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馬克士威方程組者，凡偏微分方程四。合以勞侖茲力，實肇電磁學之基。蓋明電場、磁場，皆為電荷、電流與夫場之變所生也[一]。
其列式如左：
∇ ⋅ E = ρ ε 0 ∇ ⋅ B = 0 ∇ × E = − ∂ B ∂ t ∇ × B = μ 0 ( J + ε 0 ∂ E ∂ t ) {\textstyle {\begin{aligned}\nabla \cdot \mathbf {E} \,\,\,&={\frac {\rho }{\varepsilon _{0}}}\\\nabla \cdot \mathbf {B} \,\,\,&=0\\\nabla \times \mathbf {E} &=-{\frac {\partial \mathbf {B} }{\partial t}}\\\nabla \times \mathbf {B} &=\mu _{0}\left(\mathbf {J} +\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\right)\end{aligned}}}
按： E {\displaystyle \mathbf {E} } 為電場， B {\displaystyle \mathbf {B} } 為磁場， ρ {\displaystyle \rho } 為電荷密度， J {\displaystyle \mathbf {J} } 為電流密度， ε 0 {\displaystyle \varepsilon _{0}} 為真空電容率， μ 0 {\displaystyle \mu _{0}} 為真空磁導率；至於 ∇ ⋅ {\displaystyle \nabla \cdot } 、 ∇ × {\displaystyle \nabla \times } ，則各表散度、旋度之算符也。
