Relativity: Initial velocity and e/m of Thomson's experiment

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SUMMARY

The discussion centers on calculating the initial velocity and charge-to-mass ratio (e/m) of an electron in a setup similar to Thomson's experiment. The participant initially used the equations u = E/B and e/m = q/m = u/RB, arriving at an initial velocity of 1.25×107 m/s and an incorrect e/m value of 3.125×1011. Feedback indicates the need to apply kinematic equations to accurately relate e/m to angular deflection, emphasizing the similarity to projectile motion when only the electric field is present.

PREREQUISITES
  • Understanding of electric fields and magnetic fields
  • Familiarity with Thomson's experiment and its principles
  • Knowledge of kinematic equations in physics
  • Basic concepts of charge-to-mass ratio (e/m)
NEXT STEPS
  • Review kinematic equations related to projectile motion
  • Study the derivation of charge-to-mass ratio in electric and magnetic fields
  • Learn about the effects of electric and magnetic fields on charged particles
  • Explore advanced topics in electromagnetism relevant to Thomson's experiment
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Physics students, educators, and anyone interested in the principles of electromagnetism and particle dynamics in electric and magnetic fields.

Matt21
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Homework Statement


In an experiment similar to Thomson’s, we use deflecting plates 5 cm in length with an electric field of 1.0×10^4 V/m. Without the magnetic field, we find an angular deflection of 30°, and with a magnetic field of 8×10^-4 T we find no deflection. What is the initial velocity of the electron and its e/m?

Homework Equations


u = E/B
e/m = q/m = u/RB

The Attempt at a Solution


I'm not sure if I'm using the correct equations but given the equations above, initial velocity is
u = 1.0×10^4/8×10^-4 = 1.25×10^7, and thus e/m is equal to
q/m = 1.25×10^7/(0.05*8×10^-4) = 3.125×10^11
If necessary, can anyone explain what I am doing wrong and perhaps the correct formula to use?
 
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Matt21 said:
u = 1.0×10^4/8×10^-4 = 1.25×10^7
OK. Units?

and thus e/m is equal to
q/m = 1.25×10^7/(0.05*8×10^-4) = 3.125×10^11
This is not correct. You will need to use kinematic equations to relate q/m to the angular deflection. Review the kinematics of the Thomson experiment when just the E field is present. It is similar to projectile motion.
 
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