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 given by V(x)-43, where x is the distance from the cathode and C is a constant. Assume that the distance between the cathode and anode is 25.0 mm and the potential difference between the electrodes is 425 V 7. a) b) Determine the value of C. Obtain a formula for the electric field between the electrodes as a function of x.

Explanation / Answer

Part 1: x=25.0 mm = 0.025 m

(0.025 m)^(4/3) = 0.00731 m^(4/3)

V(x)=Cx^{4/3}

425=C* 0.00731
C=58139.5 V/m^(4/3)

Part 2:
Take the derivative of V
dV/dx = C(4/3)*x^(1/3)
Ex = - C(4/3)*x^(1/3)

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