Millikan Oil-Drop Experiment

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Introduction

The Millikan oil-drop experiment stands as one of the most elegant and important experiments in physics history. Conducted by Robert A. Millikan between 1909 and 1913, this groundbreaking work provided the first precise measurement of the elementary electric charge and demonstrated that electric charge is quantized [1].

Before Millikan's work, scientists knew electrons existed (discovered by J.J. Thomson in 1897), but no one had measured the charge of a single electron. Millikan's ingenious experimental design used tiny oil droplets suspended between charged metal plates, allowing him to calculate the charge on individual droplets by balancing gravitational and electric forces.

This simulation allows you to recreate Millikan's Nobel Prize-winning experiment. Students, physics enthusiasts, and educators can manipulate the voltage, observe droplet behavior, and understand how the quantization of charge was first demonstrated experimentally.

How to Use This Simulator

Quick Start Guide

1. Choose a Preset — Click one of the four preset buttons at the top:

   • Balanced: Droplet suspended (forces equal)
   • Rising: High voltage pushes droplet up
   • Falling: Low voltage, droplet falls
   • Terminal: No electric field, observe terminal velocity

2. Spray a Droplet — Click the orange "Spray Droplet" button to release an oil droplet into the chamber.

3. Adjust Parameters — Use the sliders to modify:

   • Plate Voltage (V): Controls the electric field strength
   • Plate Separation (mm): Distance between the charged plates
   • Oil Droplet Radius (μm): Size of the droplet
   • Number of Charges (n): Electrons on the droplet

4. Observe the Forces — Watch the force arrows below the chamber:

   • Blue arrow (↑): Electric force pulling upward
   • Red arrows (↓): Gravitational and drag forces pulling downward

5. Find the Balance Point — Adjust voltage until the droplet hovers motionless. When balanced, the status will show "BALANCED" and you can record the measurement.

Recording Data

• Click Record when you have a balanced droplet to save the measurement
• Use Export to download your data as a CSV file for analysis
• The Charge Quantization Analysis section shows statistics from your recorded measurements

Keyboard Controls

• ← → Arrow Keys: Fine-tune the voltage
• Shift + Arrow Keys: Larger voltage adjustments (±5V)

Tips for Best Results

• Start with the "Balanced" preset to see a suspended droplet
• Try different numbers of charges (n) to see how charge quantization works
• Record multiple measurements to calculate the elementary charge
• Use the magnifier to observe the droplet more clearly

What Is the Millikan Oil-Drop Experiment?

The Millikan oil-drop experiment measures the electric charge of individual electrons by suspending charged oil droplets in an electric field [2]. When the upward electric force exactly balances the downward gravitational force, the droplet remains stationary, allowing precise calculation of its charge.

The key insight from Millikan's results was that all measured charges were integer multiples of a fundamental unit: e = 1.602 x 10^-19 C. This proved that electric charge is quantized and cannot exist in arbitrary amounts.

How the Simulator Works

The Physics Behind the Experiment

Force Balance

When a charged oil droplet is suspended between two parallel plates, three forces act on it:

1. Gravitational Force (Fg): Pulls the droplet downward
2. Electric Force (Fe): Pushes the droplet upward (for negative charge below positive plate)
3. Drag Force (Fd): Opposes motion through air

For a stationary droplet, Fe = Fg, which allows us to solve for the charge q.

Key Equations

The gravitational force on a spherical droplet:

Fg = mg = (4/3)pr^3 rho g

where r is the radius, rho is the oil density (about 886 kg/m^3), and g is gravitational acceleration.

The electric force:

Fe = qE = q(V/d)

where q is the charge, V is the voltage, and d is the plate separation.

At balance:

q = (4 pi r^3 rho g d) / (3V)

Terminal Velocity Method

When the electric field is turned off, the droplet falls and reaches terminal velocity when drag equals gravity:

6 pi eta r v = (4/3) pi r^3 (rho - rho_air) g

Solving for velocity allows determination of the droplet radius, which is crucial for calculating mass [3].

Learning Objectives

After completing this simulation, you should be able to:

1. Explain how gravitational and electric forces balance on a charged particle
2. Calculate the charge on an oil droplet using measured parameters
3. Understand why charge quantization was a revolutionary discovery
4. Apply Stokes law to determine droplet size from terminal velocity
5. Interpret experimental results to find the elementary charge
6. Appreciate the historical significance of precision measurements in physics

Exploration Activities

Activity 1: Finding the Balance Point

Objective: Suspend a droplet motionless by adjusting voltage

Steps:

1. Click "Spray Droplet" to release a droplet
2. Start with the voltage at 250 V
3. Slowly adjust voltage until the droplet stops moving
4. Record the voltage when the droplet is stationary

Expected Result: The droplet should hover when Fe = Fg. The "BALANCED" status will appear.

Activity 2: Observing Charge Quantization

Objective: Verify that charge comes in discrete units

Steps:

1. Set radius to 1.5 um and separation to 5 mm
2. Try different numbers of charges (n = 1, 2, 3...)
3. For each n, find the voltage needed to balance
4. Calculate q = n x e and compare with displayed charge

Expected Result: Each additional electron charge requires proportionally more voltage to balance.

