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--- 184_notes:motiv_movingq [2017/09/20 16:11] – dmcpadden
+++ 184_notes:motiv_movingq [2021/02/16 19:45] (current) – [Connecting Two Charged Plates] bartonmo
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+/*[[184_notes:batteries|Next Page: Batteries]]
+[[184_notes:patterns_fields|Previous Page: Patterns in the Electric Field]]*/
 ===== Modeling Moving Charges =====
-Over the last five weeks of class, we've have spent a lot of time modeling [[184_notes:charge|stationary charges and their interactions]], including [[184_notes:pc_force|electric force]], [[184_notes:pc_efield|electric field]], [[184_notes:pc_energy|electric potential energy]], and [[184_notes:pc_potential|electric potential]]. We've discussed these ideas in the context of point charges, [[184_notes:line_fields|lines of charge]], and volumes of charge. In particular, you used [[184_notes:gauss_motive|Gauss's Law]] last week to find the electric field and electric potential around two parallel sheets of charge ([[184_projects:project_5|Project 5A]]). This week, we will shift our focus to modeling moving charges, starting with one simple question: what would happen if we connected two charged, parallel plates with a thin, conducting wire?
+Thus far in class, we've have spent a lot of time modeling [[184_notes:charge|stationary charges and their interactions]], including [[184_notes:pc_force|electric force]], [[184_notes:pc_efield|electric field]], [[184_notes:pc_energy|electric potential energy]], and [[184_notes:pc_potential|electric potential]]. We've discussed these ideas in the context of point charges, [[184_notes:line_fields|lines of charge]], and [[184_notes:dist_charges|distributions (or volumes) of charge]]. Now, we will shift our focus to modeling moving charges - which has incredibly important applications for how electricity and circuits work. Using what we know about charges and electric field, we will start with one simple question: what would happen if we connected two charged, parallel plates with a thin, conducting wire?
+{{youtube>Xcea_cZhnPg?large}}
 ==== Connecting Two Charged Plates ====
-Suppose we start with two charged, conducting plates - one with a positive charge (+Q) on the plate and one with an equal amount of negative charge (-Q) on the plate. [[184_notes:charge_and_matter#Types_of_Matter|Because the plates are conducting]], we know that the electrons in the plates can easily move through the material, so each of the plates has a uniform distribution of charge on the surface.
+Suppose we start with two charged, conducting plates - one with a net positive charge (+Q) on the plate and one with an equal amount of excess negative charge (-Q) on the plate. [[184_notes:charge_and_matter#Types_of_Matter|Because the plates are conducting]], we know that the electrons in the plates can easily move through the material, so it is safe to assume that __//each of the plates has a uniform distribution of charge//__ on the surface.
-{{  184_notes:fullcap.jpg?200}}
+[{{  184_notes:wireandplates.png?300|Two charged plates connected by a small conducting wire}}]
 [[184_notes:charge|Based on what we know about how charges interact]], what would you expect to happen if we connect these plates with a small conducting wire? [[184_notes:charge_and_matter|Remember that in matter (and specifically in conductors)]], the electrons are the charges that are mobile.
-Any electron from the negative plate is going to feel a strong repulsion from the other excess electrons on the negative plate and will feel a strong attraction from the positive plate (from the positive nuclei of the atoms lacking electrons). When the wire is first connected, those excess electrons now have a path to travel from the negative plate to the positive plate. Generally speaking, the electron will be pushed through the wire both because of the repulsion from the other electrons on the negative plate and the attraction from the positive nuclei on the positive plate. However, the story is much richer and more complicated than that as you will learn. Charges redistribute on both plates and the sire to more electrons along and onto the positively charged plate. This happens very quickly!
+Any electron from the negative plate is going to feel a strong repulsion from the other excess electrons on the negative plate and will feel a strong attraction from the positive plate (really from the positive nuclei of the atoms lacking electrons). When the wire is first connected, those excess electrons now have a path to travel from the negative plate to the positive plate. Generally speaking, the electrons will be pushed through the wire both because of the repulsion from the other electrons on the negative plate and the attraction from the positive nuclei on the positive plate. However, the story is much richer and more complicated than that as you will learn: charges not only spread out on both plates //but also along the wire// to move electrons from the negative plate and onto the positively charged plate. **This process happens very quickly - no matter how far apart the plates are!**
-We will define the number of electrons passing through any given point in the wire per second as the **electron current**. At first, there will be many electrons traveling through the wire, so there would be a large electron current through the wire.
-{{184_notes:partcap.jpg?200  }}
-After some time has passed, the electron current through the wire decreases for three (related) reasons. First, there are fewer excess electrons available on the negative plate because many of the electrons have now traveled through the wire to the positive plate. This means that net charge on the negative plate has decreased //and// the net charge on the positive plate has decreased.  Then because the net charge has decreased, the excess electrons on the negative plate feel a weaker repulsion from the other excess electrons and a weaker attraction from the positive plate. At the same time, the charge on both plates and the wire is resitributing itself as more electrons move onto the positive plate. The net effect of this redistribution on all conductors results in fewer electrons arriving at the positive plate. Ultimately, this means that there are fewer electrons passing through the wire per second.
-After the wire has been connected for a long time, all of the excess electrons from the negative plate have moved through the wire, leaving both the (originally) negative and positive plates neutral. By this point, there are no charges moving through the wire so the electron current is zero. The charges on the plates and the wire stop redistributing and are now in a state of "static equilibrium."
-{{  184_notes:emptycap.jpg?200}}
-This example highlights a few important features about moving charges:
-  * Separation of charges - any time you have positive and negative charges separated by some distance, there is an electric field between those charges. There is also a change in electric potential between those charges. [[184_notes:pc_vefu|As you learned before]], electric field and electric potential are related to electric force and electric potential energy respectively. **This means that separated charges are a means to store energy**. Like you just read, if separated charges are then connected with a wire, those stored charges are free move, turning that stored energy into something that we can use to power a light for example. We will spend the next couple of weeks talking about how we can use that electric energy in circuits.
-  * This particular example of separated charges on two parallel sheets is called a [[184_notes:parallel_cap|parallel plate capacitor]]. Because parallel plates are relatively easy to describe mathematically, we will return to this example frequently. You can also have charge separated in other shape configurations, which we will just refer to as capacitors. We will go into more detail about [[184_notes:cap|capacitors]] and [[184_notes:parallel_cap|parallel plate capacitors]] next week.
-  * Electron current (non-constant) - there are situations where we have electrons moving now, rather than just staying in place. We will spend the next few pages of notes figuring out how to model electrons that are moving. In this particular case, the electron current is actually changing in magnitude: it starts out with a large electron current and decreases until there is ultimately no charges moving. Since a changing current is more complex to explain, we will start by making a //__steady state assumption__//, which means we will first try figure out what happens when the electron current is constant (rather than decreasing).
-The next few pages of notes will go into more detail at the micro level about what is happening as the charges move through wire, starting with steady state current assumption, and how we create a steady state current.
+The next few pages of notes will go into more detail at the micro level about what is happening as the charges move through wire, how the charges redistribute, and how we are going to simplify this model of charges of moving.