# Magnetic Bubble

I have been asked to prove or disprove the following problem:

Is it possible to arrange an array of magnetic dipoles (little magnets) in free space such that the magnetic field at the centroid of the space is higher than the field strength immediately surrounding the centroid? The field at the center is called a magnetic bubble, if exists.

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No can do using only magnetic dipoles. You have to have a magnetic monopole (yet to have discovered).

Hint: apply Gauss's law to the bubble.

Is Inverse-Square Law responsible?

With respect to the thesis that it is impossible to create a local region of higher magnetic intensity in free space using magnetic dipoles, is this not due to the inverse-square law?
For example, cancer tumors are treated using the principle of collimation of radiation; i.e. a collimated radiation beam is axially-rotated over time such that the crossing-axis passes through the tumor.
However magnetic intensity cannot (?) be collimated (due to the Divergence theorem (?)) and worse falls off at 1/r^2.
So my question, for an approach on a proof, is, is it the divergence of the magnetic intensity in free space or the inverse-square law which prevent a magnetic bubble from being formed by using an arbitrary numer of magnetic dipoles?

Some observations:
1) A high magnetic intensity is not the same as a magnetic bubble as defined before.
2) I'm not sure about the question of the collimation, but I think that you have to take into account the Electric and Magnetic field altogether (i.e. a light beam) in the case mentioned.
3) About the last point: in practice you will try to form plane waves, or more precisely, diminish the 1/r^2 factor as much as you can, until it doesn't affect your operation.
4) IIRC, the 1/r^2 can only come from monopolar sources, so I don't think you'll get such a decay for a magnetic field... At best it will be like 1/r^3.
5) According to this, you can't prove the claimed impossibility of the magnetic bubble if you use the 1/r^2 law...
6) The proof using the Divergence theorem should look very simple. Have you ever tried to prove that there's no way to achieve an equilibrium state using only electrostatic forces?

Notice that I could be wrong... I'm no specialist :p