Physics307L:People/Giannini/e/m

My partner is Richard T. Meyers

=Purpose=

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)=

First we start by determining our Magnetic field, which changes with current.
 * $$B=(7.793*10^-4weber/A*m)*I\,\!$$

We then conbined three equations together:
 * $$eV=\frac{mv^2}{2}\,\!$$
 * $$F_B=evB\,\!$$
 * $$F_c=mv^2/r\,\!$$

Solving for e/m:
 * $$F_B\!$$ is the force of the magnetic field.
 * $$F_c\!$$ is the centripetal force.
 * $$e/m=\frac{2V}{r^2*B^2}\,\!$$

From this equation we solved for r^2
 * $$r^2=\frac{2Vm}{(7.793*10^-4I)^2*e}\,\!$$


 * This equation is an equation of a line of r^2 verse V with a slope:
 * $$slope=\frac{2m}{(7.793*10^-4I)^2*e}\,\!$$

We then used LINEST in Google Docs to give us a linear fit of our data and got: $$slope=2.3(93)*10^{-5}+/-8.1(96)*10^{-6} m^2/V\,\!$$

Using this result we calculated e/m.
 * $$e/m=6.73(90)*10^{10}\,\!$$

We also calculated e/m from a plot of r verse 1/I with constant V
 * $$1/r=\sqrt{\frac{(7.793*10^-4)^2*e*I}{2Vm}}\,\!$$

The linear fit line had a slope of: $$slope=0.048(98)+/-0.0032(15)/m*A\,\!$$ We have to invert this slope to get the correct one.
 * We then calculated e/m again:
 * $$e/m=2.98(45)*10^{11}\,\!$$

The currently accepted value is:
 * $$\frac{e}{m}=1.76\times10^{11}\frac{C}{kg}\,\!$$

=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 $$69%$$ 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)

=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)=


 * r^2 Vs. V: $$+/-3.3680*10^{10}C/kg\,\!$$
 * r Vs. 1/I: $$+/-1.5394*10^{10}C/kg\,\!$$

=Citations=
 * Randy Lafler - Method for determining e/m