Theme D — Fields

D.2.2 Millikan’s Oil Drop Experiment — IB Physics HL Revision Notes & Topical Questions

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Lesson summary

D.2.2 Millikan's Oil Drop Experiment — IB PHYSICS SL notes: Explain how Millikan's experiment showed that charge is quantised and calculate drop charges from the balance of electric and gravitational forces.Who and when — Millikan and Fletcher carried out the experiment around 19…

Importance
Field direction
Terminal velocity
Stokes' law
Rising drops
Conclusion

Part 1 of 8Purpose

Who and when

Millikan and Fletcher carried out the experiment around 1909 to 1913

Aim

Aim to measure the charge on tiny oil drops and find the fundamental elementary charge

Result

Result the charge on every drop was an integer multiple of a smallest value, about 1.6 × 10⁻¹⁹ C

Importance

Importance it gave direct evidence that charge is quantised and the first accurate value of e

Part 2 of 8Apparatus

Oil mist

Oil mist a fine mist of oil drops is sprayed into a chamber
Oil is used instead of water because it does not evaporate quickly, so the mass of a drop stays constant.

Charging

Charging drops gain or lose electrons by friction with the nozzle, or are ionised by X-rays
Some drops become positive and some negative.

Plates

Plates a drop falls through a small hole between two horizontal metal plates separated by distance d
A potential difference V across them gives a uniform field E = V/d.

Viewing

Viewing a microscope with a scale lets the observer follow a single drop

Field direction

Field direction for a negative drop the upper plate is positive, so the field points down and the force on the drop is upward

Part 3 of 8Field off: terminal velocity

Motion

Motion the drop falls under gravity

Terminal velocity

Terminal velocity it is reached when the viscous drag equals the weight

Stokes' law

6πηrv = mg, where η is the viscosity of air and r the radius of the drop

Mass

Mass with oil density ρ, m = (4/3)πr³ρ, so the radius and mass follow from the measured speed

Reason

Reason the mass cannot be measured directly

Part 4 of 8Field on: balancing the forces

Rising drops

Rising drops a charged drop rises when the upward electric force exceeds its weight

Balance

Balance the voltage is adjusted until the drop is held stationary
The upward electric force qE equals the downward weight mg.
The small buoyancy force of air is neglected or corrected.

Equation

Equation qE = mg with E = V/d, so q = mgd/V
q is in C, m in kg, g in N kg⁻¹, d in m and V in V.

Forces

Forces the electric force is F = Eq and the weight is W = mg

Part 5 of 8Results and interpretation

Data

Data many drops, and one drop whose charge was changed by ionising the air, gave values such as 3.2, 4.8, 6.4 and 8.0 in units of 10⁻¹⁹ C

Pattern

Pattern all are multiples of 1.6 × 10⁻¹⁹ C, the largest common divisor, which is the charge of one electron

Conclusion

Conclusion if charge were continuous no pattern would appear, so charge comes in discrete units

Graph

Graph measured charges in order, or a histogram, show equal-sized steps or clusters

Accuracy

Accuracy the original value of e was slightly low because the air viscosity used was inaccurate

Part 6 of 8Sources of error

Evaporation of the drop

Air currents

Temperature changes that alter the viscosity

Timing of the drop's motion

Reduction

Reduction repeated measurements reduce random errors

Part 7 of 8Evaluating the method

Strength

Strength it measures a property of a single drop, so discrete values are not hidden by averaging over many particles

Weakness

Weakness the drop mass is found indirectly, and the result depends on the viscosity and on Stokes' law holding for micrometre-sized drops

Improvements

Improvements correct for air buoyancy, take the radius from repeated timing runs and keep the chamber at a stable temperature

Repeats

Repeats each drop gives one value, so many drops are needed to see the pattern

Quoting e

Quoting e it is the common difference between the plateaus of measured charge

Part 8 of 8More from the specification

1Electric and gravitational fields equilibrium

Electric and gravitational fields equilibrium balancing downward gravitational pull from Earth against upward electrostatic fields enabled precise determination of elementary charge.

2Electromagnetic fields deflection means

Electromagnetic fields deflection means applying uniform electric fields alongside perpendicular magnetic fields provides experimental means to control charged particle trajectories.

3Millikan's Oil Drop Experiment

Millikan demonstrated charge quantization by suspending charged oil drops between horizontal parallel plates, balancing electrostatic force (q E) against gravitational force (m g) to prove charges are integer multiples of e.

4Coulomb's Law and Permittivity

The electrostatic force between two charged spheres or point charges is given by Coulomb's law F = (1 / 4πε) * ,
- (|q₁ q₂| / r²
where ε is the electric permittivity of the surrounding material.

5Uniform Electric Field Between Parallel Plates

A uniform electric field of magnitude E = V / d is formed between oppositely charged parallel plates, represented by equally spaced parallel field lines directed from positive to negative.

6Magnetic Field Lines from Current Conductors

Current flowing through a conductor establishes concentric circular magnetic field lines around the wire, whose direction is given by the right-hand grip rule.

7Millikan's Oil Drop Experiment

Millikan demonstrated charge quantization by suspending charged oil drops between horizontal parallel plates, balancing electrostatic force (q E) against gravitational force (m g) to prove charges are integer multiples of e.

8Coulomb's Law and Permittivity

The electrostatic force between two charged spheres or point charges is given by Coulomb's law F = (1 / 4πε) * ,
- (|q₁ q₂| / r²
where ε is the electric permittivity of the surrounding material.

9Uniform Electric Field Between Parallel Plates

A uniform electric field of magnitude E = V / d is formed between oppositely charged parallel plates, represented by equally spaced parallel field lines directed from positive to negative.

10Magnetic Field Lines from Current Conductors

Current flowing through a conductor establishes concentric circular magnetic field lines around the wire, whose direction is given by the right-hand grip rule.

11Permittivity

A property of a medium affecting the electric force within it.

12Coulomb

Charge passing a point when a current of 1 A flows for 1 s.

13Parallel

Components on separate branches, each with the full e.m.f.

14Field lines

Lines showing the direction and strength of a magnetic field.

15Magnetic field

Area around a magnet where its effects can be detected.

16Relative permittivity

Ratio of the permittivity of a material to that of free space.

Key terms

Term	Meaning
Quantisation	Charge exists only in multiples of e.
Terminal velocity	The steady speed when drag balances weight.
Stokes' law	Viscous force on a small sphere, F = 6πηrv.
Balance condition	qV/d = mg, the electric force equals the weight.
Elementary charge	1.60 × 10⁻¹⁹ C.

Avoid these mistakes

Forgetting that the drop is held at rest by balancing weight and electric force — q = mgd/V uses the stationary balance.

What the symbols mean:

Using the plate voltage as the field strength — E = V/d.

What the symbols mean: E = uniform electric field strength (V m⁻¹) · V = p.d. between the plates (V) · d = plate separation (m)

Thinking Millikan measured the electron's mass — he measured charge.

Stating that the drops are charged by the oil — they gain charge by friction or ionisation.

Believing the experiment proved all charge is carried by electrons — it showed discrete steps.

Last updated: 18 October 2026