# Physics307L F09:People/Osinski/Eoverm

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SJK 17:03, 18 December 2008 (EST)
17:03, 18 December 2008 (EST)
I think you guys did a very good job taking data and thinking about analysis on this experiment. I think you probably (hopefully) learned how to extract uncertainty from linear regression after completing this lab.

## E/M Ratio

In this experiment we observe a beam of electrons produced by thermionic emission which is circularly deflected by a magnetic field around which the electrons travel. By varying the strength of the magnetic field and the accelerating voltage we are able to measure the radii of the different circular trajectories. Armed with the Lorentz equation and the Biot-Savart Law we are able to construct a formula that will give us the ratio e/m as the slope of a linear relation.

### Accepted Value

1.7563*10^11 C/kg

### Constant Voltage Analysis

• e/m ratio:4.3171*10^11C/kg with a whopping 146% error!!!!!!

### Constant Current Analysis

• e/m ratio:2.4038*10^11C/kg with a not so bad 36.7% error

### Final Result

$\displaystyle \frac{e}{m}=3.3605*10^011 C/kg$ with a deviation from the accepted value of $\displaystyle %error=.914%$

My procedure for determining charge was to average all the values of radii for I and V and then calculate the e/m ratio from the slope. There is nothing wrong with this method in principle, but I did it in such a way that I could only obtain one ratio from the constant I and V data each. This turned out to hinder my ability to calculate the standard deviation of the e/m ratio using the formula for the error of a slope given by Taylor. I explain this further in the lab notebook where I also discuss various other observations.