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| 184_notes:changing_e [2018/05/15 17:36] – curdemma | 184_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]] | /*[[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. |
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| {{youtube>QgIz4GQgy-E}} | {{youtube>QgIz4GQgy-E}} |
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| ==== 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. |
| $$\int \vec{B} \bullet d\vec{l} = \mu_0 I_{enc}$$ | $$\int \vec{B} \bullet d\vec{l} = \mu_0 I_{enc}$$ |
| 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). |
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| ==== 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}} |