Pre Lab
This week's lab will be exploring Gauss's Law. Gauss's Law is pretty important. In fact, it is the first of the four Maxwell's Equations that you will learn, equations that make up the backbone of all electromagnetism!
As we discovered last week, calculating electric field with Coulomb's law can get complicated. Gauss's Law allows us to find the electric field of some continuous charge distributions much more easily. It also allows us to deal with moving charges, which we couldn't do before. An important concept we need to understand before talking about Gauss's Law is Flux. Flux, which is often found via a surface integral, is how much of something passes through a given amount of area. Think about water flowing through a pipe. The flux would be how much water flows through the cross sectional area of the pipe. For electricity, we care about electric field. Electric flux is how much E field passes through a given amount of area. Electric flux, represented by a capital letter phi, can be calculated with the dot product (because it matters how parallel the vectors are) of the E field and the area vectors.
Note: The funny looking E (Greek letter epsilon) in both of these equations is the same number, the permittivity of free space. K is the dielectric constant if there is a dielectric between the plates.
Gauss's Law relates this electric flux to the charge enclosed within the surface through which the field is passing. We call this imaginary surface a "Gaussian Surface." Mathematically, Gauss's Law looks something like this: Note: The Epsilon in this equation is called the permittivity of free space. It is a constant, and we have actually seen it before. The Coulomb Constant K is actually made from this epsilon.
So Gauss's Law says that the flux passing through a Gaussian surface depends on the charge enclosed. In the left picture below, the flux would equal the charge divided by epsilon. For the picture on the right, the charge is on the outside of the surface. No charge is enclosed, so the flux would equal 0. Does this make sense? Yes! All of the field entering the surface, exits somewhere, giving us a total of 0. As it turns out, this is really useful.
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Gauss's Law Introductory Videos
A good lecture on Flux and Gauss's Law
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Pre Lab Video
Video currently unavailable
Simulation
Use the simulation at the following link to explore Gauss's Law.
Simulation: https://www.compadre.org/portal/items/detail.cfm?ID=10634
You may use the simulation to answer the pre lab quiz questions as well.
Pre-Lab Quiz is available at the course Blackboard website
Simulation: https://www.compadre.org/portal/items/detail.cfm?ID=10634
You may use the simulation to answer the pre lab quiz questions as well.
Pre-Lab Quiz is available at the course Blackboard website
Lab
This week you will be completing the Gauss's Law lab (pg. 23) found your lab manual along with some supplemental labs that will be provided.
Post Lab
Please post a reflection on the lab experience on the Gauss's Law Lab Reflection discussion board on the course Blackboard site.
Be sure to include:
Be sure to include:
- What you did
- Why you did it
- Any interesting observations
- What you learned from doing the lab