Magnetic Field and Magnetic Induction in a Cylindrical Bar Magnet

magnet magnetization M (kA/m)

10

15

20

30

50

magnet diameter d (mm)

length L (mm)

20

display field

H

B

This Demonstration shows the quantitative magnetic field and magnetic induction for a cylindrical bar magnet. The magnetization

M

is assumed to be in the

z

direction and uniform within a magnet of diameter

d

and length

L

. Colors on a logarithmic scale show field intensity and arrows show its direction. The field

H

and induction

B

outside the magnet satisfy

B=

μ

0

H

, so the field patterns are identical (the same color is used for both fields). They are different inside the magnet, since there

B=

μ

0

(H+M)

. While

H

vectors go from the north pole to the south pole (top to bottom) in all regions,

B

vectors return to the north pole through the magnetized body.