Determining the Fundamental Electric Charge (Based on Millikan S Procedure)

Determining the fundamental electric charge (Based on Millikan’s procedure)

The simulation is either on the laptop’s desktop or at http://www.physics.rutgers.edu/~jgoett/millikan/millikan.html

Observation: Open up the simulation and run the simulation multiple times, adjusting the magnitude of the electric field and observing the resulting motion of the oil droplets.

Model: Devise a model to explain the motion of the droplets. Include sketches, diagrams, and equations

Application: Devise a procedure to measure the charge on a droplet. Record relevant data and calculate its charge.

If we assume each droplet only contains a few extra electrons, we can calculate the charge of an electron. Analyze the data and determine this charge.

In real life, one does not know the mass of the droplets, cannot begin with the droplets at rest, and cannot conduct the experiment in a vacuum (why?).

Model: Using fluid dynamics, scientists have found the force of air on a sphere of radius a to have a magnitude

It acts in the direction opposite the sphere’s motion. F is the force of the air on the droplet, u is the viscosity of air, 1.73*10-5 N-s/m2, and v is the velocity of the droplet.

Devise a model of a droplet’s motion as it falls.

Application: Devise a method to measure the size of the droplet. Derive any equation needed to calculate it and specify what data needs to be recorded. (The density of the oil is effectively 710 kg/m3).

Model: Now, let’s determine the charge on a particle. Use Stokes’ Law to model the motion of a particle in an electric field. Devise a procedure for measuring the charge on a droplet. Derive any equation needed to calculate it and specify the data that needs to be recorded.

Sample data

In an experiment, you measure the downwards v1, the free-fall velocity, and the upwards velocity of the droplet with an electric field on it, v2, for different droplets. From this data determine the charge of an electron.

E (V/m) / Time (sec) to fall 2 mm under only gravity / Time (sec) to fall 2 mm under gravity and electric force / q (C)
2000 / 139.9 / 213.2
2100 / 131.6 / 749.1
1900 / 93.9 / 491.4

Millikan Oil Drop Apparatus