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184_notes:changing_e [2017/11/30 22:19] – [Extra Term to Ampere's Law] dmcpadden184_notes:changing_e [2021/07/22 13:47] (current) – schram45
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 Section 23.1 in Matter and Interactions (4th edition) Section 23.1 in Matter and Interactions (4th edition)
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 +/*[[184_notes:ac|Previous Page: Alternating Current]]*/
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 ===== Changing Electric Fields ===== ===== Changing Electric Fields =====
-We have spent the last three weeks talking about what happens when you have a changing magnetic field. We found that this changing magnetic field creates a curly electric field. A changing magnetic field then became another source of electric fields. You may then be wondering what happens if you have a changing electric field? We have already seen through Faraday's Law that electric and magnetic fields are related, so how do we account for a changing electric field? Perhaps unsurprisingly, **a changing electric field is another source of curly magnetic fields**. These notes will talk about how we amend Ampere's Law to account for a changing electric field.+We have spent the last two weeks talking about what happens when you have a changing magnetic field. We found that this changing magnetic field creates a curly electric field. A changing magnetic field then became another source of electric fields. You may then be wondering what happens if you have a changing electric field? We have already seen through Faraday's Law that electric and magnetic fields are related, so how do we account for a changing electric field? Perhaps unsurprisingly, **a changing electric field is another source of curly magnetic fields**. These notes will talk about how we amend Ampere's Law to account for a changing electric field.
  
 {{youtube>QgIz4GQgy-E}} {{youtube>QgIz4GQgy-E}}
  
-==== Extra Term to Ampere's Law ====+===== Extra Term to Ampere's Law =====
 From Faraday's Law, we learned that a changing magnetic field creates a curly electric field. As a similar parallel, we are now saying that a changing electric field (with time) creates a curly magnetic field. Conveniently, we already have an equation that describes a curly magnetic field: Ampere's Law. From Faraday's Law, we learned that a changing magnetic field creates a curly electric field. As a similar parallel, we are now saying that a changing electric field (with time) creates a curly magnetic field. Conveniently, we already have an equation that describes a curly magnetic field: Ampere's Law.
 $$\int \vec{B} \bullet d\vec{l} = \mu_0 I_{enc}$$ $$\int \vec{B} \bullet d\vec{l} = \mu_0 I_{enc}$$
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 This term that we added to Ampere's Law functions in much the same way as Faraday's law. If we can calculate the changing electric flux through a loop, then we can use that to find the magnetic field that curls around that loop. In the example below, we use a charging capacitor to illustrate how this can done; however, for the purposes of this class, we will primarily rely on this idea conceptually (rather than asking you to calculate the magnetic field from a changing electric flux).  This term that we added to Ampere's Law functions in much the same way as Faraday's law. If we can calculate the changing electric flux through a loop, then we can use that to find the magnetic field that curls around that loop. In the example below, we use a charging capacitor to illustrate how this can done; however, for the purposes of this class, we will primarily rely on this idea conceptually (rather than asking you to calculate the magnetic field from a changing electric flux). 
  
-==== Why this Matters ====+===== Why this Matters =====
 With this final piece of the puzzle, we can actually say something really important about how electric and magnetic fields work. If we //__assume that there are no current-carrying wires nearby__//, then we have a set of two equations that say that: With this final piece of the puzzle, we can actually say something really important about how electric and magnetic fields work. If we //__assume that there are no current-carrying wires nearby__//, then we have a set of two equations that say that:
  
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 ==== Examples ==== ==== Examples ====
-[[:184_notes:examples:Week14_b_field_capacitor|Magnetic Field from a Charging Capacitor]]+  * [[:184_notes:examples:Week14_b_field_capacitor|Challenge: Magnetic Field from a Charging Capacitor]] 
 +    * Video Example: Magnetic Field from a Charging Capacitor 
 +{{youtube>mWH9WHKFyTE?large}} 
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