Millikan's experiment is a force-balance argument. Without the electric field, the falling drop reaches terminal speed when gravity is balanced by viscous drag, \(mg=6\pi\eta Rv_f\), allowing the radius \(R\) to be estimated. With the electric field on, the upward electric force is added to the balance.
The resulting charge formula is useful because repeated measurements do not give arbitrary values. They cluster around \(q=ne\). This page therefore connects dynamics to discreteness: charge itself comes in units, and when combined with Thomson's \(|q|/m\), it gives the electron mass scale.
Millikan's experiment follows individual oil drops. Their terminal velocities, first falling without the electric field and then rising with the field, give enough information to infer the charge carried by each drop.
The logic is mechanical: infer the drop radius from a drag balance, then use the electric-field balance to infer \(q\).
At terminal speed the acceleration is zero, so the forces balance. During the fall, gravity is balanced by viscous drag:
Using \(m=(4/3)\pi R^3\rho\), the drop radius can be extracted from the falling speed:
The falling motion estimates the radius. The rising motion with an electric field then gives the charge magnitude.
When the electric field is applied, the upward electric force must overcome both weight and drag. With \(E=V/d\) and the radius substituted from the falling motion, the charge magnitude can be written as
The measured charges cluster around integer multiples of one elementary value. The discreteness is in the data, not imposed after the fact.
This page is designed to support short guided exercises on: Millikan's oil-drop experiment and the quantization of electric charge.
- Use from this page: the definitions, physical setup, highlighted equations and conceptual links needed to start a first calculation or explanation.
- Keep in the book: complete derivations, extended historical discussion, worked solutions and the full textbook narrative remain in the original chapter and linked book resources.
- Good exercise balance: ask the student to identify assumptions, apply one relation, and interpret the result physically, without requiring material not introduced on this page.
Use these anchors to design compact exercises. The exercise should be answerable from this page plus standard algebra, while longer derivations, full worked examples and broader context should point back to the original book.
- Focus: Millikan's oil-drop experiment and the quantization of electric charge.
- Conceptual check: state what the main result says physically before using it algebraically.
- Equation: \[F_a=6\pi\eta Rv,\qquad mg=6\pi\eta Rv_f\]
- Equation: \[R=\sqrt{\frac{9\eta v_f}{2\rho g}}\]
- Equation: \[|q|=6\pi\,\frac{d}{V}\sqrt{\frac{9\eta^3}{2\rho g}}\,(v_r+v_f)\sqrt{v_f}\]
- Boundary: use this page for setup and first-step reasoning; cite the book for longer derivations, complete experimental history or solved-problem detail.
- Typical task: derive, interpret, or apply the relation above to a simple case without introducing topics outside this page.