Formula Oil Drop Experiment (Levitation Method) Electric charge Falling velocity Oil density Medium density
$$q ~=~ \frac{9\pi \, d}{U} \, \sqrt{ \frac{2 \, \eta^3 \, v_{\downarrow}^3}{g \left( \rho_{\text o} ~-~ \rho_{\text L} \right) } }$$ $$q ~=~ \frac{9\pi \, d}{U} \, \sqrt{ \frac{2 \, \eta^3 \, v_{\downarrow}^3}{g \left( \rho_{\text o} ~-~ \rho_{\text L} \right) } }$$
Electric charge
$$ q $$ Unit $$ \mathrm{C} = \mathrm{As} $$ The charge of the oil droplet. The oil droplet carries a multiple of the elementary charge \(e\).
Distance
$$ d $$ Unit $$ \mathrm{m} $$ Distance between the two capacitor plates.
Voltage
$$ U $$ Unit $$ \mathrm{V} $$ Voltage is applied between the two capacitor plates to accelerate charged oil droplets in the electric field.
Viscosity
$$ \eta $$ Unit $$ \frac{\mathrm{kg}}{\mathrm{m} \, \mathrm{s}} $$ Viscosity (Pronounced: "Eta") describes how viscous the medium (e.g. water) is between the two capacitor plates.
Falling velocity
$$ v_{\downarrow} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$ Terminal velocity at which the oil droplet sinks downwards inside the plate capacitor.
Oil density
$$ \rho_{\text o} $$ Unit $$ \frac{ \mathrm{kg} }{ \mathrm{m}^3} $$ Oil density specifies the mass of the oil droplet per volume.
Medium density
$$ \rho_{\text L} $$ Unit $$ \frac{ \mathrm{kg} }{ \mathrm{m}^3} $$ Density (mass per volume) of the medium between the capacitor plates.
Gravitational acceleration
$$ g $$ Unit $$ \frac{\mathrm{m}}{\mathrm{s}^2} $$ Gravitational acceleration is the acceleration acting on oil droplets to the bottom. It has the value: \(g = 9.8 \, \frac{\mathrm m}{\mathrm{s}^2} \).