Millikan’s Oil-Drop Experiment

Observe a small spherical droplet falling through air with the electric field switched off. At terminal speed, viscous drag balances its effective weight. Stokes’ drag is $6\pi\eta rv$, where η is dynamic viscosity. If air buoyancy is negligible, use $mg=6\pi\eta rv$ with $m=4\pi r^3\rho/3$.

Eliminating mass gives a radius estimate from terminal speed and known oil density. If buoyancy is included, replace ρ by the density difference between oil and air in the terminal-speed balance. The simple model assumes laminar flow around a small spherical droplet.

Apply a potential difference between horizontal parallel plates so that electric force opposes gravity. Adjust it until a charged droplet is stationary. There is then no viscous drag from motion through still air. For a uniform field of magnitude V/d, balance $|Q|V/d$ against mg.

The sign of charge is inferred from the direction of the field needed for support. The force magnitude gives the magnitude of charge. Measure plate separation carefully and state whether edge effects and buoyancy are being neglected.

Droplets carry different charges, but their values cluster around integer multiples of the same elementary magnitude e. A droplet may gain or lose electrons and jump between those charge states. One droplet measurement alone does not establish quantisation; the repeated pattern is the evidence.

Millikan’s charge measurement combined with Thomson’s e/m ratio gives electron mass using $m_e=e/(e/m_e)$. Experimental uncertainty can obscure exact multiples, so identify a common step that fits several results rather than simply choosing the smallest observed droplet charge.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.