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Exercise:
Calculate the final speed of an electron accelerated through a potential difference of dVO. Express the result as a fraction of the speed of light. How much does its speed increase when a second acceleration voltage of dVO follows immediately after the first one?

Solution:
The final velocity for a particle accelerated from rest is v vF sqrtfrac-times -nce times dVncme v approx resultvS As a fraction of the speed of light this corresponds to beta fracvc fracvncc vinc approx resultvincS For an electron accelerating from v to v' through the same acceleration voltage the total increase in kinetic energy is Delta V. It follows for the final speed v' sqrtfrac- q Delta Vm sqrt vF sqrt v The increase in speed is therefore Delta v v' - v dvF v times left sqrt - right resultdvS which is significantly less than the increase during the first half of the acceleration. Due to the square root the speed is not proportional to the acceleration voltage!
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Exercise:
Calculate the final speed of an electron accelerated through a potential difference of dVO. Express the result as a fraction of the speed of light. How much does its speed increase when a second acceleration voltage of dVO follows immediately after the first one?

Solution:
The final velocity for a particle accelerated from rest is v vF sqrtfrac-times -nce times dVncme v approx resultvS As a fraction of the speed of light this corresponds to beta fracvc fracvncc vinc approx resultvincS For an electron accelerating from v to v' through the same acceleration voltage the total increase in kinetic energy is Delta V. It follows for the final speed v' sqrtfrac- q Delta Vm sqrt vF sqrt v The increase in speed is therefore Delta v v' - v dvF v times left sqrt - right resultdvS which is significantly less than the increase during the first half of the acceleration. Due to the square root the speed is not proportional to the acceleration voltage!
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Branches
Electrostatics
Tags
acceleration voltage, charge, electron, kinetic energy, voltage
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Difficulty
(1, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Decoration