In the early 1900s, Robert Millikan used small charged droplets of oil, suspende
ID: 2110229 • 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-um-diameter droplet of oil, having a charge of , 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/m^3 , and the capacitor plates are 6.0mm apart.
Part A
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
ΔV=
Explanation / Answer
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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 0.80-mu { m m}-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 { m kg/m^3}, and the capacitor plates are 6.0 mm apart.
d = 0.8 x10^-6 m
r = 0.4 x 10^-6 m
e = 1.602 x10^-19 C
? = 860 kg/m^3
m = ? x vol. = 860 x 4pi r^3 / 3 = 0.229 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 = 14057.89 N/C
The voltage between the plates = V = X E ,
where X is the distance between the plates.
V =14057.89 x 6 x10^-3 = 83.35 Volts