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Question 2

An electron of mass m and charge -e is moving through a uniform magnetic field B = (Bx, 0, 0) in vacuum. At the origin, it has velocity

v=(Vx, Vy, 0), where and Vx>0 and Vy>0. A screen is mounted perpendicular to the x axis at a distance d from the origin. Throughout, you can assume that the effect of gravity is negligible. 

(figure provided in the solution) 


Part A: First, suppose Bx=0. Find the y coordinate of the point at which the electron strikes the screen.


Part B: Now suppose , and another electron is projected in the same manner. Which of the following is the most accurate qualitative description of the electron's motion once it enters the region of nonzero magnetic field?


Part C: 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 ω 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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