4.1 Faraday's law

Faraday's law

The magnetic flux is $${\Phi }_M=\int \vec{B}\cdot d\vec{A}$$ A device that can maintain a potential difference, despite the flow of currentis a source of electromotive force. (EMF) The definition is mathematically $$\varepsilon =\oint \vec{E}\cdot d\vec{s}$$ Faraday's law statesthat $$\varepsilon =-\frac{\partial {\Phi }_M}{\partial t}$$ This is simply an experimental fact.

Faraday's law could also be written $$\oint \vec{E}\cdot d\vec{s}=-\frac{\partial }{\partial t}\int \vec{B}\cdot d\vec{A}$$

I will leave it as a problem to show that this can also be written $$\vec{\nabla }\times \vec{E}=-\frac{\partial \vec{B}}{\partial t}\text{.}$$