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https://texercises.com/exercise/electron-repelled-from-sphere/
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Exercise:
An electron is released from the surface of a metallic sphere with radius rO and a negative charge QO. Calculate the maximum speed the electron gains while it is repelled from the sphere.

Solution:
The potential difference between a po on the surface of the sphere and an infinitely distant po is given by Delta phi k_C fracQr where Q is the charge and r the radius of the sphere. It follows for the increase of the electron's kinetic energy Delta sscEkin q Delta phi frac m_e v^ k_C fracq Qr labeleq Solving refeq for the final speed leads to v vF sqrtfractimesnckctimesqtimesQrtimesm sqrtfractimesnckctimesqXtimesQrtimesmXV/c^ vapproxresultvS
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Exercise:
An electron is released from the surface of a metallic sphere with radius rO and a negative charge QO. Calculate the maximum speed the electron gains while it is repelled from the sphere.

Solution:
The potential difference between a po on the surface of the sphere and an infinitely distant po is given by Delta phi k_C fracQr where Q is the charge and r the radius of the sphere. It follows for the increase of the electron's kinetic energy Delta sscEkin q Delta phi frac m_e v^ k_C fracq Qr labeleq Solving refeq for the final speed leads to v vF sqrtfractimesnckctimesqtimesQrtimesm sqrtfractimesnckctimesqXtimesQrtimesmXV/c^ vapproxresultvS
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Branches
Electrostatics
Tags
acceleration voltage, electric potential, electric potential difference, point charge
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Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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