Millikan's original analysis can be simplified by assuming that the droplets can become suspended between the plates (eliminating any drag forces).  That meant that the droplets experienced an electric force upward, exactly equal to the gravitational force pulling them down.

If a droplet were suspended, then the electrical force pulling it up would exactly balance the gravitational force pulling it down. Therefore,

 

How did Millikan's Apparatus Work?

Lab Simulation: Millikan's Apparatus

Open the  Millikan Experiment Simulation.  This simulation is a simplified demonstration of Millikan's oil drop experiment in which the formula above can be used to determine the charge on an oil drop.  Drops are sprayed horizontally between two charged plates into a vacuum to minimize air resistance.  You will then adjust the potential difference (voltage) until one drop remains suspended.  Once the potential difference is found the formula above can be used to determine the charge and the number of excess electrons on the oil drop.


Read
Read "Millikan's Oil-drop Experiment" on pages 761 to 764 of the textbook.

 

Example Problem 1. An oil droplet with a mass of 9.80 × 10-16 kg is suspended between two horizontal charged plates. If the electric field strength between the plates is 2.0 × 104 V/m, what is the charge on the oil droplets?

Given

Required

the charge on the oil drop
Analysis and Solution

Paraphrase

The charge on the drop is 4.8 × 10-19 C.

 

 

Example Problem 2. An oil droplet with a weight of 4.80 × 10-14 N is suspended between two horizontal charged plates that are 5.00 cm apart.  If the potential difference between the plates is 3.0 × 103 V, how many excess electrons does the oil droplet carry?

Given

 

Required

the number of excess electrons the oil drop carries

Analysis and Solution

Paraphrase

The oil drop has five excess electrons.

 

Self-Check

Answer the following self-check questions then click the "Check your work" bar to assess your responses.

SC 1. An oil droplet weighs 3.84 × 10-15 N.  If the droplet is at rest between two horizontal plates with an electric field strength of 1.20 × 104 N/C , what is the charge on the oil droplet?

SC 2. An oil droplet with a mass of 4.80 × 10-16 kg is suspended between two horizontal charged plates that are 6.00 cm apart.  If the potential difference between the plates is 588 V, how many excess electrons are on the droplet?

SC 3. Is it possible to have a particle with a charge of 2.00 × 10-19 C?  Explain why or why not.

 

Self-Check

Contact your teacher if your answers vary significantly from the answers provided here.

SC 1.

Given

Required

the charge on the particle

Analysis and Solution

Paraphrase

The charge on the particle is 3.20 × 10-19 C.

 

SC 2.

Required

the quantity of excess electrons on the particle


Analysis and Solution

Start with the two equal forces.

Determine the number of electrons required to obtain the charge.

Paraphrase

The particle has three excess electrons.

 

SC. 3

No, it is not possible to have a charge of 2.00 × 10-19 C because it is not possible to have a quarter of an electron. It is only possible to have whole number multiples of 1.60 × 10-19 C; the charge must be 1.60 × 10-19 or 3.20 × 10-19 or 4.80 × 10-19 C, etc.