Editing J. J. Thomson (section)

====Measurement of mass-to-charge ratio====

[[File:JJ Thomson exp3.gif|thumb]]

In his classic experiment, Thomson measured the [[mass-to-charge ratio]] of the cathode rays by measuring how much they were deflected by a magnetic field and comparing this with the electric deflection. He used the same apparatus as in his previous experiment, but placed the discharge tube between the poles of a large electromagnet. He found that the mass-to-charge ratio was over a thousand times ''lower'' than that of a hydrogen ion (H<sup>+</sup>), suggesting either that the particles were very light and/or very highly charged.<ref name="PhilMag"/> Significantly, the rays from every cathode yielded the same mass-to-charge ratio. This is in contrast to [[anode rays]] (now known to arise from positive ions emitted by the anode), where the mass-to-charge ratio varies from anode-to-anode.  Thomson himself remained critical of what his work established, in his Nobel Prize acceptance speech referring to "corpuscles" rather than "electrons".

Thomson's calculations can be summarised as follows (in his original notation, using F instead of E for the electric field and H instead of B for the magnetic field):

The electric deflection is given by <math>\Theta = Fel / mv^2</math>, where Θ is the angular electric deflection, F is applied electric intensity, e is the charge of the cathode ray particles, l is the length of the electric plates, m is the mass of the cathode ray particles and v is the velocity of the cathode ray particles. The magnetic deflection is given by <math>\phi = Hel / mv</math>, where φ is the angular magnetic deflection and H is the applied magnetic field intensity.

The magnetic field was varied until the magnetic and electric deflections were the same, when  <math>\Theta = \phi, Fel / mv^2 = Hel / mv</math>. This can be simplified to give <math>m/e = H^2 l/F\Theta</math>. The electric deflection was measured separately to give Θ and H, F and l were known, so m/e could be calculated.
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