Magnet Strength: North vs South Pole

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The discussion centers on whether the strength of a magnet is uniform at both poles, specifically in the context of an oddly shaped magnet like a cone. It suggests that the density of magnetic field lines, or magnetic flux, may be greater at the apex (North pole) than at the base (South pole) due to the majority of lines emanating from the poles. However, an alternative viewpoint proposes that if magnetic domains are aligned parallel within the conical shape, more flux lines could emerge from the sides, potentially resulting in a lower flux density at the apex compared to the base. This leads to uncertainty about the distribution of magnetic strength in non-standard magnet shapes. The conversation highlights the complexity of magnetic field behavior in uniquely shaped magnets.
David Brenchley
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with an odd shaped magnet eg a cone .. apex = N / base = S

is the strength of the magnet the same at each pole ?
 
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Consider the density of magnetic field lines (magnetic flux), assuming the opposite poles are at apex and base, that the lines are conserved and that the majority emanate from the poles.
 
Forgive my ignorance .. I'm FAR from being a physicist ..

"that the majority emanate from the poles" .. this would imply the flux density would be greater at the apex then the base ..

if one envisions a parrallel alignment of magnetic domains within the conical shape .. it would seem reasonable to assume more flux lines emininate from the "sides". If this were the case the flux density would be less at the apex then the base ..

??
 
It may be shown from the equations of electromagnetism, by James Clerk Maxwell in the 1860’s, that the speed of light in the vacuum of free space is related to electric permittivity (ϵ) and magnetic permeability (μ) by the equation: c=1/√( μ ϵ ) . This value is a constant for the vacuum of free space and is independent of the motion of the observer. It was this fact, in part, that led Albert Einstein to Special Relativity.

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