Faraday's law of induction makes use of the magnetic flux ΦB through a surface Σ, defined by an integral over a surface:
where dA is an element of surface area of the moving surface Σ(t), B is the magnetic field, and B·dA is a vector dot product. The surface is considered to have a "mouth" outlined by a closed curve denoted ∂Σ(t). When the flux changes, Faraday's law of induction says that the work done (per unit charge) moving a test charge around the closed curve ∂Σ(t), called the electromotive force (EMF), is given by:
where is the magnitude of the electromotive force (EMF) in volts and ΦB is the magnetic flux in webers. The direction of the electromotive force is given by Lenz's law.
For a tightly-wound coil of wire, composed of N identical loops, each with the same ΦB, Faraday's law of induction states that
Faraday's law of induction makes use of the magnetic flux ΦB through a surface Σ, defined by an integral over a surface:
where N is the number of turns of wire and ΦB is the magnetic flux in webers through a single loop.
In choosing a path ∂Σ(t) to find EMF, the path must satisfy the basic requirements that (i) it is a closed path, and (ii) the path must capture the relative motion of the parts of the circuit (the origin of the t-dependence in ∂Σ(t) ). It is not a requirement that the path follow a line of current flow, but of course the EMF that is found using the flux law will be the EMF around the chosen path. If a current path is not followed, the EMF might not be the EMF driving the current.
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