User:Randy Jay Lafler/Notebook/Physics 307L/The ratio e/m for electrons Summary
My lab partner was again Emran
Purpose
SJK 01:07, 13 October 2010 (EDT)
This is a good summary. Missing is a statistical comparison of your measurements to the accepted value. We've talked more about how to do this in lecture, and you'll want to make sure to do it in future labs. As an example here, the accepted value is much, much farther away from your measurements that are your uncertainties. This means that if your uncertainties represent the standard error of a normally distributed mean, that it's very very unlikely that your measurements are consistent...thus there is significant systematic error somewhere.
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
SJK 01:25, 13 October 2010 (EDT)
It's good that you report all three of your measurements here. It's a little tough to notice them, so some formatting or something to point them out would help.
To calculate e/m we determined the magnetic field B using the equation given in the manuel. We calculated B to be:
- [math]\displaystyle{ B=(7.793*10^-4weber/A*m)*I\,\! }[/math]
We then conbined three equations together:
- [math]\displaystyle{ eV=\frac{mv^2}{2}\,\! }[/math]
- [math]\displaystyle{ F_B=evB\,\! }[/math]
- [math]\displaystyle{ F_c=mv^2/r\,\! }[/math]
- [math]\displaystyle{ F_B\! }[/math] is the force of the magnetic field.
- [math]\displaystyle{ F_c\! }[/math] is the centripetal force.
Solving for e/m:
- [math]\displaystyle{ e/m=\frac{2V}{r^2*B^2}\,\! }[/math]
From this equation we solved for r^2
- [math]\displaystyle{ r^2=\frac{2Vm}{(7.793*10^-4I)^2*e}\,\! }[/math]
- This equation is an equation of a line of r^2 verse V with a slope:
- [math]\displaystyle{ slope=\frac{2m}{(7.793*10^-4I)^2*e}\,\! }[/math]
We did a linear fit to our data and came up with a slope of [math]\displaystyle{ slope=7*10^-6+/-3*10^-7 m^2/V\,\! }[/math] Using this result we calculated e/m.
- [math]\displaystyle{ e/m=2.07*10^{11}+/-1*10^{10}\,\! }[/math]
We also calculated e/m from a plot of 1/r verse I with constant V
- [math]\displaystyle{ 1/r=\sqrt{\frac{(7.793*10^-4)^2*e*I}{2Vm}}\,\! }[/math]
The linear fit line had a slope of: [math]\displaystyle{ slope=16.66(41)/m*A\,\! }[/math]
- We then calculated e/m again:
- [math]\displaystyle{ e/m=1.83*10^{11}+/-8.5*10^{9}\,\! }[/math]
The currently accepted value is:
- [math]\displaystyle{ \frac{e}{m}=1.76\times10^{11}\frac{C}{kg}\,\! }[/math]
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.SJK 01:01, 13 October 2010 (EDT)
you distinguish between systematic error and the error in measuring the radius. Presumably, you mean that the radius measurement is random and there are other systematic errors (which would be biased towards higher or lower values). Just want to make sure you review the difference between systematic and random errors, and we should discuss in person too.
This was the case. Despite this, I feel good about our results because we were correct to the right order of magnitude, [math]\displaystyle{ 10^{11} }[/math]
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. SJK 01:04, 13 October 2010 (EDT)
would these errors be large enough to account for your discrepancies, though? How could you tell? One way would be to add or subtract some amount from all of your measurements and see how far off you'd need to be to account for difference. Unfortunately, I didn't get time to discuss this lab with you in class, in order to talk about other possible sources of systematic error, as well as to discuss how you know that the systematic error is huge--
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.
