The laws of Electromagnetic induction

The phenomena of electromagnetic induction are described in two laws.

The first of these Faraday's law, states:

when the magnetic flux through a coil is made to vary, a voltage is set up.The magnitude of the induced voltage is proportional to the rate of change of flux".

${\displaystyle \epsilon =-{\frac {d\phi }{dt}}}$

The second law , known as Lenz's law concerns the direction of the induced voltage.

A change of flux threading a closed circuit induces a voltage and sets up a current ; the direction of this current is such that its magnetic field tends to oppose the change in flux

${\displaystyle \phi =-BL=-NLI}$

The opposition to the change of flux through a circuit depends on the presence of current in the circuit; if the coil is open-circuited, the induced voltage cannot set up a current and there is no opposition.

Electromagnetic Induction

For a Faraday's coil of N circular loops

When the coil conducts current it generates magnetic field intensity

${\displaystyle B=LI={\frac {N\mu }{l}}I}$

And potential voltage

${\displaystyle {\frac {dB}{dt}}=L{\frac {dI}{dt}}}$

Magnetic field generates reverse induced magnetic field intensity

${\displaystyle \phi =-NB=-NLI}$

And induced potential voltage

${\displaystyle \epsilon =-{\frac {d\phi }{dt}}=-L{\frac {dB}{dt}}=-NL{\frac {dI}{dt}}}$

In summary,

Magnetic field intensity	${\displaystyle B}$	${\displaystyle LI}$
Induced Magnetic field intensity	${\displaystyle \phi }$	${\displaystyle -NB=-NLI}$
Magnetic Potential Difference	${\displaystyle V_{L}}$	${\displaystyle {\frac {dB}{dt}}=L{\frac {dI}{dt}}}$
Induced Magnetic Voltage	${\displaystyle \epsilon }$	${\displaystyle -{\frac {d\phi }{dt}}=-N{\frac {dB}{dt}}=-NL{\frac {dI}{dt}}}$