The magnetic field just above a lens in an electron microscope

[Philip Koeck]

I'm looking for an estimation or simulation of the magnetic field in the horizontal plane just above a typical lens in a transmission electron microscope. A rough cross section of such a lens can be seen here: electron lens - Bing images .
The lens is cylindrically symmetric around the vertical symmetry axis.
The magnetic field in the gap of the soft iron pole piece can be assumed to be in the order of 1 T.

 

[Vailanor]

The magnetic field in the vicinity of a typical electron lens can be estimated using the Biot-Savart law. This law states that the magnetic field strength at any point is proportional to the current running through the lens multiplied by the inverse of the distance between the point and the current running through the lens. Assuming a uniform current distribution in the lens, the total magnetic field can be determined by summing up the magnetic fields generated by all of the individual current elements.The exact calculation of the magnetic field around the electron lens may be complicated due to the symmetrical nature of the lens, but it is possible to make some reasonable approximations. For example, assuming that the lens has a uniform current distribution, then the magnetic field in the horizontal plane just above the lens can be estimated to be in the order of 1 T. This approximation is reasonable since the magnetic field at this position is mainly due to the current flowing through the lens and not to the soft iron pole piece.