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Motion of electrons in electric and magnetic fields.

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A beam of electrons, such as in a computer monitor CRT, traveling in the X direction enters a region which has an electric field of 3,000 volts/meter directed in the Y direction and a magnetic field of 0.004 Tesla directed in the Z direction. The two separate forces are acting on the beam of electrons. The direction and magnitude of the electric field is in such a way as to oppose and cancel out completely the force (Lorentz) caused by the electric field. I need to determine the velocity of the electrons in meters/second.

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https://brainmass.com/physics/electricity-magnetism/motion-electrons-electric-magnetic-fields-117539

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Velocity of electrons
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A beam of electrons, such as in a computer monitor CRT, traveling in the X direction enters a region which has an electric field of 3,000 volts/meter directed in the Y direction and a magnetic field of 0.004 Tesla ...

Solution Summary

Electrons move undeflected through electric and magnetic fields and to find its velocity. Motion of electrons in electric and magnetic fields are determined.

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The motion of a particle in uniform electric and magnetic fields

Full question is attached.
1) In this question we will consider the motion of a charged particle in uniform electric and magnetic fields that are perpendicular. You may ignore the effects of gravity throughout this question.

a)
i) Consider a charged particle of mass m and charge q which is moving in a uniform electric field E = Eey and a perpendicular uniform magnetic field B = Bez. Show that the equations of motion for the particle are,

ii) If the particle is at rest at time t = 0, verify that

iii) Hence determine the position of the particle at time t, assuming that it was located at the origin at t = 0

b) An infinite metal plate occupies the xz-plane (y=0). The plate is kept at zero potential, V = 0. (see figure 1 below) Photoelectrons are liberated from the plate at y = 0 by ultraviolet radiation. The initial velocity of the photoelectrons is negligible. A uniform magnetic field B is maintained parallel to the plate in the positive z-direction and a uniform electric field E is maintained perpendicular to the plate in the negative y-direction. The electric field is produced by a second infinite plate parallel to the first plate, maintained at a constant positive voltage V0 with respect to the first plate. The separation of the plated is d.

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