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184_notes:current [2018/01/27 21:07] – dmcpadden | 184_notes:current [2020/08/23 19:20] – dmcpadden |
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Sections 17.5 and 18.2 in Matter and Interactions (4th edition) | Sections 17.5 and 18.2 in Matter and Interactions (4th edition) |
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| /*[[184_notes:resistors|Next Page: Resistors]] |
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| [[184_notes:defining_current|Previous Page: Defining Current]]*/ |
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===== Current in Wires ===== | ===== Current in Wires ===== |
In the last few pages of notes, we established that when connected to a battery there are surface charges in the wire that [[184_notes:q_in_wires|create a constant electric field through the wire]]. Because [[184_notes:pc_force|electric force is directly proportional to the electric field]] ($\vec{F} = q\vec{E}$), the electric field in the wire pushes the electrons from the negative plate of the battery to the positive plate of the battery causing an [[184_notes:defining_current|electron current]] through the wire. Rather than focusing on the surface charges, these notes will focus on describing the electron current that occurs in the wire and how we find the average speed of those electrons. | In the last few pages of notes, we established that when connected to a battery there are surface charges in the wire that [[184_notes:q_in_wires|create a constant electric field through the wire]]. Because [[184_notes:pc_force|electric force is directly proportional to the electric field]] ($\vec{F} = q\vec{E}$), the electric field in the wire pushes the electrons from the negative plate of the battery to the positive plate of the battery causing an [[184_notes:defining_current|electron current]] through the wire. Rather than focusing on the surface charges, these notes will focus on describing the electron current that occurs in the wire and how we find the average speed of those electrons. |
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==== Drift speed in wire ==== | ==== Drift speed in wire ==== |
{{ 184_notes:vdrift.png?200}} | [{{ 184_notes:vdrift.png?200|Graph of electron speed in a wire vs time}}] |
Modeling all of these interactions for every electron in the electron current is quite complicated (or almost impossible). While there are several ways to model the electrons in the wire, we will use a model called the [[https://en.wikipedia.org/wiki/Drude_model|Drude Model]], which builds off of the idea that the electrons are interacting or bouncing off the positive nuclei in the wire. In this model, the electron will experience short periods of acceleration from the electric field, followed by periods where the electron drastically slows because of collision with a positive nuclei in the wire. The average speed of the electron in this stop/start motion is called the **drift velocity**, and we say that the electron "drifts" through the metal. The drift velocity of electrons in a wire is actually quite slow compared to the speed of the individual electrons (the same way that the wind has slow speed compared to the speed of the individual air molecules). | Modeling all of these interactions for every electron in the electron current is quite complicated (or almost impossible). While there are several ways to model the electrons in the wire, we will use a model called the [[https://en.wikipedia.org/wiki/Drude_model|Drude Model]], which builds off of the idea that the electrons are interacting or bouncing off the positive nuclei in the wire. In this model, the electron will experience short periods of acceleration from the electric field, followed by periods where the electron drastically slows because of collision with a positive nuclei in the wire. The average speed of the electron in this stop/start motion is called the **drift velocity**, and we say that the electron "drifts" through the metal. The drift velocity of electrons in a wire is actually quite slow compared to the speed of the individual electrons (the same way that the wind has slow speed compared to the speed of the individual air molecules). |
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$$\vec{v}_{avg}=u\vec{E}$$. | $$\vec{v}_{avg}=u\vec{E}$$. |
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Likewise, we can combine this with the expression for electron current $i=nAv_{avg}$ to get: | Likewise, we can combine this with the [[184_notes:defining_current|expression for electron current]] $i=nAv_{avg}$ to get: |
$$i=nAuE$$ | $$i=nAuE$$ |
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