User:Randy Jay Lafler/Notebook/Physics 307L/The ratio e/m for electrons Summary

My lab partner was again Emran =Purpose=

The purpose of the e/m ratio lab was to determine the value of the charge to mass ratio for electrons by using Helmholtz coils. We applied different voltages and currents to the apparatus and measured the radius of curvature of the electron beam.

Link to notebook: User:Randy Jay Lafler/Notebook/Physics 307L/2010/09/20

=Brief Data overview=

To calculate e/m we determined the magnetic field B using the equation given in the manuel. We calculated B to be:
 * $$B=(7.793*10^-4weber/A*m)*I\,\!$$

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 did a linear fit to our data and came up with a slope of $$slope=7*10^-6+/-3*10^-7 m^2/V\,\!$$ Using this result we calculated e/m.
 * $$e/m=2.07*10^{11}+/-1*10^{10}\,\!$$

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

The linear fit line had a slope of: $$slope=16.66(41)/m*A\,\!$$
 * We then calculated e/m again:
 * $$e/m=1.83*10^{11}+/-8.5*10^{9}\,\!$$

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

=Conclusion= The lab manuel predicted that based on the systematic error and the error in measuring the radius of the electron beam we would have an experimental value greater than the accepted value. This was the case. Despite this, I feel good about our results because we were correct to the right order of magnitude, $$10^{11}$$

=Error= The error in our two measurements for the charge to mass ratio are probably mostly to misreading the length of the radius. I was difficult to determine because of the glass envelope the beam was in.

Citings Emran for the pictures in my lab notebook and the data tables and plots.

Acknowledgements Professor Koch and Katie for helping us set up the experiment as well as helping us to find the proper power supplies.