In the early 1900s, Robert Millikan used small charged droplets of oil, suspende
ID: 1268001 • Letter: I
Question
In the early 1900s, Robert Millikan used small charged droplets of oil, suspended in an electric field, to make the first quantitative measurements of the electron's charge. A 0.70 micrometer diameter droplet of oil, having a charge of +e, is suspended in midair between two horizontal plates of a parallel-plate capacitor. The upward electric force on the droplet is exactly balanced by the downward force of gravity. The oil has a density of 860 kg/m3, and the capacitor plates are 4.0mm apart.
What must the potential difference between the plates be to hold the droplet in equilibrium?
Express your answer to two significant figures and include the appropriate units.
Explanation / Answer
d = 0.7 x10^-6 m
r = 0.35 x 10^-6 m
e = 1.602 x10^-19 C
? = 860 kg/m^3
m = ? x vol. = 860 x 4pi r^3 / 3 = 0.154 x10^-15 kg
g = 9.8 m/s^2
For the drop to be stationary in mid air, the mass of the drop is balanced by the upward electric force .
mg = eE,
where E is the electric field between the the plates.
E = mg / e = 9421 N/C
The voltage between the plates = V = X E ,
where X is the distance between the plates.
V = 9421 x 4 x10^-3 = 37.68 Volts