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

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.


A)The motion of the electron can be broken down into two parts: 1. constant motion in the xdirection plus 2. a periodic part, the projection of which in the yz plane is circular. Find the angular velocity ? 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.



Can someone please explain how to express this?

Explanation / Answer

We know that charge moving in magnetic field experiences a force.

F = e * (v X B)

Now, v and B are perpendicular

Thus, Force, F = e * Vy * Bx

Force = mw^2/D

Thus, mw^2 * D = e * Vy * Bx
angular velocity, w = sqrt( e * Vy * Bx / m*D)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.