Difference between revisions of "Lecture 3."
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The most important case for electromagnetic equipment (sensors, actuators, motors, etc.) is the quasistatic case often referred to as the eddy current or magnetodynamic case. For quasistatic electromagnetic field we can neglect the displacement current density term <math>\partial \vec{D}/\partial t</math>, which gives Maxwell's equations to the following form | The most important case for electromagnetic equipment (sensors, actuators, motors, etc.) is the quasistatic case often referred to as the eddy current or magnetodynamic case. For quasistatic electromagnetic field we can neglect the displacement current density term <math>\partial \vec{D}/\partial t</math>, which gives Maxwell's equations to the following form | ||
| + | |||
| + | {| width=60%, | ||
| + | |- valign=top | ||
| + | | width=40%, style="text-align: right;" | | ||
| + | <math>\nabla\times\vec{H}=\vec{J}</math> | ||
| + | | width=20%, style="text-align: left;" | | ||
| + | Ampere's law, | ||
| + | |- valign=top, | ||
| + | | width=40%, style="text-align: right;" | | ||
| + | <math>\nabla\times\vec{E}=-\frac{\partial \vec{B}}{\partial t}</math> | ||
| + | | width=20%, style="text-align: left;" | | ||
| + | Faraday's law, | ||
| + | |- valign=top | ||
| + | | width=40%, style="text-align: right;" | | ||
| + | <math>\nabla\cdot\vec{B}(\vec{r},t)=0</math> | ||
| + | | width=20%, style="text-align: left;" | | ||
| + | Gauss's law (magnetic). | ||
| + | |} | ||
| + | |||
| + | === Magnetic Vector Potential === | ||
| + | According to <math>\nabla\cdot\vec{B}(\vec{r},t)=0</math> the magnetic flux density is conservative and therefore can be described by the '''curl''' of a vector | ||
| + | |||
| + | <math> \vec{B} = \nabla\times\vec{A}, | ||
| + | |||
| + | where <math>\vec{A} is the magnetic vector potential [Wb/m]. This ansatz results for Faraday's law in the following relation | ||
| + | |||
| + | |||
</blockquote> | </blockquote> | ||
Revision as of 21:46, 12 March 2019
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Coupled Finite Element Method / Time-Dependent Magnetic Field | |
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Instructor
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Teaching Assistants:
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Contents
Csatolt végeselem-módszer (FEM)
Quasistatic Electromagnetic Field
The most important case for electromagnetic equipment (sensors, actuators, motors, etc.) is the quasistatic case often referred to as the eddy current or magnetodynamic case. For quasistatic electromagnetic field we can neglect the displacement current density term [math]\partial \vec{D}/\partial t[/math], which gives Maxwell's equations to the following form
[math]\nabla\times\vec{H}=\vec{J}[/math]
Ampere's law,
[math]\nabla\times\vec{E}=-\frac{\partial \vec{B}}{\partial t}[/math]
Faraday's law,
[math]\nabla\cdot\vec{B}(\vec{r},t)=0[/math]
Gauss's law (magnetic).
Magnetic Vector Potential
According to [math]\nabla\cdot\vec{B}(\vec{r},t)=0[/math] the magnetic flux density is conservative and therefore can be described by the curl of a vector
<math> \vec{B} = \nabla\times\vec{A},
where <math>\vec{A} is the magnetic vector potential [Wb/m]. This ansatz results for Faraday's law in the following relation
