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The Millikan Oil-Drop Experiment

In 1909 Robert Millikan measured the charge of a single electron by watching tiny oil drops hang in mid-air. A fine mist of oil is sprayed between two horizontal metal plates; friction during spraying leaves each droplet with a few extra or missing electrons. With no voltage applied, a drop falls under gravity but quickly reaches a slow terminal speed, where its weight is balanced by the viscous drag of the air, and that speed (through Stokes' law) reveals the drop's microscopic radius and mass. Then a voltage is switched on between the plates, and the electric force $qE$ on the drop's charge can be tuned until it exactly cancels gravity and the drop floats motionless. At that balance point the charge follows from the simple condition $q = m'gd/V$. The astonishing result, repeated over thousands of drops, is that the charge is never an arbitrary value: it always comes out a whole-number multiple of one fixed amount, $e = 1.6\times10^{-19}$ coulombs. Charge is quantized. The scene lets you tune the voltage to float a drop and read its charge, with the gravity, electric, and drag forces drawn as arrows. The lower panel is the punchline: a ladder of measured charges from many drops, every one of them landing exactly on an integer multiple of $e$, with nothing in the gaps between.

Figure 1. The Millikan oil-drop experiment. Top: a charged oil drop between capacitor plates; gravity (blue), the electric force qE (orange), and drag (gray) are shown, and tuning the voltage floats the drop so q = m'gd/V can be read. Bottom: the charge ladder, every drop on an integer multiple of e. Method: Stokes drag and electrostatic force balance. Source: Eisberg and Resnick, Quantum Physics, 2nd ed., Ch. 2.
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WHAT TO TRY

  • Tune the voltage until the drop floats motionless: at that balance point $qE = m'g$ and the charge is fixed.
  • Step through the drops: each has a different radius and charge, yet every charge is a whole number of $e$.
  • Switch the field off: the drop falls at the Stokes terminal speed that fixes its radius, the first half of the method.
  • Read the ladder: the dots line up on $e$, $2e$, $3e$, never between, the signature of quantized charge.