# Motion in a Magnetic Field problem

1. Feb 19, 2012

### kjlchem

1. The problem statement, all variables and given/known data
A proton (q = 1.6 X 10-19 C, m = 1.67 X 10-27 kg) moving with constant velocity enters a region containing a constant magnetic field that is directed along the z-axis at (x.,y) = (0,0) as shown. The magnetic field extends for a distance D = 0.7 m in the x-direction. The proton leaves the field having a velocity vector (vx, vy) = (4.3 X 105 m/s, 3.2 X 105 m/s).

What is h, the y co-ordinate of the proton as it leaves the region conating the magnetic field?

2. Relevant equations

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3. The attempt at a solution

I found R, the curvature of the path, but I have no idea how to find h. I tried using trig and geometry but it didn't work! This is what I did...

h/d=sin(θ)

#### Attached Files:

• ###### m.png
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2. Feb 20, 2012

### tiny-tim

hi kjlchem!

hint: what is the velocity as a function of time?

3. Feb 20, 2012

### vivekrai

You can easily work it out after what tiny has said using calculus.

4. Feb 21, 2012

### kushan

you can easily do with this figure :)

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5. Oct 5, 2013

### fredrogers3

I would like to ask something about the diagram. How does one know that the left side of the "square region" has a total length "r?"