. The Bell System technical journal . at derivation it was implicitly assumedthat the only forces which the escaping electron had to overcome werethe cathode surface forces, and that any electron which escaped fromthe cathode would reach the anode. If a retarding potential V* isapplied to the anode then only those electrons whose normal com-ponent of velocity u exceeds a value Ua can reach the anode; where Uais given by mUaVl = {ipc + Vr)e (39) in the classical case, or 7nua!2 = P,n+ eVr (40) in the quantum-mechanical case. Figure 4, curve 1, illustrates the * In discussing retarding potential
. The Bell System technical journal . at derivation it was implicitly assumedthat the only forces which the escaping electron had to overcome werethe cathode surface forces, and that any electron which escaped fromthe cathode would reach the anode. If a retarding potential V* isapplied to the anode then only those electrons whose normal com-ponent of velocity u exceeds a value Ua can reach the anode; where Uais given by mUaVl = {ipc + Vr)e (39) in the classical case, or 7nua!2 = P,n+ eVr (40) in the quantum-mechanical case. Figure 4, curve 1, illustrates the * In discussing retarding potentials it is convenient to consider retarding poten-tials as positive even though the anode potential is negative, so that Vr = — V. THERMIONIC ELECTRON EMISSION 431 potential energy of an electron at various distances between thecathode and anode when the anode is Vr volts negative to the is tentatively assumed that the anode work function (pa is the sameas the cathode work function <pc\ this is another way of saying that. Fig. 4—Potential distribution between parallel plates; Pa = Pc- the contact potential is zero. When F^ = 0 nearly all the spacebetween the cathode and anode is field free as shown in curve 2; onlyin the immediate neighborhood of the cathode or the anode is theelectron subjected to any forces. When a retarding potential isapplied the electrons must have sufficient energy to pass over themaximum in curve 1, Fig. 4, in order to reach the anode. To determine the number of electrons that can reach the anode weintegrate equation (10) or (20), from ti = Ua to u — oo where Ua isgiven by equation (39) or (40), respectively. Whether we use theclassical or the quantum-mechanical statistics we arrive at the sameresult. i = Ne = U exp. (- Vre/kT), (41a) or log i = log io — ()Vr, (41b) where io — i when Vr — 0. The slope of the straight line in Fig. 3should thus be If (pa and ifc are not equal, the field between anode and cathode willn
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