Explore BrainMass

Explore BrainMass

    Electron's motion in Electro Magnetic field

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    An electron moves in a force field due to a uniform electric field E and a uniform magnetic field B that is at right angles to E. Let E = jE and B = kB. Take the initial position of the electron at the origin with initial velocity vo = ivo in the x direction. Find the resulting motion of the particle. Show that the path of motion is a cycloid.

    x = a sin wt + bt
    y = a (1 - cos wt)
    z = 0

    © BrainMass Inc. brainmass.com December 24, 2021, 7:40 pm ad1c9bdddf


    Solution Preview

    Following is the text part of the solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear correctly here. Thank you for using Brainmass.

    Start out with writing the Lorenz force on the electron.

    F = -e [E + v x B]

    Let v = (vx, vy , vz) and F = (Fx, Fy, Fz)

    F = -e [E j + (vx,vy,vz) x B k]

    (Fx, Fy, Fz) = -e [E j + - vx j + vy i]
    Equating the components,

    Fx = - e vy B
    Fy = -e(E - B vx)
    Fz = 0

    Apply Newton's second law. F = m a

    Fx = m d^2x/dt^2 = - e vy B
    Fy = m d^2y/dt^2 = ...

    Solution Summary

    I have found the path of the electron when it is placed in a mutually perpendicular magnetic and electric fields provided that the electron is in motion. This problem and solution set will be a great practice set for a student in an Electromagnetic Theory course.