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--- 184_notes:e_flux [2017/09/25 15:50] – [Examples] tallpaul
+++ 184_notes:e_flux [2021/05/29 19:08] (current) – schram45
@@ Line 1: / Line 1: @@
 Section 21.2 in Matter and Interactions (4th edition)
+/*[[184_notes:eflux_curved|Next Page: Electric Flux through Curved Surfaces]]
+[[184_notes:gauss_motive|Previous Page: Motivation for Gauss's Law]]*/
 ===== Electric Flux and Area Vectors =====
 In general, any sort of **flux** is how much of something goes through an area. For example, we could think of a kid's bubble wand in terms of the air flux (from you blowing) through the circle (with the bubble solution in it). If you wanted to make bigger bubbles or make many more bubbles, you could do two things: increase the air flow or get a bubble wand with a bigger circle. Both of these actions (increasing the area and increasing the amount of air) will result in a larger "air flux" through the bubble wand. It's probably worth mentioning that we have assumed that you are holding the bubble wand so the circle is perpendicular to the air flow. If instead you rotate the wand 90 degrees, you will not get any bubbles since there is no air that is actually going through the circle part of the bubble wand. So the air flux not only depends on the amount of air and the area of circle, but also on how those two are oriented relative to each other. The idea of flux can be useful in many different contexts (i.e. fluids, electricity, air, etc.), but for any kind of flux, these are still the three conditions that matter: (1) the strength/amount, (2) the area, and (3) the orientation.
-**Electric flux** then is the strength of the electric field on a surface area or rather the amount of the electric field that goes through an area. For electric flux, we need to consider: the strength of the electric field, the area that the field goes through, and the orientation of electric field relative to the area. These notes will introduce the mathematics behind electric flux, which we will use to build Gauss's Law later.
+**Electric flux** then is the strength of the electric field on a surface area or rather the amount of the electric field that goes through an area. For electric flux, we need to consider: the strength of the electric field, the area that the field goes through, and the orientation of electric field relative to the area. These notes will introduce the mathematics behind electric flux, which we will use to build Gauss's Law.
 {{youtube>vmECMek6Lm8?large}}
@@ Line 43: / Line 48: @@
 Thus, we can write the electric flux for a //__constant electric field through a flat area__// as:
-$$\Phi_e=\vec{E} \cdot \vec{A}$$
+$$\Phi_e=\vec{E} \bullet \vec{A}$$
 where  $\vec{E}$  is the electric field vector,  $\vec{A}$  is the area vector, and  $\Phi_e$  is the electric flux. Note that because of the dot product, __electric flux is a scalar__ number (it has no direction). Electric flux will be positive if the area and electric field vectors point in the same direction or it will negative if they point in the opposite direction. The units of electric flux would be the units of electric field time the units of area so  $\frac{N}{C}m^2$  or  $\frac{V}{m}m^2=Vm$ . We could also [[184_notes:math_review#Vector_multiplication|simplify the dot product]] by using the angle between the two vectors ( $\vec{E}$  and  $\vec{A}$  in this case):
-$$\Phi_e=\vec{E} \cdot \vec{A}=|\vec{E}||\vec{A}|cos(\theta)$$
+$$\Phi_e=\vec{E} \bullet \vec{A}=|\vec{E}||\vec{A}|cos(\theta)$$
 ==== Electric Flux through a Flat (Closed) Area ====
@@ Line 82: / Line 87: @@
 ==== Examples ====
-[[:184_notes:examples:Week5_flux_tilted_surface|Flux through a Tilted Surface]]
+  * [[:184_notes:examples:Week5_flux_tilted_surface|Flux through a Tilted Surface]]
+    * Video Example: Flux through a Tilted Surface
-[[:184_notes:examples:Week5_flux_cylinder|Flux through a Closed Cylinder]]
+  * [[:184_notes:examples:Week5_flux_cylinder|Flux through a Closed Cylinder]]
+{{youtube>vU56A8865zs?large}}