 |
Eq. (1) |
In Millikan's original experiment a fine mist of oil was sprayed between the plates of a capacitor. The oil drops in the mist gained or lost some amount of charge ne by collisions with air, thus charging the oil drops. An electric field was then applied between the plates negatively charged particles would accelerate towards the positive plate. In a viscous medium (air in this case) the equation of motion of a charged particle in an electric field is:
|
Eq. (1) |
where the last term is the drag force due to the airs viscosity. The constant b is given by Stoke's law for a spherical ball of radius a:
 |
Eq. (2) |
where h is the viscosity of air.
At long times Eq. (1) predicts that the charged oil drop will reach a terminal velocity vtr when dv/dt=0:
 |
Eq. (3) |
For the small oil drops the terminal velocity is reached almost instantaneously (in microseconds). In Millikan's original experiment the density of oil was known but the drop's radius was not. Therefor neither m nor b was known. To determine a for each drop the field is turned off and the drops fall with a velocity vtf given by Eq. (3) with E=0.
 |
Eq. (4) |
where r is the density of the oil drop. Knowing h, g, r and vtf allows a to be measured.
Combining Eqs. (2), (3) and (4) gives:
 |
Eq. (5) |
where Ttf and Ttr are the time to fall a distance D with the field off and the time to rise a distance D with the field on, respectively.
In your experiment you will not be using oil drops but uniform diameter polystyrene spheres of a know density. Therefore you will know m exactly in Eq. (5).
Apparatus