# Charge to Mass Ratio of the Electron Essay

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Charge to Mass Ratio of the Electron
Thomas Markovich and John Mazzou
Departments of Physics University of Houston Houston, TX 77204-5006 (Dated: September 23, 2010) We sought to reproduce the experiment ﬁrst preformed by KT Bainbridge to determine the charge to mass ratio of the electron. In this paper, we derived the relationship between this ratio and measurable quantities, detailed our experimental setup, with in depth and speciﬁc circuit diagrams. We determined the mass to charge ratio to be 6.54341±.00474661e7[Cg − 1] with a percent diﬀerence of 63%. Because of the large error, we explore possible sources of error.

I.

INTRODUCTION

a perfect circle. Thus: m v2 = qvB r (II.3)

The ratio of the mass of an electron to its
The electron emitting ﬁlament was connected to an external power source and a rheostat as indicated in Figure I. The switch allows for us to change the direction of the current in the ﬁlament. We used a Helmholtz coil to provide a near stable, uniform magnetic ﬁeld as required for the experiment. Our Helmholtz coil apparatus had two coils of equal radius that are parallel and separated by their radius. The coils were attached to an external power source and a rheostat as indicated in Figure II. The emitted electrons were then excited through a potential diﬀerence as indicated by Figure III.

.

(II.12)

V Next, we want to calculate I 2 r2 which is ultimately the j i value we will use for calculations. Here, we ﬁnd that 5 j=1 V
2 2 I j rj δ Vi I 2 r2 j j 2

¯ V 2 r2 I

=

5 j=1

1
2

.

(II.13)

δ

V I 2 r2 j j

FIG. 1. Circuit Diagram for the Filament Assembly.

3 the four remaining pegs, we repeated the procedure detailed above with one slight modiﬁcation - we only did one trial instead of ﬁve. All experiments were performed with the ﬁlament current at 3.6 A.

IV.

RESULTS

FIG. 2. Circuit diagram for the Helmholtz Coils.

In our experimental method, we measured the current through the Helmholtz coil required for the outer edge of the beam to reach the peg. For each accelerating potential, we calculated a mean value and the standard