# Unit confusion

1. Oct 24, 2011

### liquidFuzz

I just derived a little formula of protons moving in a magnetic field. With the symetry etc I have I get this:

p = qrB

Now I want to calculate the angular as a function like this:

p = constant * B

Where p is Gev/C, r is in meters.

I don't know what numbers or better what form B and q should have to get all numbers right. Anyone care to shine some light on this..?

Edit, my field is 1.74T r in meters.

Last edited: Oct 24, 2011
2. Oct 24, 2011

### xts

Rule of thumb for such cases - if you are confused by units, convert everything to SI.
You need to convert GeV into Joules, and express proton charge in Coulombs and speed of light in m/s. Google for those values!

3. Oct 24, 2011

### liquidFuzz

Mhmm...

Something like this?

$$\displaystyle p = 1.602 * 10^{-19} * 5.609*10^{35} r * 1.74 =1.56*r \frac{eV}{c^2} \frac{m}{s}$$

Edit, I see that I've confused more than the units. I wanted to compute it like this p = constant * r

Last edited: Oct 24, 2011
4. Oct 24, 2011

### xts

OK, I see I must do it for you...
$$p_{[{\rm kg\,m\,s^{-1}}]} = q_{[{\rm Q}]}r_{[{\rm m}]}B_{[{\rm T}]} = 1.602\cdot 10^{-19}{\rm C}\,r_{[{\rm m}]}B_{[{\rm T}]}$$
$$p_{[{\rm GeV}/c]} = \frac{p_{[{\rm kg\,m\,s^{-1}}]}\cdot 3\cdot 10^8{\rm m\,s^{-1}}} {1.602\cdot 10^{-10}{\rm kg\,m^2\,s^{-2}\,GeV^{-1}}} = \frac{1.602\cdot 10^{-19}{\rm C}\,r_{[{\rm m}]}B_{[{\rm T}]} \cdot 3\cdot 10^8{\rm m\,s^{-1}}} {1.602\cdot 10^{-10}{\rm kg\,m^2\,s^{-2}\,GeV^{-1}}} = 0.3\, \frac{{\rm GeV}}{c}{\rm\,\,m^{-1}\,T^{-1}}\cdot r \cdot B$$

Or - in other words - easier to remember and imagine - 1GeV particle makes circles of 1m radius in 3T field.

5. Oct 25, 2011

### liquidFuzz

Thanks for taking the time to help me!