184_notes:steady_state

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184_notes:steady_state [2017/07/31 18:32] – dmcpadden184_notes:steady_state [2017/09/20 20:06] (current) – dmcpadden
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 ==== Before the wires are connected ==== ==== Before the wires are connected ====
 +{{  184_notes:opencircuit.png?200}}
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 Suppose we have a battery, with one positive end and one negative end (could be either the chemical model or mechanical model of the battery). At each end, we connect a conductive wire. Before we connect the wires, what would the charge distribution look like along the wire? Suppose we have a battery, with one positive end and one negative end (could be either the chemical model or mechanical model of the battery). At each end, we connect a conductive wire. Before we connect the wires, what would the charge distribution look like along the wire?
  
-FIXME Add Figure+{{184_notes:efieldopencircuit.png?200  }}
  
 The wire that is connected to the negative end of the battery would have a negative distribution of charge because the excess electrons would be able to spread along the length of the wire. Since the wire is a conductor, those excess charges would spread out along the surface of the wire, leaving the interior of the wire with a net electric field equal to zero. A similar process would occur for the wire connected to the positive end of the battery. An approximate charge distribution is shown in the figure, ignoring the exact details of the charge distribution. The wire that is connected to the negative end of the battery would have a negative distribution of charge because the excess electrons would be able to spread along the length of the wire. Since the wire is a conductor, those excess charges would spread out along the surface of the wire, leaving the interior of the wire with a net electric field equal to zero. A similar process would occur for the wire connected to the positive end of the battery. An approximate charge distribution is shown in the figure, ignoring the exact details of the charge distribution.
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-FIXME Add Figure 
  
 If we zoom in on the gap between the wires, We can see an electric field at the end of the wires; however that electric field is cancelled out by the electric field from the wire across the gap. So even in the ends of the wires, the net electric field is zero.  If we zoom in on the gap between the wires, We can see an electric field at the end of the wires; however that electric field is cancelled out by the electric field from the wire across the gap. So even in the ends of the wires, the net electric field is zero. 
  
 ==== Immediately after the wires are connected ==== ==== Immediately after the wires are connected ====
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 If we complete the circuit by connecting the wires, what happens to the surface charges in the wire? The charges on the ends of the wires neutralize each other (so there is no net charge in the middle of the wires). This leaves a "tube" of surface charge on the outside of the wire. In the instant that the two wires touch, there is a strong discontinuity in the charge distributions along the wires - one side of the wire is positive and one side is negative with no smooth transition between the two. This means that there is a separation of charge and therefore there is now an electric field in the now-touching ends of the wires. If we complete the circuit by connecting the wires, what happens to the surface charges in the wire? The charges on the ends of the wires neutralize each other (so there is no net charge in the middle of the wires). This leaves a "tube" of surface charge on the outside of the wire. In the instant that the two wires touch, there is a strong discontinuity in the charge distributions along the wires - one side of the wire is positive and one side is negative with no smooth transition between the two. This means that there is a separation of charge and therefore there is now an electric field in the now-touching ends of the wires.
  
 ==== A moment after the wires are connected ==== ==== A moment after the wires are connected ====
-FIXME Add Figure +{{184_notes:momentaftercircuit.png?200  }}
 Because there is now an electric field in the wire, the mobile sea of electrons will start to move, which changes the surface charge distributions. Note that this starts happening after only fractions of a nano-second. Electrons moving toward the positive region of the wire will make the surface charge in that region less positive. Likewise, electrons moving away from the negative region of the wire will make that region less negative. In the middle of the wires, this creates a region with smaller amounts of charge, making that discontinuity of positive and negative charges less drastic, and setting up an electric field between the positive and negative regions.  Because there is now an electric field in the wire, the mobile sea of electrons will start to move, which changes the surface charge distributions. Note that this starts happening after only fractions of a nano-second. Electrons moving toward the positive region of the wire will make the surface charge in that region less positive. Likewise, electrons moving away from the negative region of the wire will make that region less negative. In the middle of the wires, this creates a region with smaller amounts of charge, making that discontinuity of positive and negative charges less drastic, and setting up an electric field between the positive and negative regions. 
  
 ==== A short time after the wires are connected ==== ==== A short time after the wires are connected ====
-FIXME Add Figure +{{  184_notes:circuitefield.png?300}}
 Again moments later (fractions of nano-seconds), the charge distributions in each side of the wire have rearranged. The excess negative charges have spread out so they have shifted away from the battery and more towards the center of the wire, with a similar process occurring for the positive charges. This creates regions in the wires where close to the battery there is a more concentrated surface charge and closer to the center there is a weaker surface charge. This sets up the continuous charge distribution that we see for the steady state. With this continuous charge distribution, there is now an electric field set up within the wire, which starts to move the electrons in the electron current. Again moments later (fractions of nano-seconds), the charge distributions in each side of the wire have rearranged. The excess negative charges have spread out so they have shifted away from the battery and more towards the center of the wire, with a similar process occurring for the positive charges. This creates regions in the wires where close to the battery there is a more concentrated surface charge and closer to the center there is a weaker surface charge. This sets up the continuous charge distribution that we see for the steady state. With this continuous charge distribution, there is now an electric field set up within the wire, which starts to move the electrons in the electron current.
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 ==== How long does this process take? ==== ==== How long does this process take? ====
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 This explains why when you turn on a switch, the light comes on almost immediately. You are not waiting for an electron from the switch to travel all the way to the lightbulb. You are waiting for an electric field to be set up in the wire to push the electrons that are already in and near the light bulb. Thankfully that process is much shorter! This explains why when you turn on a switch, the light comes on almost immediately. You are not waiting for an electron from the switch to travel all the way to the lightbulb. You are waiting for an electric field to be set up in the wire to push the electrons that are already in and near the light bulb. Thankfully that process is much shorter!
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