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 effect (Hd). The greater pole spacing in longer magnets results in greater magnetic field “reachâ€, and field lines that emerge from the side surfaces of the magnet. The earth’s magnetic field is an example.
All high coercivity materials (those where the value of Hc in Oersteds approaches that of Br in Gauss), like rare earth and ceramic, have similar external field shapes. With a resistance to demagnetization (Hc) almost equal to the residual magnetization (Br), the external magnetic field strength (Bd) has less effect on internal domain alignment, so the effective poles appear to be at the polar ends of the magnets in field line plots.
Low coercivity materials, like Alnico 5, have a different external field shape because Hc is much lower than Br. Hc for Alnico 5 is about 5% of Br, so a magnet's own external field, Bd, affects internal domain alignment toward the polar ends. Thus, domains at the ends and corners of an open circuit Alnico rod magnet do not remain aligned after magnetization in an air core coil (unless keepered), and plotted external field lines appear to have a focal point below the polar surfaces of the magnet. A length factor of 0.7 is often used in calculations to account for this effect (poles offset 15% from each polar end). However, 0.85 is a more realistic length factor for Alnico magnets with a geometry that causes them to operate above the knee in their second quadrant curve.
