Page:Design and Calibration of a New Apparatus to Measure the Specific Electronic Charge.pdf/6

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Kirchner^[1], though quite different in detail. In preliminary and exploratory experiment C. H. Wilts^[2] investigated the possibilities of using cavity resonators to produce deflection fields. In the present experiment rotating magnetic fields are used to produce deflection, for as will be shown, a higher resolving power can be obtained than with non-rotating field deflection. An electron entering the cavity is acted upon by this rotating magnetic field during its time of transit, $\tau ,$ and leaves the cavity with a transverse component of velocity which depends upon this transit time, As is shown below, if the transit time is adjusted to coincide with an integral number, $n$, of cycles of the parameter $k/2\pi$; ( $k/2\pi$ is approximately equal to the rotation frequency, $f$.) then the electron emerges with no net transverse component of velocity. The cavity can accordingly be used as a sort of "phasing valve" velocity detector; for when integral cycle transit has obtained the axial, i.e. total, velocity of the electrons is approximately

where $d$ is the length of the cavity. A more accurate equation for $v$ is obtained below.

The ultimate value if $e/m_{o}$ will, by an inspection of equations (1) and (2), be seen to depend on the measurement of: a) a voltage, $V.$, b) a length, $d$, and c) a radio frequency, $f$.

1.1 The Equations of Motion of the Electrons.

Consider a system of rectangular cartesian coordinates with a uniform magnetic field, $B_{1}\sin(2\pi ft)$, in the $y$ direction and a similar field $B_{2}\cos(2\pi ft)$, in the $x$ direction. Let the electron beam

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1. F. Kirchner, Phys. Zeits., 30, 773 (1929)
2. C. H. Wilts, Doctorate thesis, Cal. Tech. Library