# Help with Faraday’s law of induction

What does faraday’s equation for induction gives us ? Now my book says it’s just the induced emf and other times it’s the average induced emf and i’am confused. For example , the book says that the average induced emf in a dynamo in a quarter cycle equals : -NBA*4f And that is derived from the farday’s equation : emf=-N*(Rate of change in magnetic flux) ... and other times when using the same equation it’s jus the ‘induced emf’ .. what is the difference?

Faraday's law of induction looks as follows:

$\epsilon=-\frac{d\Phi_B}{dt}$

The emk generated is proportional to the change in flux through the loop. With the emphasis on change. So in order to constantly generate an emk, we need a constantly changing magnetic field through our loop as well. This is usually done using a periodic signal such as a sine wave.

If you apply a sine wave to the magnetic field, you will also generate an emk that looks like a sine wave.

$\epsilon=-\frac{d\ sin(2\pi ft)}{dt}=-2\pi f\cdot cos(2\pi ft)$

You can also do a Fourier transform on Faraday's law, which makes it look like this:

$\epsilon(j\omega)=-j\omega \Phi_B(j\omega)$

And so you can see that $|\epsilon(j\omega)|=\omega\cdot|\Phi_B(j\omega)|$.

Just like with any AC signal, you can discuss its properties using the "average power" or "RMS voltage", etc. of the sine wave. This is most likely what your book is doing.