# Millikan oil drop experiment

I had a question about the Millikan Oil drop experiment. I did the experiment for my physics class where we had to determine the voltage that would make the droplet stationary. We did this ten times, so I have ten different voltages. The mass, gravity, and distance remains the same it is only the voltage that is changing. The part I am struggling with is, I must determine my own fundamental charge from this experiment and compare it to the accepted value of 1.6x10^-19. How do I determine my own fundamental charge when I am given 10 different voltages? I believe that I am supposed to use the q=mgd/V equation but I am not fully sure. My mass is: 1.57x10^-15 C My distance: 0.1 m Gravity: 9.81 m/s^2 My voltages: 400, 457, 384, 369, 400, 355, 369, 436, 384, and 369.

• Have you tried calculating q for each of your values of V? – Daddy Kropotkin Dec 12 '20 at 23:11
• Yes, I calculated all of the q values for V. – Lulu Dec 12 '20 at 23:18
• Were those q values mostly near $1.6\times10^{-19}$ C, $2 \times 1.6\times10^{-19}$ C, ... ? Or perhaps were they near $some value$, $2 \times some value$, ...? – mmesser314 Dec 12 '20 at 23:57
• They were not. They were actually around values like, 3.37x10^-18 C all the way to 4.17x10^-18 C. I calculated the differences between all the charges and then I got values around 1.6x10^-19 C to 4.9x10^-19 C. – Lulu Dec 13 '20 at 0:03
• The smallest non-zero difference between your calculations should be due to only 1 electron. – David White Dec 13 '20 at 0:33

It appears that your measurements may have been very imprecise. However, given your data, the best approach is to find a value for e such that the RMS differences between the charges $$q_i$$ you found and the nearest values of $$n_i e$$ to the $$q_i$$ is minimized. That is, minimize the square root of the sum of the squares of $$(n_i e -q_i)^2$$ by fiddling with the value of $$e$$. Choose $$n_i$$ for each $$q_i$$ so that $$n_i e$$ is as close as possible to $$q_i$$. Easy to do in a spreadsheet.