| Both sides previous revision Previous revision Next revision | Previous revision Next revisionBoth sides next revision |
| 184_notes:dist_charges [2018/06/05 15:31] – curdemma | 184_notes:dist_charges [2020/08/20 16:03] – dmcpadden |
|---|
| [[184_notes:patterns_fields|Next Page: Patterns in Fields]] | /*[[184_notes:patterns_fields|Next Page: Patterns in Fields]] |
| |
| [[184_notes:linecharge|Previous Page: Line of Charge]] | [[184_notes:linecharge|Previous Page: Line of Charge]]*/ |
| |
| ===== Distributions of Charges ===== | ===== Distributions of Charges ===== |
| Over the last three pages of notes, we have talked about [[184_notes:line_fields|how we use superposition to find the electric field or electric potential from a line of charge]], how you set up [[184_notes:dq|the dQ and the $\vec{r}$]], and how to use those steps in [[184_notes:linecharge|a specific example]]. For this class, we will expect you to be able to set up these kinds of integrals for a line a charge (1D), but we will not go into the mathematics for 2D or 3D distributions of charge. Even though we won't go into the integral set up or analytical derivation of these fields, it is useful to have an idea of what the electric field would look like around some of these shapes. These notes will show what the electric field looks like for two common shapes of charge (spheres and cylinders) and we will discuss what how these fields change when the material is an insulator or a conductor. | Over the last set of notes, we have talked about [[184_notes:line_fields|how we use superposition to find the electric field or electric potential from a line of charge]], how you set up [[184_notes:dq|the dQ and the $\vec{r}$]], and how to use those steps in [[184_notes:linecharge|a specific example]]. For this class, we will expect you to be able to set up these kinds of integrals for a line a charge (1D), but we will not go into the mathematics for 2D or 3D distributions of charge. Even though we won't go into the integral set up or analytical derivation of these fields, it is useful to have an idea of what the electric field would look like around some of these shapes. These notes will show what the electric field looks like for two common shapes of charge (spheres and cylinders) and we will discuss what how these fields change when the material is an insulator or a conductor. |
| |
| ==== Sphere of Charge ==== | ==== Sphere of Charge ==== |
| |
| 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 ("like" charges repel) because they are free to move through a conductor. This means that all of the charges will spread out over the surface of the cylinder, leaving the inside of cylinder neutral. | 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 ("like" charges repel) because they are free to move through a conductor. This means that all of the charges will spread out over the surface of the cylinder, leaving the inside of cylinder neutral. |
| | [{{ 184_notes:conductorcylinderefield.png?125|Electric field inside and around a cylindrical conductor}}] |
| 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: |
| $$E_{inside} = 0$$ | $$E_{inside} = 0$$ |
| This is actually a larger pattern in all conductors - **the electric field inside a conductor should always equal zero**. | This is actually a larger pattern in all conductors - **the electric field inside a conductor should always equal zero**. |
| [{{ 184_notes:conductorcylinderefield.png?125|Electric field inside and around a cylindrical conductor}}] | |
| 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, in the middle of the cylinder, the electric field will point radially away from the cylinder (pointing directly away from the surface of the cylinder) and is roughly constant; however, near the ends of the cylinder the electric field starts to bend around the edge and is no longer uniform. | 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, in the middle of the cylinder, the electric field will point radially away from the cylinder (pointing directly away from the surface of the cylinder) and is roughly constant; however, near the ends of the cylinder the electric field starts to bend around the edge and is no longer uniform. |
| |