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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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