Projekt Elektronik
Mess- und Regelungstechnik GmbH
Am Borsigturm 54 • 13507 Berlin
Fon
+4930 43 03 22 40
Fax
+4930 43 03 22 43
e-mail: info@projekt-elektronik.com
http://www.projekt-elektronik.com
Application Note PE007
Flux Density Of A Magnet In Distance X
General Formula ................................................................................................................................................... 1
Example ................................................................................................................................................................ 2
General Formula
B
(x)
L
x
Figure 1: round magnet
For the flux density caused by a round magnet on its magnetic axis the following formula applies.
(1)
B X ( X) =

BR 
L+X
X


−
2
2
2
2  R 2 + (L + X)
R + X 

Thereby BR is the remanence of the magnet. It is indicated in Tesla (T) or Millitesla (mT) or in the cgs system in
Gauss (G or Gs). The remanence is the residual magnetization or flux density of a magnet who had been
magnetized in a closed magnetic circuit up to saturation.
For the flux density direct at the surface of the magnet the formula can be simplified as follows.
(2)
B X (0 ) =
BR
L
⋅
2
R 2 + L2
If the formula (2) is transposed to BR and used to replace BR in (1) one can calculate the flux density on the
magnetic axis without knowledge of the remanence but only with the (e.g. determined by measurement) surface
flux density.
(3)
B X ( X ) = B X (0 )

R 2 + L2 
L+X
X


−
L
 R 2 + (L + X )2
R 2 + X2 
The drawing and formulas listed above have been adopted by courtesy of the company IBS-Magnete in Berlin.
The formulas are not valid for AlNiCo500.
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Projekt Elektronik
Mess- und Regelungstechnik GmbH
Am Borsigturm 54 • 13507 Berlin
Fon
+4930 43 03 22 40
Fax
+4930 43 03 22 43
e-mail: info@projekt-elektronik.com
http://www.projekt-elektronik.com
Example
Assume a round magnet with a diameter of 6 mm and a high of 4 mm. This is given with a BR of 1.2 T ( a
typical value of neodymium magnet). What is the surface flux density?
For this formula (2) is used:
(4)
B X (0 ) =
BR
L
⋅
2
2
R + L2
If the given values are inserted the following is obtained:
(5)
B X (0) =
1,2 T
⋅
2
4 mm
( 3 mm )
2
+ ( 4 mm )
2
Consequently it results in:
1,2 T 4 mm
⋅
2 5 mm
(6)
B X (0) =
(7)
B X (0) = 0,48 T = 480 mT
So the flux density at the surface is not even half of the remanence flux density.
With increased distance the flux density decreases even more.
The following graphic shows the course of the flux density of the example magnet. The flux density on the
magnetic axis is plotted for distances up to 10 mm. For calculation formula (1) had been used.
1000 mT
100 mT
10 mT
0 mm
1 mm
2 mm
3 mm
4 mm
5 mm
6 mm
7 mm
8 mm
9 mm
10 mm
Figure 2: flux density course
Clearly visible is the heavy decrease of the flux density with increase in distance. At only 10 mm the flux
density has been dropped to one-hundredth of the remanence flux density.
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