Faraday's Law

As a PDE: \[ \nabla \times \mathbf{E} = -\frac{ \partial \mathbf{B}}{\partial t}. \]

Here:

• $E$: electric field, also called • the electric field intensity;
• $B$: magnetic field, also called • the magnetic induction• the magnetic field density, • the magnetic flux density;

Now, reconsidered as differential forms:

• $E$: 1-form on $TM$ or the primal complex in the discrete case,
• $B$: 2-form on $TM$ or on the primal complex in the discrete case,

For these forms: $$\oint_P E = -\frac{d}{dt} \int_A B.$$

And: $$d E dt= -d_t B.$$