README.md

Electron_charge2mass_exp

Short script to process experimental results and compute the electron charge to mass ratio with the distributions.

Code to run on Signaloid

File: charge2mass.c

Simply copy and paste this code into the Signaloid Cloud code editor and run it to obtain the predicted results and distributions.

Experiment Details

The repository mimics results taken from an experiment for which the aim is to measure the electron's charge-to-mass ratio. The accepted value is 1.758820 × 10 ¹¹ C/kg.

The experiment follows the Thompson method for measuring the charge-to-mass ratio of electrons. The main physical equation governing the experiment is given by,

$$\frac{q}{m} = \frac{2V}{B^{2} R^{2}}$$

where the left-hand term is the charge-to-mass ratio, $V$ is the accelerating voltage, $B$ the magnetic field that induces circular paths of the emitted electrons and $R$ is the radius of their trajectory. $B$ is expressed in terms of the current $I$, used to generate the field, $B = kI$. $k$ is a constant, taken to be $7.5\pm0.51 \times 10^{-4}$ T/A. In this repository, the experimental noise on $V$, $I$ and $R$ is assumed to be gaussian, with parameters:

Variable	$\mu$	$\sigma$
$V$ (V)	82.8	2.0
$I$ (A)	1.4	0.1
$R$ (cm)	2.92	0.11

The data for these, taken across 1000 samples is given in csv files (V.csv, I.csv, R.csv).

From the mean values, the estimated ratio is 1.77 $\pm$ 0.37 $\times 10^{11}$ C/kg. However, if one calculates this "on the fly", using the individual entries of each distribution and averaging the computed ratios, the value is of 1.81 $\times 10^{11}$ C/kg.

The estimated relative uncertainty through error propagation (assuming independence of variables) on the ratio is given by,

$$ \sqrt{\left( \frac{\sigma_{V}}{\mu_{V}} \right )^{2}+\left( \frac{2\sigma_{I}}{\mu_{I}} \right )^{2}+\left( \frac{2\sigma_{R}}{\mu_{R}} \right )^{2}+\left( \frac{2\sigma_{k}}{\mu_{k}} \right )^{2}}. $$

Jupyter-notebook

There is also a jupyter-notebook (Perform_Experiment.ipynb) to generate the results and show the distributions there as well. It also gives results on uncertainty estimates.