Differences

This shows you the differences between two versions of the page.

--- 184_notes:what_happens [2021/04/08 13:50] – dmcpadden
+++ 184_notes:what_happens [2021/04/08 13:56] – dmcpadden
@@ Line 30: / Line 30: @@
 [{{  184_notes:week12_4.png?200|Fig. 4: Curly electric field (or non-Coulombic Electric Field)}}]
-Notationally, because this is a curly electric field, which is very different than the other kinds of electric fields that we have talked about, we will write a curly electric field from a changing magnetic field as $\vec{E}_{nc}$ because it is this as the "non-coulombic" electric field, whereas we will keep $\vec{E}$ to be for an electric field from static charges.
+Because this is a curly electric field, which is very different than the other kinds of electric fields that we have talked about, we will write a curly electric field from a changing magnetic field as $\vec{E}_{nc}$. The "nc" is because this is referred to as the "non-coulombic" electric field, whereas we will keep $\vec{E}$ to be for an electric field from static charges.
 Mathematically, we represent this relationship using [[https://en.wikipedia.org/wiki/Curl_(mathematics)|a vector operation called curl]]; however, for this class, we will generally simplify the curl operation (using [[https://en.wikipedia.org/wiki/Stokes%27_theorem|Stokes' Theorem]]) to be:
-$$-\int \vec{E}_{nc} \bullet d\vec{l} = \frac{d\Phi_{B}}{dt}$$
+$$\int \vec{E}_{nc} \bullet d\vec{l} = - \frac{d\Phi_{B}}{dt}$$
-Where this equation (called [[https://en.wikipedia.org/wiki/Faraday%27s_law_of_induction|Faraday's Law]]) says that the electric field around a loop is equal to the change in the magnetic flux through that loop. The next few pages of notes will go through each part of this equation in detail (including where the negative sign came from) and how to use it, but it's important to remember that the relationship behind this equation is that a changing magnetic field will create a curly electric field.
+Where this equation (called [[https://en.wikipedia.org/wiki/Faraday%27s_law_of_induction|Faraday's Law]]) says that the curly electric field ($ \vec{E}_{nc}$) around a loop ($d\vec{l}$) is equal to the //opposite// change in the magnetic flux ($\frac{d\Phi_{B}}{dt}$) through that loop. The next few pages of notes will go through each part of this equation in detail (including where the negative sign came from) and how to use it, but it's important to remember that the relationship behind this equation is that a changing magnetic field will create a curly electric field.
 ==== Examples ====
 Video example showing a constant flux, rotating loop, and the magnetic being pushed towards and away from the loop:
 {{youtube>mMh9pyxa0o8?large}}