Lab 2: Coulombic Force (DRAFT)
Concepts
1. Hooke’s Law
2. Coulomb’s Law
3. Uncertainty
Format
Open Ended
Objective
To verify Coulomb’s Law in a thought experiment.
Introduction
The fundamental relation of electrostatics is Coulomb’s Law:
F =k
q1 q 2
r2
This inverse square law can be used to determine any and all electrical properties of
system of stationary charges. You should already be familiar with inverse square laws
from your mechanics class: Coulomb’s law of electric attraction has the exact same
mathematical form as Newton’s law of gravitational attraction! One note: to be a little
more rigorous we should specify directionality in our equation.
Figure 1: Force by Particle 2 on Particle 1
F12 = k
q1 q 2
r̂12
r2
So we read this as the force on charge one from charge two, and the direction of the force
is along the direction of the unit vector r12 which points to charge one from charge two.
Be aware that not all books use the same notation!
Equipment
While it’s great that we have a straightforward law for electrostatics, we have a
problem because it’s very hard to come up with quantitative electrostatic experiments to
test it. You can’t just reach into a “bag-o-charge” and pull out whatever amount you want
in real life; forces don’t magically come from out of nowhere; it’s tricky to get objects
moving at exactly the right velocity; the list of difficulties seems endless! So, we won’t:
instead we will simulate doing so on a computer! Go to
http://www2.hawaii.edu/~jmcfatri/JPhysicsApplets/Gedanken1.html to load the program.
Using the Program
The basic idea behind the program is as follows: you can place the charges
wherever you want, place masses wherever you wish, put in electrostatic and
gravitational forces, and basically do whatever you want. The following guide takes you
through placement and shows you how to take data from the simulation.
Placing a Charge
Figure 2: Adding Charge
First, go to the “Add” menu and select “Add Charge”
Figure 3: Entering Parameters
A dialogue box should pop up as seen above. This allows you to select the
charge’s location, its initial velocity, its mass, and its charge. You cannot have a
massless particle in this simulation. Once all fields are filled out to your liking,
click “Ok”.
I’m going to put a 1 uC charge at position (3, 10). It will have a mass of .4 kg and
will initially be stationary.
Figure 4: Example
Once you have entered the desired parameters, press “okay” and the charge will
appear at the location you chose.
Figure 5: Placed Charge
The sign of the charge will be indicated on the point representing the charge.
Adding a Mass
Adding a mass is just like adding a charge.
Figure 6: Selecting Mass Addition
_
Figure 7: Entering Parameters
_
Figure 8: Placed Mass
Note that the uncharged mass looks different than the charged mass.
Adding a Spring
First you must have two objects to run the spring between. This can be two
charges, two masses, or a charge and a mass
Figure 9: Select "Add Spring Scale"
_
Figure 10: Input parameters and select “OK”
_
Figure 11: Click on the pair of objects you want the spring to run between
Adding Forces
Select “Add Force/Interaction” from the Add menu.
From here you’ll be able to add outside forces like gravity to the system or to
individual components in the system. Note: electrostatic forces are not included
by default. You must select this option if you want them in your system!
Setting the Sample Rate
The program displays “snapshots” of the system at intervals that you can control.
Click the camera button
and a dialogue box will appear, asking for the display
interval in seconds.
Running the Program
After you have entered your desired initial conditions, press the play button .
The objects will move, leaving a “trail” of their positions at the interval specified
in the sample rate.
Collecting Data
At any point in the simulation you can read force meter by clicking the
magnifying glass icon
spring.
.This gives the last known Hooke’s Law force from the
Restarting
Once you are done with a trial select “Delete All”
Procedure
This is left up to the student; however in your experiment you should verify
1) The inverse-square nature.
2) The coefficient of proportionality (k).
3) The dependence on the sign of the charge.