Physics307L:People/Callow/chargetomassratio

Links to lab notebook and procedure used
Link to Dr. Gould's manual

Link to my lab notebook

Purpose of the lab
The main purpose of the lab was to find the charge to mass ratio of an electron. Other qualitative experiments are also done to get a feel for how a charged particle is effected by a magnetic field.

Summary of my data
Three sets of data were taken using slightly different methods to find the charge to mass ratio of an electron. The first set is just a set of random voltages, currents, and resulting radii that plugging into the equation

$$ \frac{e}{m} = \frac{2*V}{{B^2}*{r^2}}$$

I solved for in my lab notebook will output e/m. The value from this data found e/m to be

$$ 2.67(15)*{10^{11}} \frac{coul}{kg} $$

My second set of data had the voltage set to be constant with varying current. Using maple I found the linear best fit line

$$\frac{1}{I} = 0.0803+.182*r$$

were the radius is in centimeters and after multiplying r by 100 to make this equation work for r given in meters and dropping the constant term as it felt insignificant and complicated things I found

$$ \frac{e}{m} = \frac{2*V}*{(.182*100)^2}$$

which plugging in 250 volts for voltage led to the e/m value

$$ \frac{e}{m} = 2.72*{10^{11}} \frac{coul}{kg}$$

Finally, for the third set of data the current was held constant and using maple found the linear best fit

$$ V = 125+6.78*r^2 $$

Which adjusted so things are in meters became

$$ V = 125+(6.78*100*r)^2 $$

which when substituted into my equation for e/m and plugging in B I found the value to be

$$ \frac{e}{m} = 1.42*{10^{11}} \frac{coul}{kg}$$

The accepted value is

$$ 1.76*{10^{11}} \frac{coul}{kg} $$

and I found my percent error to be 51.7%, 55%, and 19% in the order I gave the data above.

While the order of magnitude of my data matches the accepted value's other then that my numbers do not agree. Using the standard error I found from the first set of data I'm 606 times my standard error off. My data also seems to nicely line up on my plots and such so there is likely something wrong either with the way I did the lab or the measurements the equipment gave. As I mention in the lab notes, I don't know what to do to get something like standard error for my linearly fitted lines. I know maple takes the standard error into account when making the line (or well I think it does) but I don't know how to retrieve it myself. I'd guess those are all significantly off too though.

It is interesting that my data while keeping the current constant came out much different than the other two sets. There really doesn't seem to be a good reason for this other than what I mentioned in the lab notebook about the power supply maybe being flaky.

What I learned
Though there isn't anything new in this lab I haven't already done before a lot of experience was gained in using the math notations for formula's on wikipedia and rediscovered how to do lines of best fit and plot them with the data points.

The major thing for me in this lab was discovering something unexpected being the color of the electron beam and how it changes. This gave me something of my own to look into and experiment with outside of what the lab manual asks for. Though the actual experiment is definitely cool, having this unexpected effect has done a much better job keeping me thinking about the physics in this lab. Hopefully when I have more time or if I chose this lab for a formal report I'll be able to find out more.

What I'd do differently if doing the lab again
From what I hear a new bulb is on its way which may help improve the ability to see the beam, though the one I used still worked fairly well. The one power supply for the coils did seem to have minor issues. Given the chance to try out different equipment or trying to find a better way to measure the radius would probably help me understand why my data is so far off. The current method of finding the radius isn't too great to begin with and is probably the largest source of error.

Also, the questions I answered in the lab manual were all based around why everything happens in this lab. Usually I have a section on the physics of the lab in my summary but everything there is to say is pretty much covered there. My question is should I restate them here, move them to the summary being that they are more centered around how the lab works, or is it fine to just leave them in the lab notebook since a link is provided at the top.