Measuring Magnetic Field Strength of a Cylindrical Magnet

[PhDnotForMe]

Hello,
Today I am wondering if anyone can help me quantify the strength of the magnetic field created by a permanent cylindrical magnet. I have been able to find equations online for the strength of the field within the z axis, (ie. the longitudinal length) but I would like to know the strength of the magnetic field in the transverse direction, or the strength of the magnetic field in the outward direction rather than on top or below.

 

[Pythagorean]

A cylindrical magnet is finite and, therefore, has edging effects. It's not a straightforward calculation, but Wolfram Alpha briefly touches the calculation superficially (and notes that the guts are complicated) favoring a numerical approach.

http://demonstrations.wolfram.com/MagneticFieldOfACylindricalBarMagnet/

 

[PhDnotForMe]

A cylindrical magnet is finite and, therefore, has edging effects. It's not a straightforward calculation, but Wolfram Alpha briefly touches the calculation superficially (and notes that the guts are complicated) favoring a numerical approach.

http://demonstrations.wolfram.com/MagneticFieldOfACylindricalBarMagnet/

Thanks for that great reference. The equations listed are pretty intense. If you considered a point in the transverse direction REAALLY far away, and the length and diameter of the magnet are small in comparison, would the strength of magnetic field be roughly proportionate to 1/R^2? 1/R? 1/R^3? The integral listed in the reference is way to difficult for me to estimate the macro-behavior.

 

[vanhees71]

At a very long distance (compared to the extension of the magnet) you can use the leading-order multipole, which in this case is a dipole. The magnitude goes like $1/r^3$.