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Difference between revisions of "Maxwell's Equations"

(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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They are as follows:
 
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),
+
<ul> <li> <math>\oiint \mathbf{E} \cdot d\mathbf{A} = \frac{q_{enc}}{\varepsilon_0} \text{V} \cdot \text{m}</math> (Gauss's law of electricity),
−
<li> <math>\oiint \mathbf{B} \cdot d\mathbf{A} = 0</math> (Gauss's law of magnetism),
+
<li> <math>\oiint \mathbf{B} \cdot d\mathbf{A} = 0 \text{Wb}</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{E} \cdot d\mathbf{\ell} = -\frac{d}{dt} \iint \mathbf{B} \cdot d\mathbf{A} \text{V}</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).
+
<li> <math>\oint \mathbf{B} \cdot d\mathbf{\ell} = \mu_0I + \mu_0\varepsilon_0 \frac{d}{dt}\iint \mathbf{E} \cdot d\mathbf{A} \text{T} \cdot \text{m}</math> (Ampere's law).
 
</ul>
 
</ul>
−
 
+
Where:
 +
<math>\mathbf{E}</math> is the electric field in <math>\frac{\text{V}}{\text{m}}</math>,
 +
<math>\mathbf{B}</math> is the magnetic field in <math>\text{T}</math>,
 +
<math>\varepsilon_0</math> is the electric permittivity constant in <math>\frac{\text{F}}{\text{m}}</math>,
 +
<math>\mu_0</math> is the magnetic permeability constant in <math>\frac{\text{H}}{\text{m}}</math>,
 +
<math>I</math> is electric current in <math>\text{A}</math>,
 +
<math>q_{enc}</math> is the electric charge in <math>\text{C}</math>,
 +
and <math>t</math> is time in <math>\text{s}</math>.
 
{{stub}}
 
{{stub}}

Latest revision as of 15:20, 13 November 2024

Maxwell's equations are a set of four equations that govern electricity and magnetism in physics.

They are as follows:

  • $\oiint \mathbf{E} \cdot d\mathbf{A} = \frac{q_{enc}}{\varepsilon_0} \text{V} \cdot \text{m}$ (Gauss's law of electricity),
  • $\oiint \mathbf{B} \cdot d\mathbf{A} = 0 \text{Wb}$ (Gauss's law of magnetism),
  • $\oint \mathbf{E} \cdot d\mathbf{\ell} = -\frac{d}{dt} \iint \mathbf{B} \cdot d\mathbf{A} \text{V}$ (Faraday's law),
  • $\oint \mathbf{B} \cdot d\mathbf{\ell} = \mu_0I + \mu_0\varepsilon_0 \frac{d}{dt}\iint \mathbf{E} \cdot d\mathbf{A} \text{T} \cdot \text{m}$ (Ampere's law).

Where: $\mathbf{E}$ is the electric field in $\frac{\text{V}}{\text{m}}$, $\mathbf{B}$ is the magnetic field in $\text{T}$, $\varepsilon_0$ is the electric permittivity constant in $\frac{\text{F}}{\text{m}}$, $\mu_0$ is the magnetic permeability constant in $\frac{\text{H}}{\text{m}}$, $I$ is electric current in $\text{A}$, $q_{enc}$ is the electric charge in $\text{C}$, and $t$ is time in $\text{s}$. This article is a stub. Help us out by expanding it.

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