
391Basics of Microwave Tubes
d y
y
= =
2
0
(11.19b)
dU
d z
z
= =
2
0
(11.19c)
In view of Appendix A2, Equation 11.19 leads to
U eV m= √
2 /
(11.20)
where V = E ⋅ x = V
0
⋅ x/d is the potential at any point.
The substitution of the values of e (= 1.602 × 10
−19
C) and m (= 9.1091 × 10
−31
kg)
in Equation 11.20 gives
U V x d x d V= × √ = × √ √5 932 1 / 5 932 1 /
5 5
. { ( )} . ( )0 0
0 0
(11.21a)
At x = d, the expression for velocity reduces to
U V= × √0 0
0
.5932 1 m/s
6
(11.21b)
As the force is directly proportional to E (F = QE), the electron will travel
from the cathode to the anode along a straight line. Figure 11.5b illustrates
the movement of