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)\[\mathcal{E} = - \oint_C {\bf e} \cdot d{\bf l} = V\]
  • faraday_lenz_time

    (4)\[\mathcal{E} = - \, \frac{\partial {\boldsymbol \Phi_b}}{\partial t}\]
  • faraday_time

    (5)\[\boldsymbol{\nabla} \times \mathbf{e} = -\frac{\partial \mathbf{b}}{\partial t}\]
  • faradays_law_diff_freq

    (6)\[\nabla \times {\bf E} = - \, i \omega {\bf B}\]
  • faradays_law_diff_time

    (7)\[\nabla \times {\bf e} = - \, \frac{\partial {\bf b}}{\partial t}\]
  • faradays_law_int_freq

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

    (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)\[\mathbf{j} = \sigma \mathbf{e}\]