# Equation BankΒΆ

• ampere_maxwell_time

(1)$\boldsymbol{\nabla} \times \mathbf{h} = \mathbf{j} + \frac{\partial \mathbf{d}}{\partial t}$
• dcr_fwd

(2)$\boldsymbol{\nabla} \cdot \sigma\boldsymbol{\nabla}\phi = \boldsymbol{\nabla}\cdot\mathbf{j}_{source}.$
• electromotive_force_time

(3)$\mathcal{E} = - \oint_C {\bf e} \cdot d{\bf l} = V$

(4)$\mathcal{E} = - \, \frac{\partial {\boldsymbol \Phi_b}}{\partial t}$

(5)$\boldsymbol{\nabla} \times \mathbf{e} = -\frac{\partial \mathbf{b}}{\partial t}$

(6)$\nabla \times {\bf E} = - \, i \omega {\bf B}$

(7)$\nabla \times {\bf e} = - \, \frac{\partial {\bf b}}{\partial t}$

(8)$\oint_C {\bf E} \cdot d{\bf l} = - \, i \omega \int_A {\bf B} \cdot \hat n \, da$

(9)$\oint_C {\bf e} \cdot {\bf d}{\bf l} = - \int_S \frac{\partial {\bf b}}{\partial t} \cdot \hat {\bf n} \, da,$
• gauss_electric_frequency

(10)$\boldsymbol{\nabla \cdot} \mathbf{D} = \rho_f$
• gauss_electric_time

(11)$\boldsymbol{\nabla \cdot} \mathbf{d} = \rho_f$
• gauss_magnetic_frequency

(12)$\nabla \cdot \mathbf{B} = 0$
• gauss_magnetic_int_time

(13)$\oint_S \mathbf{b} \cdot \mathbf{da} = 0$
• gauss_magnetic_time

(14)$\boldsymbol{\nabla \cdot} \mathbf{b} = 0$
• magnetic_flux_freq

(15)${\boldsymbol \Phi_B} = \int_A {\bf B} \cdot \hat n \, da$
• magnetic_flux_time

(16)${\boldsymbol \Phi_b} = \int_A {\bf b} \cdot \hat {\bf{n}} \, da$
• ohms_law_freq

(17)$\mathbf{J} = \sigma \mathbf{E}$
• ohms_law_time

(18)$\mathbf{j} = \sigma \mathbf{e}$