Finding Momentum with Uniform Magnetic Field: q, B, a, d

[Bhumble]

Homework Statement

A particle of charge q enters a region of uniform magnetic field B (pointing into the page). The field deflects a particle a distance d above the original line of flight. Is the charge positive or negative? In terms of a, d, B, and q, find the momentum of the particle.

x displacement is a
y displacement is d
particle is initially moving in the x direction

Homework Equations

p = QBR

The Attempt at a Solution

Charge is +q via the right hand rule with the magnetic field pointing into the page and force initially upward.

I'm just not sure how to find the radius. I tried finding a reference somewhere so if someone knows a good place to find the trig on this that would be great.

 

[zhermes]

That equation won't work in this situation (it applies to circular motion, e.g. in a cyclotron or something). Write out an equation for the y displacement... try to squeeze the x-displacement into it, then work that into momentum.

 

[Bhumble]

Isn't this situation a cyclotron except that there is no velocity in the direction along the magnetic fields axis (which is normally conserved) and there is no electric field so the particle is just spinning in a circle. My professor derived this equation with a similar problem so I'm pretty sure it is applicable.

 

[zhermes]

Its the exact same conditions/setup... but the particle isn't moving in a circle. So there is no well-defined radius.

 

[rwisz]

In terms of momentum, we can use the equation p = QBR. This means that the momentum of the particle is dependent on its charge, the magnetic field strength, and the distance it is deflected from its original path. The positive charge of the particle indicates that its momentum is in the same direction as its displacement, which is in the x direction. Therefore, the momentum of the particle can be expressed as p = +qBd.