Question

Motion of Electrons in a Magnetic Field

An electron of mass m and charge -e is moving through a uniform magnetic field \(\vec{B}=\left(B_{x}, 0,0\right)\) in vacuum. At the origin, it has velocity \(\vec{v}=\left(v_{x}, v_{y}, 0\right)\), where vx>0 and vy >0. A screen is mounted perpendicular to the x axis at a distance D from the origin.15939.jpg


The motion of the electron can be broken down into two parts: 

1. constant motion in the x direction plus

2. a periodic part, the projection of which in the yz plane is circular. Find the angular velocity w of the electron associated with the circular component of its motion. Express the magnitude of the angular velocity in terms of Bx, the magnitude of the electric charge e, and other known quantities.

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