Maxwell's equations

Also called Maxwell equations, The four Maxwell equations

Maxwell's equations are the four laws that together describe electromagnetism: Gauss's law, Gauss's law for magnetism, Faraday's law of induction, and Ampere's law with Maxwell's addition. AP Physics C names and numbers them in exactly that order.

AP Physics C: E&M does not teach these as a block. It states the same sentence four times, once in each unit where a law turns up, and assigns that law a number.

Number	Law	Form the CED prints	Source
First	Gauss's law	$\oint \vec{E} \cdot d\vec{A} = q_{\text{enc}} / \varepsilon_0$	EK 8.6.A.6
Second	Gauss's law for magnetism	$\oint \vec{B} \cdot d\vec{A} = 0$	EK 12.1.A.3.i
Third	Faraday's law of induction	$\mathcal{E} = \oint \vec{E} \cdot d\vec{\ell} = -\dfrac{d\Phi_B}{dt}$	EK 13.2.A.3
Fourth	Ampere's law with Maxwell's addition	$\oint \vec{B} \cdot d\vec{\ell} = \mu_0 I + \mu_0 \varepsilon_0 \dfrac{d\Phi_E}{dt}$	EK 12.4.A.4

The equation sheet is not identical to that table. It prints the first three in those forms, and prints Ampere's law as $\oint \vec{B} \cdot d\vec{\ell} = \mu_0 I_{\text{enc}}$ , with no correction term. The corrected fourth equation appears in the course framework and not in the appendix.

Two boundary statements set the ceiling. Topic 12.4 says the course does not expect students to use Maxwell's fourth equation with a changing electric field, but does expect them to understand that a changing electric field generates a magnetic field. Topic 13.2 attaches $c = 1/\sqrt{\varepsilon_0 \mu_0}$ to EK 13.2.A.4 and then says students are not expected to derive the speed of light from Maxwell's equations, the relationship being included solely as a pointer to later courses.

The differential forms, the ones written with divergence and curl, appear nowhere in the CED. Treat them as beyond the course. AP Physics 2 does not have Maxwell's equations at all: its only Maxwell is the Maxwell-Boltzmann distribution, in thermodynamics.

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