45 lines
1.1 KiB
Markdown
45 lines
1.1 KiB
Markdown
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title = "Electromagnetism"
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author = ["Dehaeze Thomas"]
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draft = false
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category = "Mechanics and Physics"
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## Maxwell equations for magnetics {#maxwell-equations-for-magnetics}
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### Gauss law {#gauss-law}
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"Magnetic fieldlines are closed loop."
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\begin{equation}
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\oiint\_S (\bm{B} \cdot \hat{\bm{n}}) dS = 0
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\end{equation}
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### Faraday's law {#faraday-s-law}
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A changing magnetic field causes an electric field over a wire
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\begin{equation}
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\oint\_L \bm{E} \cdot d\bm{l} = -\frac{d}{dt} \iint\_S(\bm{B} \cdot \bm{n}) dS
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\end{equation}
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The line-integral of the electrical field over a closed loop L equals the change of the field through the open surface S bounded by the loop L.
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This is a voltage source (EMF), where the current is driven in the direction of the electric field.
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### Ampère's law {#ampère-s-law}
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"Current through a wire gives a magnetic field".
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\begin{equation}
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\oint\_L \bm{B} \cdot dl = \mu\_0 I
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\end{equation}
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The line integral of the magnetic field over a closed loop L is proportional to the current through the surface S enclosed by the loop L.
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