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| 184_notes:gauss_motive [2017/09/21 02:37] – [Motivation for Gauss's Law] pwirving | 184_notes:gauss_motive [2018/07/24 14:47] – [Conceptualizing Gauss's Law around a Point Charge] curdemma |
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| | [[184_notes:e_flux|Next Page: Electric Flux and Area Vectors]] |
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| ===== Motivation for Gauss's Law ===== | ===== Motivation for Gauss's Law ===== |
| | Last week we learned about Ampere's Law for finding magnetic fields. This week we will look into Gauss's Law in order to be better able to find Electric Fields. |
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| We have been analyzing the kinds of electric fields that are produced by charges. We started by finding the [[184_notes:pc_efield|electric field of a point charge]] and then used the electric field from a point charge to build up the [[184_notes:linecharge|electric field from a line of charge]]. The method of building a field from a point charge can also be used for a 2D sheet of charge or a 3D volume of charge and will //always// work; however, the mathematical calculation needed to determine the field can become much more complicated (you have to use either a double or triple integral). In some cases, we can use the symmetric nature of the situation to apply Gauss's Law as a shortcut for finding the electric field, even though there are trade offs for using this shortcut (it is alway true, but only useful in highly symmetric situations). In the end, both of these methods can tell us the same thing, even though the mathematics we will use is different: **charges create electric fields**. These notes will introduce the general concept of Gauss's law before we talk about the mathematics and the advantages and disadvantages to using it. | Back at the beginning of the semester, we talked about how to find the electric field from [[184_notes:pc_efield|point charges]], [[184_notes:line_fields|lines of charge]], and [[184_notes:dist_charges|distributions of charge]] (i.e., cylinders, spheres, or planes of charge). The method of building a field from a point charge can also be used for a 2D sheet of charge or a 3D volume of charge and will //always// work; however, the mathematical calculation needed to determine the field can become much more complicated (you have to use either a double or triple integral). In some of these cases, Gauss's Law works as a shortcut for finding the electric field from complicated charge distributions. However, there are trade offs for using this shortcut -- it is alway true, but only useful in highly symmetric situations. In the end, both of these methods are built around the same idea, even though the mathematics we will use is different: **charges create electric fields**. These notes will introduce the general concept of Gauss's law before we talk about the mathematics and the advantages and disadvantages to using it. |
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| {{youtube>_oktQiCNfEw?large}} | {{youtube>_oktQiCNfEw?large}} |
| - The area of the imagined bubble or imagined Gaussian surface increases. The increase in area is proportional to $r^2$ because the [[https://en.wikipedia.org/wiki/Sphere#Surface_area|surface area of a sphere]] is $A=4\pi r^2$. | - The area of the imagined bubble or imagined Gaussian surface increases. The increase in area is proportional to $r^2$ because the [[https://en.wikipedia.org/wiki/Sphere#Surface_area|surface area of a sphere]] is $A=4\pi r^2$. |
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| This suggests that the electric field at the surface of the imaginary sphere multiplied by the surface area of the imaginary sphere is a constant; this product is called [[ | This suggests that //the electric field at the surface of the imaginary sphere multiplied by the surface area of the imaginary sphere is a constant//; this product is called [[ |
| 184_notes:e_flux|electric flux]]. | 184_notes:e_flux|electric flux]]. |
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