Art of Problem Solving

Maxwell's equations: Difference between revisions

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Created page with "'''Maxwell's equations''' are a set of four equations that govern electricity and magnetism in physics. They are as follows: <ul> <li> <math>\oiint \mathbf{E} \cdot d\ma..."
 
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'''Maxwell's equations''' are a set of four equations that govern electricity and magnetism in [[physics]].
#REDIRECT[[Maxwell's Equations]]
 
They are as follows:
 
<ul> <li> <math>\oiint \mathbf{E} \cdot d\mathbf{A} = \frac{q_{enc}}{\varepsilon_0}</math> (Gauss's law of electricity),
<li> <math>\oiint \mathbf{B} \cdot d\mathbf{A} = 0</math> (Gauss's law of magnetism),
<li> <math>\oint \mathbf{E} \cdot d\mathbf{\ell} = -\frac{d}{dt} \iint \mathbf{B} \cdot d\mathbf{A}</math> (Faraday's law),
<li> <math>\oint \mathbf{B} \cdot d\mathbf{\ell} = \mu_0\iint \mathbf{J} \cdot d\mathbf{A} + \mu_0\varepsilon_0 \frac{d}{dt}\iint \mathbf{E} \cdot d\mathbf{A}</math> (Ampere's law).
</ul>
 
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Latest revision as of 19:48, 4 May 2022