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Quiz 5 - Vacuum Tube Physics
A Planar Vacuum Diode (Figure 3) has a heated cathode at z = 0 (potential V(z = 0) = 0)
and an anode at z = d (potential V(z = d) = Vo). If an electron escapes from the cathode
with zero initial velocity, then it can be shown that the potential V(z) as a function of
distance z from the cathode is given by:
V(z) = Vo(z/d)4/3
(a) Find the electric field E (magnitude and direction) as a function of z.
(b) Find the space charge density ρ(z) as a function of z.
(c) Determine the velocity u(z) of the electron as a function of z. The electron
mass is me, and charge e.
(d) Determine the current density J(z).
(e) Determine the conductivity σ(z).
Solution:
Physics key words: vacuum tube, cathode, anode, electric field, physics, mass,
gravity, potential, energy, velocity, density, current, voltage, electron,
conductivity, charge, EM, magnitude, theory, properties.
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