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===== Distributions of Charges ===== | ===== Distributions of Charges ===== | ||
- | Over the last three pages of notes, we have talked about [[184_notes: | + | Over the last set of notes, we have talked about [[184_notes: |
==== Sphere of Charge ==== | ==== Sphere of Charge ==== | ||
In the [[184_notes: | In the [[184_notes: | ||
- | === Conducting Sphere of Charge === [{{184_notes: | + | === Conducting Sphere of Charge === |
+ | |||
+ | [{{ 184_notes: | ||
For the sake of illustration, | For the sake of illustration, | ||
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If instead we have an insulating, plastic sphere (rather than a metal, conducting one), we would see a very different charge distribution. In an insulator, excess charges cannot move freely and are stuck where they were placed. Thus, if we place a collection of electrons inside the ball, they will stay distributed through the volume of the sphere rather moving to the surface. For the purposes of our class, we will //__assume that any charge on an insulator will be evenly distributed__// | If instead we have an insulating, plastic sphere (rather than a metal, conducting one), we would see a very different charge distribution. In an insulator, excess charges cannot move freely and are stuck where they were placed. Thus, if we place a collection of electrons inside the ball, they will stay distributed through the volume of the sphere rather moving to the surface. For the purposes of our class, we will //__assume that any charge on an insulator will be evenly distributed__// | ||
- | [{{184_notes: | + | [{{ 184_notes: |
Now that we know where the charges are located, we can think about what the electric field should look like around the plastic charged ball. Similar to the metal ball, at any point outside of the plastic ball we would expect the electric field to point in towards the plastic ball since the electric field points in toward a negative point charge. If you actually do the math (again either with an integral over the volume of the sphere or with a computational code), you will exactly the same electric field outside the plastic ball as you would if the ball (with the same amount of charge) were metal: | Now that we know where the charges are located, we can think about what the electric field should look like around the plastic charged ball. Similar to the metal ball, at any point outside of the plastic ball we would expect the electric field to point in towards the plastic ball since the electric field points in toward a negative point charge. If you actually do the math (again either with an integral over the volume of the sphere or with a computational code), you will exactly the same electric field outside the plastic ball as you would if the ball (with the same amount of charge) were metal: | ||
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==== Cylinders of Charge ==== | ==== Cylinders of Charge ==== | ||
- | [{{ 184_notes: | + | [{{ 184_notes: |
Another common example that we will frequently talk about is the idea of a charged cylinder. This will become particularly relevant when we start talking about wires in circuits next week. For now, we'll talk about the shape of the electric field for a conducting and an insulating cylinder of charge. | Another common example that we will frequently talk about is the idea of a charged cylinder. This will become particularly relevant when we start talking about wires in circuits next week. For now, we'll talk about the shape of the electric field for a conducting and an insulating cylinder of charge. | ||
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Much like what happened with the metal sphere, if we place an excess charge - let's say it's positive this time - on a metal cylinder (like a wire), those charges will spread out as far as they possibly can from one another (" | Much like what happened with the metal sphere, if we place an excess charge - let's say it's positive this time - on a metal cylinder (like a wire), those charges will spread out as far as they possibly can from one another (" | ||
+ | [{{ 184_notes: | ||
If we think about the electric field inside the cylinder, we would see a similar effect as we did with the metal ball. There will always be a contribution to the electric field from the charges on one side of the cylinder that opposes the electric field contribution from the charges on the other side of cylinder. This means that: | If we think about the electric field inside the cylinder, we would see a similar effect as we did with the metal ball. There will always be a contribution to the electric field from the charges on one side of the cylinder that opposes the electric field contribution from the charges on the other side of cylinder. This means that: | ||
$$E_{inside} = 0$$ | $$E_{inside} = 0$$ | ||
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Outside the cylinder, we would expect the electric field to generally point away from the positively charged cylinder since the electric field points in away from a positive charge. If you actually do the math (either with an integral over the volume of the cylinder or with a computational code), you will see something like this. Particularly, | Outside the cylinder, we would expect the electric field to generally point away from the positively charged cylinder since the electric field points in away from a positive charge. If you actually do the math (either with an integral over the volume of the cylinder or with a computational code), you will see something like this. Particularly, | ||
- | [{{184_notes: | + | |
=== Insulating Cylinder of Charge === | === Insulating Cylinder of Charge === | ||
- | [{{ 184_notes: | + | [{{ 184_notes: |
For an insulating cylinder (like a plastic pipe) if we add excess charges, those will stay in place (as charges are not free to move in an insulator). We will again make the assumption in these cases of __//a uniform charge distribution// | For an insulating cylinder (like a plastic pipe) if we add excess charges, those will stay in place (as charges are not free to move in an insulator). We will again make the assumption in these cases of __//a uniform charge distribution// | ||
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Inside the insulating cylinder, the electric field would be non-zero. The contributions to the electric field from the charges in the middle of the cylinder do not completely cancel out, leaving an electric field that points away from the center of the cylinder for a positive charge (it would point towards the center for a negative charge). The electric field inside will be strongest at the edge of the cylinder and will be smallest (or exactly zero) in the center. | Inside the insulating cylinder, the electric field would be non-zero. The contributions to the electric field from the charges in the middle of the cylinder do not completely cancel out, leaving an electric field that points away from the center of the cylinder for a positive charge (it would point towards the center for a negative charge). The electric field inside will be strongest at the edge of the cylinder and will be smallest (or exactly zero) in the center. | ||
- | [{{184_notes: | + | [{{184_notes: |