BALANCE THE FORCES. MEASURE THE CHARGE.
Millikan’s oil drop experiment.
Hold a drop still, let it fall, or make it rise. The drag always opposes its motion.
Between the plates
The drop is enlarged. Weight, electric and drag arrows share a length scale. The very small buoyancy is labelled separately with its direction and value.
Inspect the fast response
Micrometre drops settle to terminal motion very quickly. These graphs magnify the first 12 time constants after the latest voltage change. The curves show that response; the dot marks the current point.
Velocity against time
Acceleration against time
Inspecting the fast response pauses and rewinds to that instant. Resume to continue from there. Normal playback uses physical time at the selected playback speed.
Measure the drop’s charge
Use the same droplet for both measurements. The model has no measurement noise.
1. Terminal fall, field off
Switch the field off and let the drop settle to its downward terminal speed.
Not recorded yet.
2. Hold it stationary
Apply the balance voltage. Once the drop is stationary, its drag is zero.
Not recorded yet.
Record both states to infer the radius and charge.
The force balance
Upwards is positive. Weight acts downwards, buoyancy acts upwards, and the electric force depends on the charge and field directions. Stokes drag opposes velocity and is exactly zero when the droplet is stationary.
At rest, the electric force balances the weight minus buoyancy. At a non-zero terminal velocity, the drag is non-zero and all forces still add to zero.
Model assumptions and measurement equations
The model uses a spherical oil drop, a uniform electric field, constant densities and viscosity, and classical Stokes drag. Air-slip (Cunningham) corrections, Brownian motion, evaporation and field-edge effects are omitted, so this is a teaching model rather than a precision recreation of the laboratory. Droplet charge is set in whole multiples of the elementary charge e.
Only vertical free motion is modelled. The simulation pauses at first contact with either plate, showing the velocity just before contact; subsequent contact forces are outside the model. Gravity is 9.81 m s⁻².
Physics background: Lancaster University · Millikan’s oil drop experiment.
Balance the forces and measure the charge
Adjust the voltage between parallel plates and observe a charged oil drop rise, fall or remain suspended. Compare electric force, weight, buoyancy and Stokes drag, then inspect velocity and acceleration during the transition to terminal motion.
Explore electric fields and force balance for IB and A Level Physics, alongside electrostatics and mechanics practice for AP Physics. Record terminal fall with the field off and the suspension voltage to infer the radius and charge. This teaching model uses classical Stokes drag without the air-slip correction.