Potential created by two magnetic monopoles

[Carmen_8]

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

 

[kuruman]

Determine the expression for the potential ...

What kind of potential? Please explain.

... the line that joins the two monoples is inclined, ...

Inclined with respect to what?

 

[Carmen_8]

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.

 

[kuruman]

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?

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?