==== Project 11A: Electric Field inside a Capacitor ====

The EM-Boar Tigers have been fought back for now but your team needs to get a message out that you all are under attack. Cellular and radio signals are being somehow blocked from an external source but you know that the annex building that is within sight of your compound has an emergency telegraph machine for just such attacks. You need to get a message to the telegraph operator. You notice that there is an old-fashioned camera that produces flashes via a capacitor. You decide that you might be able to communicate with the annex via morse code and go to the roof to try and send your message.

You measure the capacitor and find that the capacitor plates are 2 cm by 3 cm and separated by a distance of 40 $\mu m$. When hooked up to a battery, the plates become fully charged with $Q = 1.5*10^{-7}C$. The team leader however is concerned that the electric field inside the capacitor is going to be too large and cause sparking between the plates and destroy your only chance at getting out a message. 

With your team, build a model for the capacitor that allows you to calculate the electric field inside and outside the parallel plates. Make sure you have a diagram of the electric field, a graph of the electric field, and a graph of the electric potential to convince him that the electric field is either safe or unsafe so that you can get out the rescue message.

<WRAP info>
===Learning Goals===
  * Use Gauss's Law to calculate the electric field in between two charged parallel plates.
  * Explain why you picked your Gaussian surface and how it helped you simplify your calculations.
  * Describe how the magnitude and direction of the electric field changes both inside and outside the capacitor.
  * Explain the general steps that you take when using Gauss's Law.
</WRAP>


==== Project 11B: Protecting An Experiment ====

We may have the answer to the question of where the EM Boar Tigers have come from. Unidentified flying objects have descended into a near-Earth orbit and in a weird turn of events have raised pipelines all over the world to float in the air. The speculation is that the EM Boar Tigers want the pipes to eat just as they did in the scrap yard. The mechanism by which the pipes are floating is unknown but your team has been tasked with investigating this phenomenon. Your specific task at this moment in time is to determine the electric field both inside and outside the pipe if it is struck by lightning as you want to put a measuring device in the pipe to find out what is going on. You need to find the right pipe. At the moment you are focused on a 6-meter wide cylindrical pipe that is 2 km long near Laredo, Texas. Your initial investigations is that a pipe with walls that are at least 25 cm thick should protect the apparatus inside from lightning strikes. Your supervisors indicate a 10 cm thick pipe could work also, which would be better?

 

<WRAP info>
===Learning Goals===
  * Use Gauss's Law to calculate the electric field in between two charged parallel plates.
  * Explain why you picked your Gaussian surface and how it helped you simplify your calculations.
  * Explain the general steps that you take when using Gauss's Law.
  * Explain what would change about your solution if the pipe were metal vs plastic.
</WRAP>