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Exercise:
Electrons from an electron gun acceleration voltage VO enter a uniform magnetic field with strength BO perpicularly to the field lines. Their trajectory is a circle with radius rO. Based on this experiment calculate the mass of an electron.

Solution:
The cyclotron radius is r_C fracm vq B Solving for the velocity yields v fracq B r_Cm labeleq:v The acceleration voltage leads to an increase in kinetic energy q Delta V frac m v^ labeleq:Ek Substituting refeq:v o refeq:Ek yields q Delta V frac m leftfracq B r_Cmright^ frac m fracq^ B^ r_C^m^ fracq^ B^ r_C^ m Solving for the mass yields m mF fracnce times B^ times r^times V m approx resultmS This is in good agreement with the accepted value for the electron mass m_e ncme.
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Exercise:
Electrons from an electron gun acceleration voltage VO enter a uniform magnetic field with strength BO perpicularly to the field lines. Their trajectory is a circle with radius rO. Based on this experiment calculate the mass of an electron.

Solution:
The cyclotron radius is r_C fracm vq B Solving for the velocity yields v fracq B r_Cm labeleq:v The acceleration voltage leads to an increase in kinetic energy q Delta V frac m v^ labeleq:Ek Substituting refeq:v o refeq:Ek yields q Delta V frac m leftfracq B r_Cmright^ frac m fracq^ B^ r_C^m^ fracq^ B^ r_C^ m Solving for the mass yields m mF fracnce times B^ times r^times V m approx resultmS This is in good agreement with the accepted value for the electron mass m_e ncme.
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Attributes & Decorations
Branches
Magnetism
Tags
acceleration voltage, circular motion, cyclotron radius, electron, elementary charge, magnetic force
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Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Decoration