~~NOTOC~~
===== Project 11 =====
==== 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 and need support in order to evacuate the town. Cellular and radio signals have somehow become blocked from an external source which began at the same point you encountered the Em-Boar Tigers in the subway tunnel. However, you know that the military has set-up a perimeter base outside of the storm front and it is within sight of the Hawkion compound where you are positioned. 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 people on the perimeter 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 ====

Unbeknownst to S.P.A.R.T.A.N force, massive electrical storm fronts have formed over specific research facilities all across the world. Without warning, unidentified flying objects have emerged from the deep dark clouds 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 consume 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. 

T.R.O.J.A.N force has been sent to investigate and your specific task at this moment in time is to determine the electric field both inside and outside the pipe if it was to be struck by lightning. You need this information as your group plan to put a multi-purpose scanner in the pipe to find out what is going on. You need to be sure that it will still be okay if the pipe is struck by lightning. You need to find the right pipe to do your tests on as some pipes might be safer than others if they are struck by lightning. At the moment, your team is focused on a 6-meter wide cylindrical pipe that is 2 km long near Roswell, New Mexico. Your initial investigations are 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 inside and outside a charged cylinder.
  * 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>