# Differences

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184_notes:q_enc [2017/09/20 22:41] pwirving [Enclosed Charge] |
184_notes:q_enc [2021/06/03 20:34] (current) schram45 |
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Section 21.1 from Matter and Interactions (4th edition) | Section 21.1 from Matter and Interactions (4th edition) | ||

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===== Enclosed Charge ===== | ===== Enclosed Charge ===== | ||

One of the coolest, yet strangest, features of Gauss' | One of the coolest, yet strangest, features of Gauss' | ||

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{{youtube> | {{youtube> | ||

==== Charge Density and Charge ==== | ==== Charge Density and Charge ==== | ||

- | [[184_notes:Before we talked about charge density]] in terms of finding a dQ, where we //__assumed a uniform (or constant) charge density__// | + | [[184_notes:We have talked about charge density]] in terms of finding a $dQ$, where we //__assumed a uniform (or constant) charge density__// |

If we know the total charge and the total length/ | If we know the total charge and the total length/ | ||

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=== Spheres of Charge === | === Spheres of Charge === | ||

- | {{184_notes: | + | [{{184_notes:|Spherical guassian surface around a sphere of charge}}] |

For a sphere of charge, (much like a point charge), the electric field vectors point radially away (for positive charge) or radially toward (for negative charge) the sphere. Since the electric field vectors point radially, we would want to choose a sphere as a Gaussian surface to enclose the charge because the $\vec{dA}$' | For a sphere of charge, (much like a point charge), the electric field vectors point radially away (for positive charge) or radially toward (for negative charge) the sphere. Since the electric field vectors point radially, we would want to choose a sphere as a Gaussian surface to enclose the charge because the $\vec{dA}$' | ||

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=== Lines or Cylinders of Charge === | === Lines or Cylinders of Charge === | ||

- | {{184_notes: | + | [{{184_notes:|Cylindrical guassian surface around a line or cyliner of charge}}] |

In the middle of a line (1D) or cylinder of charge (3D), the electric field vectors point radially away from a line of positive charge or radially toward a line of negative charge. If we make the line extremely long or zoom in to focus on a very small portion of the line/ | In the middle of a line (1D) or cylinder of charge (3D), the electric field vectors point radially away from a line of positive charge or radially toward a line of negative charge. If we make the line extremely long or zoom in to focus on a very small portion of the line/ | ||

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=== Sheets of charge === | === Sheets of charge === | ||

- | {{184_notes: | + | [{{184_notes:|Rectangular prism around a plate of charge}}] |

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__// | ||

- | If we wanted to find the electric field from a large plate of charge, then we would want to choose a (smaller) cylinder or rectangular prism as the Gaussian surface around the plate of charge because the electric field vectors would then point parallel to the dA vectors through the top and bottom surfaces. | + | If we wanted to find the electric field from a large plate of charge, then we would want to choose a (smaller) cylinder or rectangular prism as the Gaussian surface around the plate of charge because the electric field vectors would then point parallel to the $dA$ vectors through the top and bottom surfaces. |

==== Examples ==== | ==== Examples ==== | ||

- | [[:Week5_flux_dipole|Flux from a Dipole]] | + | *[[:Week5_flux_cylinder_line|Flux through a Cylinder on a Line of Charge]] |

- | | + | * Video Example: Flux through a Cylinder on a Line of Charge |

- | [[:|Flux through a Cube on a Charged Plane]] | + | {{youtube> |

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- | [[:184_notes:Flux through a Cylinder on a Line of Charge]] | + |