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--- 184_notes:relating_e [2017/11/01 15:14] – dmcpadden
+++ 184_notes:relating_e [2021/06/29 17:03] (current) – bartonmo
@@ Line 1: / Line 1: @@
-===== Relating back to Electric Fields =====
+Sections 22.1-22.3 in Matter and Interactions (4th edition)
-At the beginning of the notes, we said that induction and Faraday's law was the start of tying magnetic fields back to electric fields, but so far we haven't used the electric field yet. These notes will use the [[184_notes:pc_vefu|relationship between electric potential and electric field]] to make this connection more obvious.
-==== Relating Faraday's Law back to Electric Field ====
+/*[[184_notes:b_flux_t|Next Page: Changing Magnetic Field With Time]]
-We have already talked about how Faraday's Law says that when the magnetic flux is changing, it can produce an induced current or an induced voltage. If there is an induced current, this means that there are charges moving in a wire that is not (necessarily) connected to a battery. So what is actually making those charges move?
-If we go back to our equation for Faraday's Law, we have a way to relate the electric potential to the changing magnetic flux:
+[[184_notes:ind_i|Previous Page: The Curly Electric Field and Induced Current]]*/
-$$V_{ind} = - \frac{d \Phi_B}{dt}$$
-We can then use the relationship between electric potential ($V_{ind}$) and the electric field to rewrite the right hand side of the equation. Namely that:
+===== Putting All of Faraday's Law Together =====
-$$\Delta V=-\int_{r_i}^{r_f} \vec{E}\bullet d\vec{r}$$
+To summarize what we just learned, we found that a **changing magnetic flux will create a curly electric field**. This means that we now have two source of electric fields - one being the static charges (that we talked about at the beginning of the semester) and the second being changing magnetic fields.
-FIXME Find the negative problem....
+Mathematically, we represent this relationship by thinking about how curly the electric field is around a loop and relate that to the changing magnetic flux through that loop. Namely:
+$$\int \vec{E}_{nc} \bullet d\vec{l}= - \frac{d \Phi_B}{dt}$$
+We can also rewrite this to be in terms of the induced voltage or induced current in the loop if that better suits what we would like to find.
+$$V_{ind}=I_{ind}R=-\frac{d \Phi_B}{dt}$$
-So we see that:
+We also have a new right hand rule that let's us figure out what will be the direction of the induced current (or the direction of the curly electric field) in the wire.
-$$ \int \vec{E} \bullet d\vec{l} = - \frac{d \Phi_B}{dt}$$
-This tells that **the changing magnetic flux actually creates an electric field**. It is this electric field that is pushing the charges, creating the induced current and the induced electric potential. This is a very different situation than when we talked about current in circuits. Before in circuits, we said that the battery created a surface charge gradient, which in turn created an electric field in the wire and created current in the wire. In this case, we do not have battery or surface charges. Instead, it is the changing magnetic flux that creates the electric field, which in turn creates the current through the wire.
+Faraday's law is conceptually extremely important because **it tells us how electric and magnetic fields are related** (finally!). From a more practical stand point, Faraday's law provides a means of creating an electric current when there previously was not any - as long as you can provide the energy to change the flux. This is actually how electric generators work to create the electricity that comes out of the wall outlets. There is generally some sort of coil placed in a large magnetic field. The coil is then moved by some mechanical means (i.e., by wind in a turbine or by steam from burning coal or nuclear material in power plant). When the coil rotates in the magnetic field, the flux through the coil changes and creates a current that can then be used.
-Faraday's law is conceptually very important because it tells us how electric and magnetic fields are related (finally!). From a more practical stand point, Faraday's law provides a means of creating an electric current when there previously was not any. This is actually how electric generators work to create the electricity that comes out of the wall outlets. There is generally some sort of coil placed in a large magnetic field. The coil is then moved by some mechanical means (i.e., by wind in a turbine or by steam from burning coal or nuclear material in power plant). When the coil rotates in the magnetic field, the flux through the coil changes and creates a current that can then be used.