# Magnetic Field of a Hollow Cylindrical Magnet

Magnetic Field of a Hollow Cylindrical Magnet

This Demonstration shows the magnetic induction for a homogeneously axially magnetized hollow cylindrical magnet.

L

R

1

R

2

The magnetization A/m (remanent field =1T).

M=/=1/(4π)

B

r

μ

0

7

10

B

r

Consider the hollow cylindrical magnet as two cylindrical magnets with radii and , of equal length and magnetization. The magnetization directions of the cylinders are opposite. Therefore the magnetic field induction is calculated as the total of two cylindrical magnetic inductions .

R

1

R

2

(B=+)

B

1

B

2

Figure (z) shows the component of total magnetic induction along the axis.

B

Oz

z

Oz

Figure (r) shows dependence of the component of total magnetic induction on at .

B

r

r

r

z=L/2

Field lines of a hollow cylindrical permanent magnet involve the calculation of a large number of integrals. To improve accuracy, increase the number of points in the integrations or the number of points in the field-line plots. This will, however, increase the time required for computation.

You can change the sizes of the permanent magnet, but it it will take some time for the new calculations to run.