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184_notes:b_current [2020/08/23 21:42] – dmcpadden | 184_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: |
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[{{ 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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