An electron gun in a cathode-ray tube must send electrons toward a screen at a speed of

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

An electron gun in a cathode-ray tube must send electrons toward a screen at a speed of 5.0×107 m s−15.0\times10^{7}\,\text{m}\,\text{s}^{-1}. Each electron starts from rest at the cathode, which is at zero electric potential. Ignore relativistic effects. (a) Calculate the kinetic energy of one electron when it reaches the required speed. Express your answer in joules. (b) Determine the magnitude of the potential difference through which the electron must be accelerated to reach this speed. (c) If, in operation, the accelerating potential were accidentally increased by 10%10\%, describe qualitatively how the brightness and position of the electron spot on the screen would be affected. Explain your reasoning.

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