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15.7: Maxwell's Fourth Equation

Last updated

Mar 5, 2022
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- 15.6: The Magnetic Equivalent of Poisson's Equation
- 15.8: Summary of Maxwell's and Poisson's Equations

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This is derived from the laws of electromagnetic induction.

f $\textbf{E} \cdot \textbf{ds}$ e $\textbf{E}$ is $\textbf{E}$ around the closed circuit is equal to the surface integral of its curl. The rate of change of B-flux through a circuit is the surface integral of $\dot{\textbf{B}}$ . Therefore

$\textbf{curl}\, \textbf{E} = - \dot{ \textbf{B}} \tag{15.7.1} \label{15.7.1}$

or, in the nabla notation,

$\boldsymbol{\nabla} \times \textbf{E} = - \dot{ \textbf{B}}. \tag{15.7.2} \label{15.7.2}$

This is the fourth of Maxwell's equations.

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