine the expression for the potential created by two magnetic monopoles (one positive, the other negative) that are equidistant from Earth's center (a/2 is the distant from each monopole to the Earth's center) and that are placed in the rotation axis.

Homework Equations


The problem that I have with this exercise is that the line that joins the two monoples is inclined, since they are on Earth's rotation axis.

The Attempt at a Solution

 
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Carmen_8 said:
Determine the expression for the potential ...
What kind of potential? Please explain.
Carmen_8 said:
... the line that joins the two monoples is inclined, ...
Inclined with respect to what?
 
The magnetic dipole created by the two monopoles, i.e. two charges. They ask for this, because they want us to compare this potential (using superposition) with the magnetic potential that is created by a magnetic dipole.

The monopoles are on the Earth's rotation axis, so they are inclined with respect a vertical axis, perpendicular to the equator. Rotation axis forms an angle θ with this vertical axis perpendicular to equator.
 
So you want to show that the magnetic scalar potential produced by two magnetic "monopoles" is, to some approximation, that of a point magnetic dipole. Is that right? Even if the line joining the two monopoles were at an angle with respect to some other axis, you can always define the monopole-to-monopole line as the z-axis conventionally and proceed from there. Why should the existence of this other z-axis affect the potential that you are seeking?
Carmen_8 said:
Rotation axis forms an angle θ with this vertical axis perpendicular to equator.
What defines this "vertical" direction? Are you saying that the equatorial plane is not perpendicular to the axis of rotation of the Earth?
 

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