8 The Electron Microscope 



That is, the angular momentum changes proportionally to the 

 magnetic flux which passes between the tzvo coaxial circles drawn 

 through the initial and final positions respectively. 



This result can be put into an even simpler form if we intro- 

 duce the vectorpotential A, from which the vector H of the 

 magnetic field intensity can be derived by the operation 

 H = curl A. In the case of axially symmetrical fields the vector 

 A has always tangential direction, therefore, we can write it in 

 the following as a scalar quantity, A. This is connected with 

 the magnetic flux M by the simple relation 



M = 27rrA (3) 



Fig. 2. Electron trajectories in magnetic lens. Curves orthogonal to the 

 trajectories are drawn to show the variation of the pitch 



The magnetic field lines, i.e., the meridian curves of the tubes 

 which carry a constant flux ]\I have therefore equations 

 rA =^ const. Their shape is shown in an example in the upper 

 part of figure 3. 



The equation (2) becomes now 



e 



r(mvt — —A) = const. (4) 



The expression in brackets can be interpreted as the total 



momentum of the electron in the magnetic field. It consists of 



the mechanical momentum mz\ and a term of electromagnetic 



. . e 



origm, — -A. (K. Schwarzschild, 1903.) Familiarity with this 



concept is a great help in understanding the somewhat compli- 

 cated motion of electrons in magnetic fields. 



