Electron through electric and magnetic field

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SUMMARY

The discussion centers on calculating the initial accelerating voltage (V) required for an electron to travel undeflected in the presence of an electric field (E) of 1000 V/m and a magnetic field (B) of 1 × 10^(-5) T. The forces acting on the electron are given by the equations F=qE for the electric force and F=Bqv for the magnetic force. To maintain a straight trajectory, these forces must be equal, leading to the relationship V=E/q=(0.5mv^2)/q, where m is the mass of the electron (10^(-30) kg) and e is its charge (1.6×10^(-19) C).

PREREQUISITES
  • Understanding of electric fields and forces (F=qE)
  • Understanding of magnetic fields and forces (F=Bqv)
  • Basic knowledge of kinematics and energy (kinetic energy equation)
  • Familiarity with the properties of electrons (mass and charge)
NEXT STEPS
  • Calculate the velocity (v) of the electron using the relationship between voltage and kinetic energy.
  • Explore the implications of Lorentz force on charged particles in electromagnetic fields.
  • Investigate the effects of varying electric and magnetic field strengths on electron trajectories.
  • Learn about the applications of charged particle motion in devices like cathode ray tubes and particle accelerators.
USEFUL FOR

Physics students, educators, and professionals in fields related to electromagnetism and particle physics will benefit from this discussion.

Alb
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Homework Statement



An electron, initially at rest, is accelerated by a potential V in a vacuum and
then travels horizontally in a region of space where there is an electric field,
E, and a magnetic field, B. The fields are aligned such that the electron
is subjected to a force eE upwards and a force evB downwards, where e
is the charge of the electron and v is its velocity. If E = 1000 V/m and
B = 1 × 10^(-5) T, what is the value of the initial accelerating voltage V for
the electron to continue flying undeflected?
(Take m=10^(-30) kg and e=1.6×10^(-19) C)

Homework Equations



No idea.

The Attempt at a Solution



No idea.
 
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some equations for you:

upward F=qE
downward F=Bqv

(travelling straight so upward F=downward F)

Then, regarding voltage:

V=E/q=(0.5mv^2)/q

can you find the voltage from these equations?
 

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