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| 184_notes:gauss_motive [2018/05/15 16:49] – curdemma | 184_notes:gauss_motive [2018/07/24 14:47] – [Conceptualizing Gauss's Law around a Point Charge] curdemma |
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| ===== Motivation for Gauss's Law ===== | ===== Motivation for Gauss's Law ===== |
| So far in this course, we have talked about the sources of electric fields, how electric fields are applied to circuits, and the sources of magnetic fields. Over the next two weeks, we are going to talk about two mathematical shortcuts for calculating the electric and magnetic fields: Gauss's Law and Ampere's Law. We'll start by talking about Gauss's Law, which is an alternative method for calculating the electric field. | 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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| 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. | 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. |
| - 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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