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| 184_notes:motiv_amp_law [2018/07/19 13:45] – [Motivating Ampere's Law] curdemma | 184_notes:motiv_amp_law [2018/07/24 14:36] – [Motivating Ampere's Law] curdemma |
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| ====== Motivating Ampere's Law ====== | ====== Motivating Ampere's Law ====== |
| This week, we are going to talk about a mathematical shortcut for finding magnetic fields, called Ampere's Law. While there are definitely some differences between Gauss's Law and Ampere's Law, the process for solving these kinds of problems should seem very similar - starting with the fact that we require highly symmetric magnetic fields to be able to solve Ampere's Law. | So far in this course, we have talked about the sources of electric fields, how electric fields are applied to circuits, and the sources of magnetic fields. Over the next two weeks, we are going to talk about two mathematical shortcuts for calculating the electric and magnetic fields: Gauss's Law and Ampere's Law. We'll start by talking about Ampere's Law, which is an alternative method for calculating the magnetic field. We require highly symmetric magnetic fields to be able to solve Ampere's Law. Next week we will learn about Gauss's Law, the electric field equivalent of Ampere's Law. |
| {{youtube>M6FRK4aY90E?large}} | {{youtube>M6FRK4aY90E?large}} |
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| ===== What is Ampere's Law? ===== | ===== What is Ampere's Law? ===== |
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| Given the analogy to Gauss' Law, you might think the approach is going to be similar - we integrate the magnetic field over an imagined closed surface area and that tells us something. Unfortunately, as far as a we know ([[http://physicstoday.scitation.org/doi/full/10.1063/PT.3.3328|and people are looking!]]), there are no single magnetic 'charges', termed '[[https://en.wikipedia.org/wiki/Magnetic_monopole|magnetic monopoles]].' That is, everywhere we look magnetic poles come in pairs - a north pole and a south pole. For example, if we think about enclosing a bar magnet with a Gaussian-like surface (an imaginary bubble), the magnetic flux through the whole bubble would be zero! For every magnetic field vector pointing into the bubble, there is also a magnetic field vector pointing out. | As far as a we know ([[http://physicstoday.scitation.org/doi/full/10.1063/PT.3.3328|and people are looking!]]), there are no single magnetic 'charges', termed '[[https://en.wikipedia.org/wiki/Magnetic_monopole|magnetic monopoles]].' That is, everywhere we look magnetic poles come in pairs - a north pole and a south pole. For example, if we think about enclosing a bar magnet with a Gaussian-like surface (an imaginary bubble), the magnetic flux through the whole bubble would be zero! For every magnetic field vector pointing into the bubble, there is also a magnetic field vector pointing out. |
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| {{184_notes:Week11_flux_vol.png?300 }} | [{{184_notes:Week11_flux_vol.png?300|Permanent magnet enclosed in an "imaginary bubble" }}] |
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| It turns out that this is true no matter what the source of your magnetic field is (bar magnet, moving charge, or current-carrying wire) - the integral of the magnetic field over a //closed// surface is always zero. That is, a closed volume never has net magnetic flux //__assuming that the magnetic field is constant__//. Mathematically, we would write this as: | It turns out that this is true no matter what the source of your magnetic field is (bar magnet, moving charge, or current-carrying wire) - the integral of the magnetic field over a //closed// surface is always zero. That is, a closed volume never has net magnetic flux //__assuming that the magnetic field is constant__//. Mathematically, we would write this as: |