# Physics307L F08:People/Gibson/Notebook/071008

## Introduction

SJK 15:51, 18 November 2007 (CST)
15:51, 18 November 2007 (CST)
Actually, it's not because they're small that they only have a few extra electrons. It's because the oil starts out neutral, and through spraying for some reason the drops become slightly charged. The alpha particles are not required to make them charged, just to change the charge of a given drop.

This lab was designed in the end measure the charge of an electron. The drops used in the experiment are very tiny so only a few electrons would be present on each of the drops. You are also required to introduce alpha particles to the oil drops, when introducing the drops to an electric field we are then able to control rise and fall times. These times are measured then we use equations found in the lab manual to determine the charge we find on each drop, and thus the charge of an electron.

## Intro Measurements

We measured the spacer to be 7.511 mm (.0007511 meters)

Following the instructions given in the lab manual

Plate voltage: 500.6 V

Density of Oil 886 kg/m^3

Measure of Resistance between plates: 2.101 Ohms relates to 23.5 C

## Data

Fall Time | Rise Time

 7.18                2.97
6.22                3.01
6.43                2.72
5.98                2.44
6.63                2.97
6.27                2.57
6.51                2.55
7.09                2.73
7.18                2.78
6.93                2.98
7.2                 3.74
6.49                3.47
6.61                3.87


Fall Time Rise Time

 5.54                3.73
5.47                4.32
5.26                4.16
5.75                4.67
5.34                4.07
5.83                4.6
5.73                4.33
5.63                3.83
6.07                4.38
5.58                4.12
5.79                4.16
5.69                4.44
6.32                4.51


• Drop 3

Fall Time | Rise Time

 7.81                2.08
7.78                1.87
7.49                2.03
8.45                1.96

• Drop 4

Fall Time | Rise Time

 8.07                1.98
8.19                2.02
8.24                2.19
8.07                1.96


## Equations

${\displaystyle \alpha ={\sqrt {{\frac {b^{2}}{{4p}^{2}}}+{\frac {9\eta V_{f}}{2g\rho }}}}-{\frac {b}{2p}}}$

Where:

${\displaystyle \alpha }$ is the radius of the drop in m,
${\displaystyle b}$ is a constant (8.20x10^-3 Pa*m),
${\displaystyle p}$ is the pressure in pascals
${\displaystyle \rho }$ is the density of oil in kg/m^3
${\displaystyle \eta }$ is the viscosity of air in poise (Ns/m^2)
${\displaystyle g}$ is the acceleration of gravity in m/s^2
${\displaystyle V_{f}}$ is the velocity of fall in m/s

${\displaystyle m={\frac {4}{3}}\pi \left({\sqrt {{\frac {b^{2}}{{4p}^{2}}}+{\frac {9nV_{f}}{2g\rho }}}}-{\frac {b}{2p}}\right)^{3}\rho }$
${\displaystyle E={\frac {V}{300d}}}$
${\displaystyle Q=mg{\frac {\left(V_{f}+V_{r}\right)}{EV_{f}}}}$
${\displaystyle Q={\frac {4}{3}}\pi \rho g\left({\sqrt {{\frac {b^{2}}{{4p}^{2}}}+{\frac {9nV_{f}}{2g\rho }}}}-{\frac {b}{2p}}\right)^{3}{\frac {\left(V_{f}+V_{r}\right)}{EV_{f}}}}$

## Results

Using the equations above we determined the charges.

Total charges from Drop 1:

   8.8183e-019
9.9109e-019
1.0321e-018
1.1862e-018
9.4522e-019
1.0979e-018
1.0692e-018
9.4674e-019
9.2446e-019
9.0721e-019
7.5149e-019
8.6793e-019
7.9566e-019


Total charges for Drop 2:

   9.6276e-019
8.9552e-019
9.5124e-019
8.1552e-019
9.4861e-019
8.1101e-019
8.5381e-019
9.3304e-019
8.0116e-019
9.0186e-019
8.6478e-019
8.4769e-019
7.5696e-019


Total charges from drop 3:

   1.0749e-018
1.1736e-018
1.1323e-018
1.0576e-018


Total charges from drop 4:

   1.0897e-018
1.0602e-018
9.8943e-019
1.0987e-018


## Analysis

We calculated the mean values from the 4 drops:

  Drop 1: 9.5361e-019 C
Drop 2: 8.7261e-019 C
Drop 3: 1.1096e-018 C
Drop 4: 1.0595e-018 C


From this we determined the approximate values of electrons on the drops:

  Drop 1: 9.7981e-019 C  +/- 1.01831e-019
Drop 2: 8.7261e-019 C  +/- 6.563e-019
Drop 3: 1.1096e-018 C  +/- 5.3289e-20
Drop 4: 1.0595e-018 C  +/- 4.9527e-20