The equation of motion of an oil drop immersed in a fluid in the presence of a gravitational field and an electric field is given by

,

where

is the mass calculated through the oil density of the drop,

is the electronic charge,

is gravitational acceleration,

is the drag force due to air friction (in the case of low velocities, it depends linearly on velocity

),

is the electric field force (negative when the field is upward, positive when the field is downward), and

is the buoyancy force. Solving the differential equation yields that the drop reaches a drift velocity

, where

and

is the initial velocity.

To a good approximation, the drift velocity is reached after a time

; this Demonstration assumes that drift velocity has already been reached.

The measurement of

allowed Millikan to calculate the elementary electron charge, about

coulombs [3].

Snapshot 1: only the gravitational field is present; all drops move downward at the same velocity

Snapshot 2: added to the gravitational field, an upward electric field dominates for particles with a positive charge

Snapshot 3: the upward electric field also dominates for particles with a negative charge