The Charge to Mass Ratio

Cody DianopoulosMac Eder

Margaret BonnellJosh Streger

January 19, 2013

Abstract

In 1897, J.J. Thomson became the first man to observe the charge tomass ratio using the apparatus he designed, which is the same apparatusused in this experiment. Using a large magnetic field (created from theHelmholtz Coils), a current can be created from cathode rays (beams ofelectrons), which can be measured to find out the charge to mass ratio of

the electron itself. Using classical variables, since mv2

2= eV and Bve =

mv2

r, it follows algebraically that e

m= 2V

B2r2, where B is the magnetic field

created by the Helmholtz coil given by B = 8µ0NI

R√125

= 0.000535I for the coilused in the experiment. Along with the fact that V = 177.5V = const. in

this apparatus, the equation can be rearranged to find that em

= 1.24×109

(Ir)2.

Using different values for current I, the cathode ray formed a radius r, twodata points (I, r) were collected: (4.4A, 0.02m) and (5.4A, 0.015m). Fromthese points, the predicted values of e

mwere calculated and averaged to

yield em

≈ 1.745×1011 Ckg

. Comparing the calculated value with the actual

value, 1.76 × 1011 Ckg

, yields a very small 0.85% percent error. The causeof error is mainly dedicated to the lack of precision in the technology, as itwas necessary to estimate when measuring the radius of the cathode ray’spath. From these results, it can be verified that the value of the chargeto mass ratio for an electron is 1.76 × 1011 C

kg.

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