Week 6: Moving Charges and Magnetic Force 207
wasn’t until Rutherford did his famous experiment a few years laterthat scattered alpha particles
(helium nuclei) from gold foil and observed that many of the alpha particles scatteredstraight back,
something that they could only do if the positive charge was tiny and extremely massive, that it
became clear that the nucleus reallywasa proton, a tiny massive charge at the center of the hydrogen
atom, with some 1872 times the mass of the electron.
This, in turn, spelled the death of classical physics. Plum pudding wasspoiled forever. This
was no great loss; it couldn’t explain e.g. the spectral lines visible in lightemitted by superheated
hydrogen gas. However, the alternative was now a return to the classical orbital model with electrons
orbiting protons the same way a planet orbits the sun, in elliptical orbits wherein the electron
is constantly accelerating. Maxwell’s equations had long since proventhat such an atom would
instantly collapse, radiating away electromagnetic energy inallfrequencies as it did so, not in some
subset of discrete frequencies. Thomson’s experiment, simple as itis to us today in terms of our
modern models and knowledge of electromagnetism, truly deservedthe Nobel Prize because it paved
the way in a critical way for the invention of quantum mechanics and our current understanding of
atomic structure.
Example 6.2.6: The Mass Spectrometer
Brq ,m
q ,mr 1 21 1
2 2Voofilm/detector"goop"Figure 70: The Mass Spectrometer uses a region with a uniform magnetic field to create aspectrum
of particles that collide with a film or other detector matrix in places that indicate the radius of the
circle they are bent in by the field. This, in turn, is related to the ratioofq/mfor the particle, and
by assuming a charge that is a low integral multiple ofeone can determine the mass.
Another use of magnetism is in the construction of amass spectrometer. A mass spectrom-
eter is a device that takes some chemical “goop”, perhaps a samplecreated in a lab, perhaps a
sample obtained through some forensic process, and measures the masses of its chemically stable
components.
In the schematic above, a cooker heats some unknown chemical “goop”. This vaporizes it, and
the vapor comes in contact with a high voltage source that ionizes it. Ions of massm 1 , m 2 , m 3 ...
and (associated) chargeq 1 , q 2 , q 3 ...are then accelerated by a potential difference to an energy (re-
spectively) ofq 1 V 0 , q 2 V 0 , q 3 V 0 .. >, passed through a pair of collimating slits as a beam, and then
piped into a region containing a uniform magnetic fieldB 0 (out of the page as drawn). Positive ions
(for example) are then bent into circular trajectories depending on their mass, charge, and entrance
energy/velocity. The ions impact on a detector of some sort – perhaps a piece of photographic film –
where each particularq, mcombination registers as adistinctsignal a distance 2rfrom its entrance