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--- 184_notes:q_in_wires [2021/02/23 20:22] – [Hypothesis 1 - Electric field comes from the battery alone] bartonmo
+++ 184_notes:q_in_wires [2021/06/08 00:38] (current) – schram45
@@ Line 38: / Line 38: @@
 Because the wire is made of metal, electrons are free to move and any excess charge will move to the surface of the wire. Thus, when connected to the battery, **there are charges on the surface of the wire**, which contribute to the net electric field in the wire (in addition to the field from the battery).
-For example, near the negative end of the mechanical battery, there are negative charges on the surface of the wire. Near the positive end of the mechanical battery, there are positive charges on the surface of the wire. Moving farther from the negative end of the battery will result in less and less negative surface charges, with the same effect as you move farther from the positive end. In the middle, there must be a place where the surface charge is zero (where the surface charge switches from positive to negative). **This creates a __continuous charge gradient__ along the wire - from the positive end of the battery to the negative end of the battery.** When we say a gradient in this context, we mean that the amount of surface charge changes as you move along the wire. An example of the surface charge gradient is shown in the figure below, where the surface starts as large and positive near the positive plate, decreases along the wire, and ends as large and negative near the negative plate.
+For example, near the negative end of the mechanical battery, there are negative charges on the surface of the wire. Near the positive end of the mechanical battery, there are positive charges on the surface of the wire. Moving farther from the negative end of the battery will result in less and less negative surface charges, with the same effect as you move farther from the positive end. In the middle, there must be a place where the surface charge is zero (where the surface charge switches from positive to negative). **This creates a //continuous charge gradient// along the wire - from the positive end of the battery to the negative end of the battery.** When we say a gradient in this context, we mean that the amount of surface charge changes as you move along the wire. An example of the surface charge gradient is shown in the figure below, where the surface starts as large and positive near the positive plate, decreases along the wire, and ends as large and negative near the negative plate.
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 The electric field around the circuit then follows the charge gradient, pointing from more positive areas of the wire to less positive areas (or from less negative areas to more negative areas). Ultimately, this means that the **electric field follows the wire pointing from the positive end of the battery to the negative**. Remember that because electrons are negative charges, [[184_notes:pc_force|they will move in the direction opposite of the electric field]]. In a circuit then, the electrons that are driven by the mechanical battery follow the wire opposite to the electric field that is set up by the surface charges.
-The contributions of the surface charges generate an electric field that adds with the electric field due to the battery (via [[184_notes:superposition|superposition]]). The result //__in steady state__// is that **the surface charges in the wire and the battery's electric field set up a __constant electric field__ along the wire, which pushes the electron current in the opposite direction of the electric field** (from the negative end to the positive end of the battery). Now, when the wire is physically far away from the battery, the electric field due to the battery is small. So often, we just assume __// that the constant electric field in the wire is due (mostly) to the surface charges//__. This is a pretty good assumption anywhere far from the battery (which is pretty much everywhere in macroscopic terms). This might violate your intuition a bit as you expect the field to die off away from the source of charges, but rest assured the electric field is constant through the wire.
+The contributions of the surface charges generate an electric field that adds with the electric field due to the battery (via [[184_notes:superposition|superposition]]). The result //__in steady state__// is that **the surface charges in the wire and the battery's electric field set up a //constant electric field// along the wire, which pushes the electron current in the opposite direction of the electric field** (from the negative end to the positive end of the battery). Now, when the wire is physically far away from the battery, the electric field due to the battery is small. So often, we just assume __// that the constant electric field in the wire is due (mostly) to the surface charges//__. This is a pretty good assumption anywhere far from the battery (which is pretty much everywhere in macroscopic terms). This might violate your intuition a bit as you expect the field to die off away from the source of charges, but rest assured the electric field is constant through the wire.
 If we consider the surface charge hypothesis, this is much more consistent with what we observe when we connect a wire to a battery:
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 ==== Examples ====
-[[:184_notes:examples:Week6_charges_circuit|Charge Distribution on the Bends of a Circuit]]
+  * [[:184_notes:examples:Week6_charges_circuit|Charge Distribution on the Bends of a Circuit]]
+    * Video Example: Charge Distribution on the Bends of a Circuit
+{{youtube>9f2EJedXHP0?large}}