Investigating Electron Beam Deflections by a Long Straight Wire Carrying a Constant Current using Direct Action, Emission-based and Field Theory Approaches of Electrodynamics

Abstract

Results are presented for the transverse de ection of an electron beam by a long, straight wire carrying direct current. The experimental de ections are compared with three calculation methods based on the Lorentz force law (field theory) and both the Weber (direct action) and Ritz (emission) force formulae. The Lorentz force calculation is the conventional approach expressed in terms of electric and magnetic eld components. By contrast the force formulae of Weber and Ritz do not contain any eld vectors relating to E or B. The Weber force is based on direct action whereas the Ritz force expression is based on an emission/ballistic principle and is formulated in terms of a dimensionless constant, λ. The experimental beam de ections are for low speed (non-relativistic) electrons. Good agreement between experiment and theory is demonstrated for each approach. In fact, for the case of an innitely long wire, all three calculation methods give identical results. Finally, the three approaches are contrasted when applied to the case of high speed electrons.