What is the relationship between field shape and magnet proportions and does the material type make a difference?
Flux lines take the easiest (lowest reluctance) route they can from one polar surface to the other. This means that all flux lines passing through an isolated magnet will bend to the side as soon as they can. Because flux crowds toward the edges on polar ends, radial flux density increases. Using iron filings to see the field shape, this gives the appearance of bowed flux lines passing from pole to pole, with a higher concentration toward the magnet ends, and some flux lines bowing from the sides of the magnet. If the off-axis flux vector amplitude is greater than the coercivity of domains in that portion of the magnet, weaker domains will align with the vector. Field shape is also dictated by magnet geometry, or permeance coefficient (PC), which is related to the magnet’s effective l/d (equivalent length / diameter ratio). Total resistance to demagnetization is proportional to the product of length and coercivity (Hc), so longer magnets have a higher PC and less self demagnetizing eff
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