A droplet of mass 1.0 \times 10^{-14} kg is suspended by an electric field of 2.0 \times 10^5 V/m. What is the charge on the droplet?

4.9 \times 10^{-19} C Using q = mg/E, q = (1.0 \times 10^{-14} \times 9.8) / (2.0 \times 10^5) = 4.9 \times 10^{-19} C. This is approximately 3 electrons.

Millikan Oil Drop Experiment

Q: If Millikan found charges of 3.2 \times 10^{-19} C and 4.8 \times 10^{-19} C, what would he conclude is the elementary charge?

1.6 \times 10^{-19} C He would look for the greatest common divisor of the measured charges, which represents the smallest possible unit of charge.

Recreate the 1909 Nobel-winning experiment. Adjust the voltage across two capacitor plates to suspend falling oil drops in mid-air (qE = mg). Fire the X-Ray ionizer to randomly step the charge up or down in discrete quantized increments of 'e'.

THE QUANTIZATION OF CHARGE

In 1909, Robert Millikan performed a landmark experiment to measure the elementary charge of an electron. By suspending tiny, charged oil droplets between two horizontal metal electrodes, he was able to balance the downward force of gravity with the upward electric force. He discovered that the charge on every droplet was always an integer multiple of a fundamental value: Coulombs, proving that electric charge is **quantized**.

FORCES IN EQUILIBRIUM

When a droplet is suspended (stationary), the net force is zero. The upward electric force must exactly equal the downward gravitational force . By knowing the electric field strength (from the voltage and plate separation) and the mass of the droplet (derived from its terminal velocity and density), the charge can be calculated: .

HOW TO USE THIS VISUALIZATION

1. **Spray the Oil**: Click the atomizer to release a cloud of droplets into the chamber. 2. **Adjust the Voltage**: Use the slider to change the potential difference between the plates. Observe how some droplets rise, some fall, and some can be perfectly suspended. 3. **Measure a Droplet**: Select a specific droplet and adjust the voltage until it stops moving. Record the voltage and use the provided mass to calculate its charge. **Try This**: Find three different droplets and calculate their charges. Are they all the same? Divide each by . What do you notice about the resulting numbers?

CORE FORMULAS

Electric force on a charge in a uniform field

Charge calculation at equilibrium (suspended drop)

Electric field between parallel plates

AP EXAM CONNECTION

Unit: Unit 3: Electric Force, Field, and Potential (Topic 3.1)
Learning Objective: LO 3.A.1

COMMON MISCONCEPTIONS

Thinking all droplets have the same charge (they have different numbers of electrons).
Forgetting to account for the buoyant force of air (in high-precision versions).
Confusing the mass of the electron with the charge of the electron.