I'm trying to do some calculations to see just how strong a magnet you'd have to have, in order for curvature to be noticeable in a rudimentary cloud chamber, with lead-210 as an alpha particle source. I'm guessing that this would have to be huge, but I'm not getting through my back of the envelope calculations successfully. Starting from the tensor expression:
$$\frac{d^2 x^\mu}{d\tau^2}=\frac{q}{m}F^\mu_\nu \frac{dx^\nu}{d\tau}$$
and expanding using the relation $d\tau=\frac{dt}{\gamma}$, I find:
$$\frac{q}{m}F^\mu_\nu \frac{dx^\nu}{dt}=\gamma\ddot{x}^\mu+\dot{x}^\mu \frac{d}{dt}\gamma$$
Assuming the electric field is zero, no work is done, so $\frac{d\gamma}{dt}$=0, this gives in vector form (zero $ct$ component):
$$\gamma^{-1} \frac{q}{m}\dot{\vec{x}}\times \vec{B}=\ddot{\vec{x}}$$
Plugging numbers in, with the mass being about four times that of a proton, and the charge being twice that of a proton, and the energy released by lead 210 in alpha decay $3792 \text{KeV}$, I find that the emitted particles have a velocity around $\frac{1}{20}c$, and I get an acceleration on the order of $10^{15}$ in a 1 tesla field, and calculating $v^2/a$ for the radius of curvature gives me a radius of .28 meters.
I'm skeptical of my result because it seems great, but I haven't seen any images or stories of this being tried with a homemade cloud chamber and a neodymium magnet. Is this result correct? Is there something I'm not taking into account? It would be disappointing to set the experiment up and see no result!
(I can post the Mathematica code used to query these values and calculate everything, on request.)
Best Answer
it is prohibitively expensive to get a 1T magnet around the size comparable to the expected radius of curvature of the charged particles. assuming cost was not the issue, you would still have trouble finding one that size. a 6" Nd disc is $800--with a magnet this "small" you just might detect some curvature in the cloud tracks with some luck.
if you tried to build a solenoid you would still need a few thousand turns of wire running 10 amps...