184_notes:b_current

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184_notes:b_current [2020/08/23 21:42] dmcpadden184_notes:b_current [2021/07/07 15:29] (current) schram45
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 {{youtube>4cIpX1HK7GM?large}} {{youtube>4cIpX1HK7GM?large}}
-==== Magnetic field from Many Charges ====+===== Magnetic field from Many Charges =====
 [{{ 184_notes:Week9_4.png?400|Magnetic field on point P from many moving charges in a wire}}] [{{ 184_notes:Week9_4.png?400|Magnetic field on point P from many moving charges in a wire}}]
  
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 We can now use the definition of [[184_notes:q_in_wires#conventional_current_vs_electron_current|current]] as the amount of charge passing a point per second ($I=\frac{dq}{dt}$) to give the Biot-Savart Law in terms of current instead of charge: We can now use the definition of [[184_notes:q_in_wires#conventional_current_vs_electron_current|current]] as the amount of charge passing a point per second ($I=\frac{dq}{dt}$) to give the Biot-Savart Law in terms of current instead of charge:
 $$\vec{B}_{tot}= \int \frac{\mu_0}{4 \pi}\frac{I \cdot d\vec{l}\times \hat{r}}{r^2}$$ $$\vec{B}_{tot}= \int \frac{\mu_0}{4 \pi}\frac{I \cdot d\vec{l}\times \hat{r}}{r^2}$$
-**Note that $I$ here is the //conventional// current**, not the electron current. Otherwise many of the pieces of this equation would be what you expected:+**Note that $I$ here is the conventional current, not the electron current**. Otherwise many of the pieces of this equation would be what you expected:
  
 [{{  184_notes:Week9_5.png?300|B field contribution of a little bit of length ($dl$) on point P}}] [{{  184_notes:Week9_5.png?300|B field contribution of a little bit of length ($dl$) on point P}}]
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 We will go into detail about how to put the pieces of this equation together in an example; however, it is important to realize that this equation doesn't really tell us anything new - we are still saying that **moving charges will create magnetic fields that point in a perpendicular direction and can be calculated for every point in space around the charge**. We also did not make very many assumptions in this derivation - only that //__we have many charges that are moving along the wire__//. Thus, this is a general equation that can be used for any current. We will go into detail about how to put the pieces of this equation together in an example; however, it is important to realize that this equation doesn't really tell us anything new - we are still saying that **moving charges will create magnetic fields that point in a perpendicular direction and can be calculated for every point in space around the charge**. We also did not make very many assumptions in this derivation - only that //__we have many charges that are moving along the wire__//. Thus, this is a general equation that can be used for any current.
-==== Magnetic Field from a Very Long Wire ====+===== Magnetic Field from a Very Long Wire =====
 [{{  184_notes:Week9_6.png?300|Problem set up to find the magnetic field at a point from a very long wire}}] [{{  184_notes:Week9_6.png?300|Problem set up to find the magnetic field at a point from a very long wire}}]
 Let's look at a particular example of finding the magnetic field a distance $s$ away from a very long wire with some //__constant, steady state current__// I flowing from top to bottom. Since the wire is very long, we will //__assume for our purposes that it stretches from $+\infty$ to $-\infty$ in the y direction__//. If we start with the general magnetic field equation for a current, then we can start to fill in the pieces. Let's look at a particular example of finding the magnetic field a distance $s$ away from a very long wire with some //__constant, steady state current__// I flowing from top to bottom. Since the wire is very long, we will //__assume for our purposes that it stretches from $+\infty$ to $-\infty$ in the y direction__//. If we start with the general magnetic field equation for a current, then we can start to fill in the pieces.
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 ==== Examples ==== ==== Examples ====
-[[:184_notes:examples:Week10_current_segment|Magnetic Field from a Current Segment]]+  * [[:184_notes:examples:Week10_current_segment|Magnetic Field from a Current Segment]] 
 +    * Video Example: Magnetic Field from a Current Segment 
 +  * [[:184_notes:examples:Week10_current_ring|Challenge Example: Magnetic Field from a Ring of Current]] 
 +    * Video Example: Magnetic Field from a Ring of Current 
 +{{youtube>nGrFo80MMzM?large}} 
 +{{youtube>HN0cHcbYcSo?large}} 
  
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  • Last modified: 2020/08/23 21:42
  • by dmcpadden