A vacuum tube diode consists of concentric cylindrical electrodes, the negative

Question

A vacuum tube diode consists of concentric cylindrical electrodes, the negative cathode and the positive anode. Because of the accumulation of charge near the cathode, the electric potential between the electrodes is not a linear function of the position, even with planar geometry, but is given by V(x) = Cx4/3 where x is the distance from the cathode and C is a constant, characteristic of a particular diode and operating conditions. Assume that the distance between the cathode and anode is 13.6 mm and the potential difference between electrodes is 264 V. (a) Determine the value of C. C = V/m4/3 (b) Obtain a formula for the electric field between the electrodes as a function of x. (Use your result from part (a). Use the following as necessary: x.) Ex = (c) Determine the force on an electron when the electron is halfway between the electrodes. F = N

Explanation / Answer

Part 1: 14.0 mm = 0.014 m (0.014 m)^(4/3) = .00337 m^(4/3) 290 V / .00337 m^(4/3) = ......................... > Part 2: Take the derivative of V dV/dx = (4/3)*x^(1/3) Ex = ........................................… > Part 3: F = E*q q = -1.602*10^(-19) E = -(85946.32) * (4/3) * (.014/2)^(1/3) E = -21921.25 F = (-1.602*10^(-19)) * (-21921.25) = ................. > Part 4: The electron has a negative charge; it will be repelled by the negative cathode and attracted to the positive anode ........................................…

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