Millikan Oil-Drop Laboratory

PHYS.RUN / ELECTRIC CHARGE · EXPERIMENT 03

About

Experiment controls

+0.1 s pauses and advances 0.10 simulated seconds in native 1/120 s steps.

01Plate potential

DC supply 0–500 V

Plate potential

Plate separation7.620 mm

Diameter / entry aperture60 / 0.5 mm

LED on Brownian motion

02Prepare and observe

Selected droplet

Capture one ion is a teaching intervention of exactly one air-ion capture, not a calibrated radiation rate.

Reveal true charge

Net charge · model truth

Hidden model truth, kept apart from measurement. The inverse calculation never reads it.

03Measure, then infer

Free fall · field off

Time a 0.50 mm displacement

Driven motion · field on

Same drop, same charge state

Virtual Earth

LatitudeElevation

Effective local gravity

Latitude and elevation change the forces, not just the globe. Pressure stays at the chamber setting unless explicitly reset.

Environment and analysis settings

Chamber temperaturePressureOil density Apply slip correction in analysis

Slip is always present in the physical model. Omitting it here demonstrates analysis bias.

Air viscosity

Air density

Effective local gravity

A drop. A charge.

A documented apparatus, a measurable trajectory.

Assembling the laboratoryGeometry · optics · droplet dynamics

Local gravity

Plate field · up positive

Mean vertical drift

Drag relaxation

Through the microscope

30× · erect

Minor divisions 0.1 mm · major divisions 0.5 mm, in the object plane

Droplet focus

Digital tracking view

Tracked droplet

Height from midplane

Measured radius

Inferred charge

What makes it move?

m d⟨v⟩/dt = qE − W_eff − γ⟨v⟩

Effective weight

Electric force · vertical

Mean drag · vertical

Arrows share one force scale. Brownian fluctuations are shown in the trajectory, not as a fictitious constant force.

The experimental question

Does electric charge come in indivisible steps?

Time a fall, switch the field, time a rise. Repeat after an ion changes the same drop’s charge. Look for a common increment in the notebook.

Selected droplet

Mode

Droplet · charge revision

Fall time

Field-on time

Inferred radius

Inferred charge

Measurements

Latest |q|

Same-drop charge change

Collect free-fall and field-on measurements. Charge is inferred continuously; no rounding to elementary-charge multiples is applied.

Drop / event	t fall (s)	t on (s)	V top−bottom	r (μm)	q (10⁻¹⁹ C)	σq (10⁻¹⁹ C)

Your observations will appear here. Start with Run paired measurement.

CSV includes signed velocities, settings, timestamps, timing distances, inferred charge, laboratory mode, model version and replay run. The hidden charge is not exported. Uncertainties are model estimates, not a complete instrument calibration.

Raw observations and inferred quantities, one row per timed trial. No snapping to integer charge.

Trial / drop	Mode	Δy / mm	Δt / s	ΔV / V	â / μm	q̂ / 10⁻¹⁹ C

No measurements yet. Time a field-free fall, then motion with the field on.

Test an integer-multiple hypothesis

Candidate spacing (× 10⁻¹⁹ C)

The fit searches 1.0–2.2 × 10⁻¹⁹ C and assumes integer multiples. Sparse charge data can have ambiguous common divisors. The simulation was constructed with quantized charges; this is an inference exercise and internal consistency check, not a new measurement of nature.

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1909–1913 · Physics

Millikan Oil-Drop Experiment

Time charged oil droplets between two brass plates and infer each droplet's charge from its fall and rise, on a bench or a virtual Earth.

Robert Millikan and Harvey Fletcher balanced tiny charged oil droplets against gravity in the electric field between two plates. A droplet's steady fall reveals its size through air drag; its motion with the field switched on reveals its charge. Repeated on many drops, and on one drop whose charge changed, the results clustered around multiples of a smallest step.

This exhibit reconstructs a commercial teaching apparatus rather than Millikan's 1909–1913 instrument. The bench mode times 0.50 mm displacements between microscope reticle lines, with optical localization noise, and stores paired fall/field results with an uncertainty estimate. The Virtual Earth mode times each trial separately on a tiltable platform, with spray and ionization settling, a manual stopwatch and a common-step fit.

Motion is calculated, not animated: a three-dimensional Langevin model with buoyancy, slip-corrected Stokes drag, thermal diffusion and WGS 84 gravity for the chosen latitude and elevation. The field is the central parallel-plate approximation. Droplet charges are generated as whole multiples of the SI elementary charge and stay hidden unless revealed, so the notebook tests a measurement method rather than offering new evidence that charge is quantized.

Specifications

Reference apparatus: Teaching apparatus: 60 mm brass plates, 7.62 mm gap, 0–500 V
Measurement: Timed 0.50 mm fall and field-on motion of the same droplet
Inference: Radius from fall speed with slip correction; charge from field-on speed
Model: Exact Ornstein–Uhlenbeck Langevin steps at 1/120 s (bench) or 1/240 s (Earth lab)
Environment: WGS 84 gravity, ideal-gas air density, Sutherland viscosity
Honest limit: Synthetic integer charges; tests the method, not nature

All exhibits

Millikan Oil-Drop Laboratory

A drop. A charge.

Measurement notebook

Test an integer-multiple hypothesis

The model behind the instrument

01 / Which apparatus is this?

02 / Motion is calculated, not animated

03 / Independent inference

04 / Where this model stops

01 / Which apparatus is this?

02 / Motion is calculated, not animated

03 / Independent inference

04 / Where this model stops

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