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184_notes:gradient [2020/09/22 16:01] – dmcpadden | 184_notes:gradient [2021/02/23 20:18] (current) – bartonmo | ||
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==== What is a gradient? ==== | ==== What is a gradient? ==== | ||
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A gradient is simply a change in the amount of something. For example, you may have seen a color gradient (like the one shown at the right), where you start with a single color that slowly fades to white. In this case, the color is what is changing, so we call it a "color gradient." | A gradient is simply a change in the amount of something. For example, you may have seen a color gradient (like the one shown at the right), where you start with a single color that slowly fades to white. In this case, the color is what is changing, so we call it a "color gradient." | ||
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It would be impossible to actually count or draw every single electron along the surface of a wire. There are simply too many, and it would make our picture too messy to be useful. Instead, we draw a small representative amount of charges on our picture. For example, if we go back to the picture with the battery and surface charges: | It would be impossible to actually count or draw every single electron along the surface of a wire. There are simply too many, and it would make our picture too messy to be useful. Instead, we draw a small representative amount of charges on our picture. For example, if we go back to the picture with the battery and surface charges: | ||
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There are a few things to notice: | There are a few things to notice: | ||
- We have drawn a small amount of charges on the surface of the wire. For example, in the top right corner, we have drawn a total of eight negative signs on the outside of the wire. This does not mean that there is exactly eight electrons on the wire. Instead, **this just shows that we expect this area of the wire to have a large concentration of negative charge**. There is no particular reason why we drew eight - we could have picked 12 or 6 or any other number to start with. The important part is that there are more negative signs in this area than any other part of the wire. | - We have drawn a small amount of charges on the surface of the wire. For example, in the top right corner, we have drawn a total of eight negative signs on the outside of the wire. This does not mean that there is exactly eight electrons on the wire. Instead, **this just shows that we expect this area of the wire to have a large concentration of negative charge**. There is no particular reason why we drew eight - we could have picked 12 or 6 or any other number to start with. The important part is that there are more negative signs in this area than any other part of the wire. | ||
- | - As we move along the wire on the right side, the number of negative decreases from 8 to 6 to 4 to 2. **This represents the gradient of surface charges.** As we move along the wire, we expect there to be a lot of negative surface charges near the battery, and as you get further away along the wire, there should be fewer and fewer negative surface charges. Remember, the //change// in the amount of charge is what makes it a gradient. Similarly, as we approach the positive side of the battery, we draw 2 to 4 to 6 to 8 positive signs to represent the increase in the amount of positive surface charges. Note that there is an area between the negative and positive signs where we have zero surface charges. Together, this means our gradient is continuous along the whole wire (it goes from negative to zero to positive). | + | - As we move along the wire on the right side, the number of negative |
+ | - The last thing to notice here is the electric field arrows. We said already that the gradient is what creates the electric field field. **This means that the electric field arrows need to match your surface charge gradient and vice versa**. Remember from [[184_notes: | ||
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+ | In the next page of notes, we'll talk more about how the surface charge gradient and electric field create a current in the wire. | ||