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| 184_notes:q_enc [2017/07/09 07:22] – [Patterns of Electric Fields] pwirving | 184_notes:q_enc [2018/07/24 15:17] – [Charge Density and Charge] curdemma |
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| | Section 21.1 from Matter and Interactions (4th edition) |
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| | [[184_notes:gauss_ex|Next Page: Putting together Gauss's Law]] |
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| | [[184_notes:eflux_curved|Previous Page: Electric Flux through a Curved Surface]] |
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| ===== Enclosed Charge ===== | ===== Enclosed Charge ===== |
| One of the coolest, yet strangest, features of Gauss's Law is that the electric flux through the imagined Gaussian surface is related to the total amount of charge //__inside__// the surface (the "enclosed charge"). For a point charge or multiple point charges, it is fairly easy to find the total amount of enclosed charge - you simply sum the amount of charge that inside the surface you pick. However, if you have a line, sheet, or volume of charge, we need to rely on charge density to find the enclosed charge. These notes will review charge density and show how we find the enclosed charge for various shapes or distributions of charge. | One of the coolest, yet strangest, features of Gauss's Law is that the electric flux through the imagined Gaussian surface is related to the total amount of charge //__inside__// the surface (the "enclosed charge"). For a point charge or multiple point charges, it is fairly easy to find the total amount of enclosed charge - you simply sum the amount of charge that is inside the surface you picked. However, if you have a line, sheet, or volume of charge, we need to rely on charge density to find the enclosed charge. These notes will review charge density and show how we find the enclosed charge for various shapes or distributions of charge. |
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| | {{youtube>YhTl8JmBQ6E?large}} |
| ==== Charge Density and Charge ==== | ==== Charge Density and Charge ==== |
| [[184_notes:dq|Before we talked about charge density]] in terms of finding a dQ, where we //__assumed a uniform (or constant) charge density__//. We will make that same assumption again here (the more complicated non-uniform charge densities may be covered in upper division courses). For a uniform charge distribution, the charge density tells you how much charge there is per unit length (for 1D lines of charge), per area (for 2D sheets of charge), or per volume (for 3D shapes of charge). For 1D charge distributions, we use $\lambda$ as the charge density (which has units of $C/m$); for 2D charge distributions, we use $\sigma$ as the charge distribution (which has units of $C/m^2$); and for 3D charge distributions, we use $\rho$ as the charge density (which has units of $C/m^3$). | [[184_notes:dq|We have talked about charge density]] in terms of finding a $dQ$, where we //__assumed a uniform (or constant) charge density__//. We will make that same assumption again here (the more complicated non-uniform charge densities may be covered in upper division courses). For a uniform charge distribution, the charge density tells you how much charge there is per unit length (for 1D lines of charge), per area (for 2D sheets of charge), or per volume (for 3D shapes of charge). For 1D charge distributions, we use $\lambda$ as the charge density (which has units of $C/m$); for 2D charge distributions, we use $\sigma$ as the charge distribution (which has units of $C/m^2$); and for 3D charge distributions, we use $\rho$ as the charge density (which has units of $C/m^3$). |
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| If we know the total charge and the total length/area/volume, we can calculate the charge density using: | If we know the total charge and the total length/area/volume, we can calculate the charge density using: |
| === Sheets of charge === | === Sheets of charge === |
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| {{184_notes:electricflux10.jpg?350}} | {{184_notes:planecharge.jpg?350}} |
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| Similar to the lines of charge, the electric field for a positive plate of charge points perpendicularly away (and perpendicularly toward the plate for negative charge) in the middle of the plate. Near the edges of the plate (similar to the line of charge) the electric field vectors change directions and magnitudes, making it much harder calculate. Typically, we will make //__the assumption that the charged plate is very large (or infinite) or that we only care about the field close to the center of the plate away from the edges__//. | Similar to the lines of charge, the electric field for a positive plate of charge points perpendicularly away (and perpendicularly toward the plate for negative charge) in the middle of the plate. Near the edges of the plate (similar to the line of charge) the electric field vectors change directions and magnitudes, making it much harder calculate. Typically, we will make //__the assumption that the charged plate is very large (or infinite) or that we only care about the field close to the center of the plate away from the edges__//. |
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| ==== Examples ==== | ==== Examples ==== |
| Dipole and flux | [[:184_notes:examples:Week5_flux_cylinder_line|Flux through a Cylinder on a Line of Charge]] |
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| Single sphere | |