[{{ 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=dqdt) 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=dqdt) to give the Biot-Savart Law in terms of current instead of charge:
→Btot=∫μ04πI⋅d→l׈rr2
→Btot=∫μ04πI⋅d→l׈rr2
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**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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**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.
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==== Magnetic Field from a Very Long Wire ====
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===== 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 +∞ to −∞ 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 +∞ to −∞ 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 ====
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[[:184_notes:examples:Week10_current_segment|Magnetic Field from a Current Segment]]
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* [[:184_notes:examples:Week10_current_segment|Magnetic Field from a Current Segment]]
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* Video Example: Magnetic Field from a Current Segment
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* [[:184_notes:examples:Week10_current_ring|Challenge Example: Magnetic Field from a Ring of Current]]
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* Video Example: Magnetic Field from a Ring of Current