THE MAGNETIC-FIELD ELECTRON LENS 



339 



equilibrium, the sum of these two forces is equal to zero; hence the radius 

 of the circular path of deflection is 



r = 



mv 



For a given magnetic field of intensity H the radius of curvature is 

 therefore proportional to the velocity of the electron. The time of a 

 complete revolution of an electron, of charge e = 1.602 X 10 -: 

 is 



2irr 2tt m 3.57 



77 7 ~ ~h~ 



emu, 



t = 



10 7 second 



If a pencil of electrons, of mixed velocities, leaves a point source and 

 moves at right angles to the magnetic lines of force, each electron will 



Fig. VIII-18. 



describe a circle having a radius proportional to its velocity. If they all 

 start from the same point at the same time, they will all converge at 

 the same point at the end of one complete revolution, because the time 

 of the circular excursion depends only on the field strength. 



If an electron is projected into a uniform magnetic field set at some 

 small angle 6 with the direction of its motion, the field acts as a focusing 

 device. Under these circumstances the motion of the electron may 

 be resolved into two components, one parallel and the other at right 

 angles to the magnetic field. The parallel-velocity component, Fig. 

 VIII-18, will translate the electron in a direction parallel to the mag- 

 netic field with velocity v cos 6, while the right-angled component v sin 

 directed perpendicular to the magnetic field will give the electron a 

 circular motion. The composite motion is therefore screwlike. The 

 figure shows two such paths. 



Suppose that the point Pi emits an electron beam in which all the 

 electrons have the same velocity, but leave the point at various small 

 angles 6 with the direction of the horizontal magnetic field H x . They 

 will all arrive at the point P/ at the same time. A point P 2 in a small 

 circular area in the same plane with Pi, under identical circumstances, 



