Charged particle entering velocity selector

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SUMMARY

The discussion focuses on the mechanics of a velocity selector, which utilizes a parallel plate capacitor within a magnetic field to control the trajectory of charged particles. The magnetic force acts upward while the electric force acts downward on the particles. The condition for a particle to pass through without deflection is derived as v = B/E, where B is the magnetic field strength and E is the electric field strength. For protons with an electric field of E = 2.0 × 10^5 N/C and a magnetic field of B = 0.30 T, the required speed for no deflection is calculated to be 1.5 × 10^-6 m/s.

PREREQUISITES
  • Understanding of electric fields and magnetic fields
  • Knowledge of the Lorentz force equation
  • Familiarity with vector cross products
  • Basic principles of charged particle motion in electromagnetic fields
NEXT STEPS
  • Study the Lorentz force and its applications in particle physics
  • Explore the concept of velocity selectors in mass spectrometry
  • Learn about the behavior of charged particles in electric and magnetic fields
  • Investigate the effects of varying electric and magnetic field strengths on particle trajectories
USEFUL FOR

Students and educators in physics, particularly those focusing on electromagnetism and particle dynamics, as well as professionals working with particle accelerators and mass spectrometers.

britt
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1. The problem
A velocity selector consists of a parallel plate capacitor placed in an outside magnetic field (see figure). Charged particles entering the velocity selector experience an electric and a magnetic force (neglect effects due to gravity). Given is the setup in the figure below (attached)

a) What is the direction of the magnetic force?
b) What is the direction of the electric force?
c) When the two forces are equal the particle will move straight through the velocity selector. Derive an expression for the speed v that fulfills this condition.
d) What happens to particles that have a speed larger than v? What happens to particles that have a speed smaller than v?
e) Protons move through a velocity selector with E = 2.0 · 10^5 N/C and B= 0.30 T. What is the speed of a proton that is not deflected?

Homework Equations

(negatives are supposed to be vectors)
\overline{}FB=q\overline{}v x \overline{}B
\overline{}Fe = q\overline{}E
FB=qVB
Fe=qE

The Attempt at a Solution


a) up
b) down
c) qVB=qE
VB=E
V=B/E
d)it will deflect up, it will deflect down
e) v=(.30)/(2.0*10^5)= 1.5*10^-6 m/s
Just want to know if I am doing this correctly
 

Attachments

  • velocity selector.png
    velocity selector.png
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Physics news on Phys.org
It looks correct.

ehild
 

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