# Physics307L:People/Giannini/e/m

My partner is Richard T. Meyers

## Contents

# Purpose

^{SJK 22:12, 13 October 2010 (EDT)}To determine the charge to mass ratio of electrons using Helmholtz Coils (by applying different voltages and currents and then recording the new radii).

# Calculating e/m (Overview)

^{SJK 21:45, 13 October 2010 (EDT)}First we start by determining our Magnetic field, which changes with current.

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle B=(7.793*10^-4weber/A*m)*I\,\!}**

We then conbined three equations together:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle eV=\frac{mv^2}{2}\,\!}****Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle F_B=evB\,\!}****Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle F_c=mv^2/r\,\!}**

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle F_B\!}**is the force of the magnetic field.**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle F_c\!}**is the centripetal force.

Solving for e/m:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle e/m=\frac{2V}{r^2*B^2}\,\!}**

From this equation we solved for r^2

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle r^2=\frac{2Vm}{(7.793*10^-4I)^2*e}\,\!}**

- This equation is an equation of a line of r^2 verse V with a slope:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle slope=\frac{2m}{(7.793*10^-4I)^2*e}\,\!}**

We then used LINEST in Google Docs to give us a linear fit of our data and got:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle slope=2.3(93)*10^{-5}+/-8.1(96)*10^{-6} m^2/V\,\!}**

^{SJK 21:38, 13 October 2010 (EDT)}Using this result we calculated e/m.

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle e/m=6.73(90)*10^{10}\,\!}**

We also calculated e/m from a plot of r verse 1/I with constant V

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 1/r=\sqrt{\frac{(7.793*10^-4)^2*e*I}{2Vm}}\,\!}**

The linear fit line had a slope of: **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle slope=0.048(98)+/-0.0032(15)/m*A\,\!}**
We have to invert this slope to get the correct one.

- We then calculated e/m again:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle e/m=2.98(45)*10^{11}\,\!}**

The currently accepted value is:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{e}{m}=1.76\times10^{11}\frac{C}{kg}\,\!}**

# Conclusions

The r vs 1/I part of this experiment seems to yield better results then r^2 vs. V, in our case.**Also, that we ended up with a value that is about**

^{SJK 21:46, 13 October 2010 (EDT)}**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 69%}**more then the currently expected value seems to show that this experiment has some sort of systematic error (since our measurements were representative of a r^2 vs V curve)

^{SJK 21:47, 13 October 2010 (EDT)}# Error(Experimental)

Possible sources of error: Human, Systematic: the equipment heating up over time, the lights being turned on and off during our experiment, the ruler we used being manufactured incorrectly, our old voltage sources may not supply constant voltage at all times.

# Error(e/m)

^{SJK 21:49, 13 October 2010 (EDT)}**r^2 Vs. V:****Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle +/-3.3680*10^{10}C/kg\,\!}****r Vs. 1/I:****Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle +/-1.5394*10^{10}C/kg\,\!}**

# Citations

- Randy Lafler - Method for determining e/m