Magnetic Field of a Hollow Cylindrical Magnet

L (cm)

1

2

4

6

10

20

r

1

(cm)

0

1

2

3

5

r

2

(cm}

1

4

6

10

15

L

plot range

details

z

0

L/2

L

2L

points

16

25

50

field lines

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

L

is the length;

R

1

,

R

2

are the inner and outer radii of a magnet, respectively.

The magnetization

M=

B

r

/

μ

0

=1/(4π)

7

10

A/m (remanent field

B

r

=1T

).

Consider the hollow cylindrical magnet as two cylindrical magnets with radii

R

1

and

R

2

, 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

(B=

B

1

+

B

2

)

.

Figure

B

Oz

(z)

shows the

z

component of total magnetic induction along the

Oz

axis.

Figure

B

r

(r)

shows dependence of the

r

component of total magnetic induction on

r

at

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.