| Both sides previous revision Previous revision Next revision | Previous revision |
| 184_notes:gauss_motive [2018/11/07 19:57] – dmcpadden | 184_notes:gauss_motive [2020/08/24 13:42] (current) – dmcpadden |
|---|
| [[184_notes:e_flux|Next Page: Electric Flux and Area Vectors]] | /*[[184_notes:e_flux|Next Page: Electric Flux and Area Vectors]]*/ |
| |
| ===== Motivation for Gauss's Law ===== | ===== Motivation for Gauss's Law ===== |
| {{ 184_notes:bigsphere.jpg?300}} | {{ 184_notes:bigsphere.jpg?300}} |
| |
| **Gauss's Law is built around this idea that the total electric flux is constant through the imagined bubble (no matter where we draw the surface of the bubble)** and that electric flux is related to the amount of charge **//inside//** the bubble (the point charge in this case). It turns out this relationship is always true - for any shape of charge (line, sphere, blob, etc.) and for any closed Gaussian surface, the electric flux on that surface is directly related to the charge inside the surface. | **Gauss's Law is built around this idea that the total electric flux is constant through the imagined bubble (no matter where we draw the surface of the bubble)** and that electric flux is related to the amount of charge **//inside//** the bubble (the point charge in this case). It turns out this relationship is always true - for any shape of charge (line, sphere, blob, etc.) and for any closed Gaussian surface, the electric flux on that surface is directly related to the charge inside the surface. Mathematically, we will write this idea behind Gauss's law as: |
| | $$\Phi_{tot}=\int \vec{E} \bullet \vec{dA}=\frac{Q_{enclosed}}{\epsilon_0}$$ |
| | Where $\Phi_{tot}$ is the total electric flux through the Gaussian surface (which is calculated from the electric field $\vec{E}$ along the surface area of the Gaussian surface $d\vec{A}$) and $Q_{enclosed}$ is the amount of charge enclosed by the Gaussian surface. $\epsilon_0$ is the same constant that we used in the beginning of class: $8.85*10^{-12}\frac{C^2}{Nm^2}$. |
| |
| //__Note that the Gaussian surface is completely imaginary__// - we are not physically placing some surface around the charge. As we will talk about later, the choice of where to draw the surface and what shape to draw it is up to you; however, certain choices will lead to math that is virtually impossible, so we will want to be careful in our choice of surface. We will spend the next few pages of notes talking about the mathematical formalism for Gauss's Law, but this is the general conceptual idea behind the math. | //__Note that the Gaussian surface is completely imaginary__//, just like the Amperian Loop - we are not physically placing some surface around the charge. As we will talk about later, the choice of where to draw the surface and what shape to draw it is up to you; however, certain choices will lead to math that is virtually impossible, so we will want to be careful in our choice of surface. We will spend the next few pages of notes talking about each of the pieces of Gauss's Law, but this is the general conceptual idea behind the math. |
| |
| |
| |