Activity 3: Terminal Velocity Measurement

Objective: Observe droplet falling without electric field

Steps:

1. Set voltage to 0 V (Terminal preset)
2. Spray a droplet and observe it falling
3. Note the terminal velocity in the results
4. This velocity relates to droplet radius via Stokes law

Expected Result: Droplet falls at constant terminal velocity of about 0.1-2 mm/s depending on size.

Activity 4: Effect of Plate Separation

Objective: Understand how geometry affects the electric field

Steps:

1. Set up a balanced droplet at d = 5 mm
2. Increase separation to 8 mm while watching the droplet
3. Re-balance by adjusting voltage
4. Compare the required voltages

Expected Result: Larger separation requires higher voltage for the same electric field strength.

Real-World Applications

1. Ink-jet printing — Charged droplets are steered by electric fields to precise locations on paper, using principles from Millikan's experiment [4]

2. Electrostatic precipitators — Industrial pollution control devices charge particles to collect them on plates, removing up to 99% of particulates from smokestacks

3. Mass spectrometry — The charge-to-mass ratio measurement technique, conceptually related to Millikan's work, identifies unknown compounds in chemistry and medicine

4. Electron microscopy — Understanding electron properties enables imaging at atomic resolution, with applications in materials science and biology

5. Particle physics detectors — Modern particle accelerators use electric and magnetic fields to measure particle charges, building on Millikan's pioneering techniques

Reference Data

Challenge Questions

1. Easy: If you double the voltage while keeping other parameters constant, what happens to the electric force on the droplet?

2. Easy: Why must oil droplets be very small (micrometers) for this experiment to work?

3. Medium: A droplet with charge q is balanced at voltage V. If the charge increases to 2q, what voltage is needed to maintain balance?

4. Medium: Calculate the gravitational force on a 2 um radius oil droplet. (Use rho = 886 kg/m^3)

5. Hard: Millikan found that all droplet charges were multiples of 1.6 x 10^-19 C. If he measured charges of 3.2, 4.8, 6.4, and 8.0 x 10^-19 C, what does this tell us about charge quantization?

Common Misconceptions

Frequently Asked Questions

Why did Millikan win the Nobel Prize for this work?

Millikan received the 1923 Nobel Prize in Physics for "his work on the elementary charge of electricity and on the photoelectric effect." His oil-drop experiment provided the first precise value of the electron charge, e = 1.592 x 10^-19 C (his original value, within 1% of the modern accepted value) [1].

How accurate was Millikan's original measurement?

Millikan's published value was about 0.6% lower than the currently accepted value. This small discrepancy was partly due to using an incorrect value for air viscosity [8].

Can this experiment be done at home?

A simplified version is possible but challenging. You need a high-voltage power supply (dangerous), a microscope, and very small oil droplets. Educational kits exist, but the full experiment requires laboratory conditions.

Why is charge quantization important?

Charge quantization means all electric charges in nature are integer multiples of e. This fundamental property underlies our understanding of atoms, chemistry, and all electromagnetic phenomena [2].

What if the droplet has too many charges?

With many charges, the electric force becomes large even at low voltages. The droplet may rise too fast to observe or be pulled to the top plate. Typical experiments use droplets with 1-10 excess electrons.

References

1. Nobel Prize Organization — Robert A. Millikan Nobel Prize biography. Available at: https://www.nobelprize.org/prizes/physics/1923/millikan/biographical/

2. HyperPhysics — Millikan Oil Drop Experiment. Georgia State University. Available at: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/millikan.html

3. MIT OpenCourseWare — 8.02 Physics II: Electricity and Magnetism. Available at: https://ocw.mit.edu/courses/8-02-physics-ii-electricity-and-magnetism-spring-2007/

4. American Physical Society — This Month in Physics History: Millikan's Oil Drop Experiment. Available at: https://www.aps.org/publications/apsnews/200608/history.cfm

5. NIST — CODATA Recommended Values of Fundamental Constants. Available at: https://physics.nist.gov/cuu/Constants/

6. Engineering Toolbox — Oil Densities. Available at: https://www.engineeringtoolbox.com/oil-density-specific-weight-d_2138.html

7. Engineering Toolbox — Air Viscosity. Available at: https://www.engineeringtoolbox.com/air-absolute-kinematic-viscosity-d_601.html

8. Goodstein, D. — In Defense of Robert Andrews Millikan. American Scientist, 2001. Available via academic libraries.

About the Data

All physical constants used in this simulation come from NIST CODATA 2018 recommended values [5]. Oil density (886 kg/m^3) represents typical watch oil or other low-vapor-pressure oils used in actual Millikan experiments. Air viscosity is temperature-dependent; we use the value at 20C standard conditions.

How to Cite

Simulations4All. (2026). Millikan Oil-Drop Experiment Simulator. Retrieved from https://simulations4all.com/simulations/millikan-oil-drop-experiment

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