The force of a homogeneous magnetic field B and the velocity of an electron normal to this field v⊥​ results in a circular motion of the electron about the optic axis with the radius of the trajectory r given as: r=mv⊥​/eB=[2m0​E(1+E/2E0​)]1/2/eB where m= relativistic mass of electron and the other terms have the same meaning as in Problem 2.1. (a) Assuming that v⊥​ is approximately equal to the velocity of the incoming electron, calculate the radius that an electron traveling at 100 and 400kV would make about the optic axis with a magnetic field of 2.5 Wb/m2 (Tesla). See Appendix A.13 for the velocity of an electron as a function of kV. (b) A field of 2.5 Wb/m2 is about the maximum value that can be obtained due to the saturation magnetization of the pole-piece material. What consequence does this result have on the focusing of electrons at higher accelerating voltages?
