An electron of mass m and charge ?e is moving through a uniform magnetic field B

Question

An electron of mass m and charge ?e is moving through a uniform magnetic field B? =(Bx,0,0) in vacuum. (Figure 1) At the origin, it has velocity v? =(vx,vy,0), where vx>0 and vy>0. A screen is mounted perpendicular to the x axis at a distance Dfrom the origin.

Throughout, you can assume that the effect of gravity is negligible.

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?

A The electron decelerates before coming to a halt and turning around while always moving along a straight line.
B The electron's motion will be unaffected. (It will continue moving in a straight line with the same constant velocity.)
C The electron moves in a circle in the xy plane.
D The electron moves along a helical path about an axis parallel to the field lines with constant radius and constant velocity in the xdirection.

Explanation / Answer

PART A

We know that D = Dx = Vt * t and that t = Dx/vx

y = Dy = Vy * t
y = Vy *Dx/Vx

y = Vy * D/ Vx

PART B

The answer is D. There is a magnetic field, but the vx component of the electron's velocity remains unchanged, because vx is parallel to Bx . So the electron starts moving in a circle respect to the y axis, while simultaneously moving along the x axis. If you trace the path of the electron now, it will look like a helical path

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