How Does the Millikan Oil Drop Experiment Illustrate the Balance of Forces?

[General_Sax]

Homework Statement

An oil drop with a mass of 7.20*10^-16kg moves upward at a constant speed of 2.50 m/s between two horizontal, parallel plates. If the electric field strength between these plates is 2.20*10^4 V/m, what is the magnitude of the charge on the oil drop?

Homework Equations

F = ma
Fg = mg
Fe = qE
E = V/d

The Attempt at a Solution

F = ma
F = m(0)
Fnet = 0

Fnet = Fe - Fg
Fg = Fe
q = mg/E

q = 3.2*10^-19C

My problem is conceptual. I don't really understand how the particle can have a constant velocity and a net Force of zero upon it.

How did the particle accelerate from stationary to it's current velocity?

 

[LowlyPion]

The history of the particle isn't all that important. The mention of constant velocity is to reinforce the idea that it is not accelerating, and hence no net force.

 

[nlightner]

As a scientist, it is important to understand the underlying concepts and principles rather than just solving for a numerical answer. In this experiment, the oil drop is suspended between two plates due to the balance of two forces: gravitational force (Fg) and electric force (Fe). Initially, the oil drop is at rest and the net force on it is zero. However, when a voltage is applied between the plates, an electric field (E) is created which exerts a force (Fe) on the charged oil drop. This force is equal in magnitude but opposite in direction to the gravitational force (Fg). As a result, the oil drop experiences an upward acceleration and reaches a constant velocity when the two forces are balanced.

To address your concern about the initial acceleration, it is important to note that the oil drop is not initially stationary. It is constantly moving due to random thermal motion. When the electric field is applied, the direction of this motion is affected and the drop accelerates in the direction of the electric force until it reaches a constant velocity.

In terms of the charge on the oil drop, the magnitude can be determined using the equation q = mg/E, where m is the mass of the drop and g is the acceleration due to gravity. This equation assumes that the electric field is uniform and the drop is spherical in shape. The Millikan Oil Drop Experiment is a classic example of how the principles of physics can be used to determine the charge of a single particle, and it is important to understand the underlying concepts in order to fully appreciate the significance of the results.