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184_notes:q_in_wires [2018/09/19 18:07] – dmcpadden | 184_notes:q_in_wires [2021/02/18 21:17] – bartonmo | ||
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Sections 17.1, 17.5, and 18.1-18.5 in Matter and Interactions (4th edition) | Sections 17.1, 17.5, and 18.1-18.5 in Matter and Interactions (4th edition) | ||
- | [[184_notes: | + | /*[[184_notes: |
- | [[184_notes: | + | [[184_notes: |
===== Surface Charges around a Circuit ===== | ===== Surface Charges around a Circuit ===== | ||
We have already talked about how to model a battery as a separation of charges. However, if we connect the two ends of the battery with a conducting wire, what happens to the charge distribution in the wire? Using [[184_notes: | We have already talked about how to model a battery as a separation of charges. However, if we connect the two ends of the battery with a conducting wire, what happens to the charge distribution in the wire? Using [[184_notes: | ||
- | {{youtube> | + | {{youtube> |
==== Simple Circuit ==== | ==== Simple Circuit ==== | ||
- | [{{ 184_notes: | ||
We will start with the simplest circuit possible: a battery connected by a conducting wire (shown to the right). If we //__assume the battery is a mechanical battery__//, | We will start with the simplest circuit possible: a battery connected by a conducting wire (shown to the right). If we //__assume the battery is a mechanical battery__//, | ||
- | If the electrons are moving, there has to be some sort of force that is making those charges move. From what we talked about before, we know we can write this force on the electron in terms of the electron charge and the electric field it is in: | + | If the electrons are moving, there has to be some sort of force that is making those charges move. [[184_notes: |
$$\vec{F}_{e^-}=q_{e^-}\vec{E}$$ | $$\vec{F}_{e^-}=q_{e^-}\vec{E}$$ | ||
Since the electrons move through the wire, we know there must then be an electric field in that wire - but where is that electric field coming from? One reasonable hypothesis could be that there is an electric field in the wire from the battery. | Since the electrons move through the wire, we know there must then be an electric field in that wire - but where is that electric field coming from? One reasonable hypothesis could be that there is an electric field in the wire from the battery. | ||
- | === Hypothesis 1 - Electric field comes from the battery alone === | + | [{{ 184_notes: |
+ | |||
+ | ==== Hypothesis 1 - Electric field comes from the battery alone ==== | ||
If this were true, the electric field at Point 1 in the wire would point to left given that it is near the positive plate. Likewise, the electric field at Point 2 would also point to the left, given that it is near the negative plate. At Point 3, we would expect the electric field to be point to the right because it is between the positive and negative plates, though it would be smaller because it is further away from the plates. | If this were true, the electric field at Point 1 in the wire would point to left given that it is near the positive plate. Likewise, the electric field at Point 2 would also point to the left, given that it is near the negative plate. At Point 3, we would expect the electric field to be point to the right because it is between the positive and negative plates, though it would be smaller because it is further away from the plates. | ||
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This tells us that while the battery certainly contributes to the electric field in the wire, **there must be something else that is adding to the electric field in the wire**. | This tells us that while the battery certainly contributes to the electric field in the wire, **there must be something else that is adding to the electric field in the wire**. | ||
- | === Hypothesis 2 - There are stationary charges on the surface of the wires === | + | ==== Hypothesis 2 - There are stationary charges on the surface of the wires ==== |
- | [{{ 184_notes: | + | [{{ 184_notes: |
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). | 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). | ||
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- | === Electric field in the wire follows the surface charge gradient === | + | ==== Electric field in the wire follows the surface charge gradient |
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: | 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: | ||
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- If the force that pushes the electrons comes from the surface of the wires, then the proximity to the battery doesn' | - If the force that pushes the electrons comes from the surface of the wires, then the proximity to the battery doesn' | ||
- | Thus, surface charges as the model for how charges move through wires is far more consistent with the observations we have in real circuits in everyday life. If you have a very large battery (also called a high voltage power supply) it is actually possible to observe the surface charges on a wire. Here's a video demonstrating | + | Thus, surface charges as the model for how charges move through wires is far more consistent with the observations we have in real circuits in everyday life. If you have a very large battery (also called a high voltage power supply) it is actually possible to observe the surface charges on a wire. |
+ | |||
+ | {{ youtube> | ||
+ | |||
+ | In this video, you can see the mechanical effects of surface charge when a piece of foil is held by the positive end, negative end, and neutral center of the wire. On the ends of the wire, the foil is initially attracted, polarized, and then repelled. Since the surface charge at the center of the wire is 0 nothing happens to the foil. A metal pen can also be used to see what kind of charge the foil has picked up based on if it is attracted to or repelled by the pen. | ||
- | {{ youtube> | ||
==== Examples ==== | ==== Examples ==== | ||
[[: | [[: |