Focus Question: What is the purpose of Maxwell’s Equations?
Maxwell’s equations are four equations that unite electricity and magnetism and can be used (along with Lorentz force) as the basis of all phenomena in these areas.
Gauss’s Law – The total flux through any closed surface equals the net charge inside that surface divided by the permittivity of free space.
$
\oint E \cdot d A=\frac{Q}{\varepsilon_0}
$
* Charges create electric fields.
Gauss’s Law for Magnetism – The net magnetic flux through a closed surface is zero.
$
\oint B \cdot d A=0
$
*Isolated monopoles cannot exist.
- Gauss’s Law for Magnetism – The net magnetic flux through a closed surface is zero.
$
\oint B \cdot d A=0
$
*Isolated monopoles cannot exist.
- Ampere’s Law – The line integral of the magnetic field around any closed path is determined by the net current and the rate of change of electric flux through any surface bounded by that path.
$
\oint B \cdot d l=\mu_0 I+\varepsilon_0 \mu_0 \frac{d \phi}{d t}
$
* An electric current and a changing electric field create a magnetic field. - Faraday’s Law of Induction – The line integral of the electric field around any closed path equals the rate of change of magnetic flux through any closed surface bounded by that path.
$
\oint E \cdot d r=\varepsilon=-\frac{d \phi}{d t}
$
${ }^* A$ changing magnetic field creates an electric field.