Now we look at the calculus
based version of Faraday's law.
As a quick reminder
of what we've already
seen with Faraday's law,
a changing magnetic flux
creates an induced emf, and how
much emf depends on the rate.
When I had the average formula,
I used the delta symbol
to represent my change.
And so it was the
delta phi per delta t
or the change in flux divided
by the change in time.
Well, when I shift over
to a calculus view,
that means I'm taking
the continuous limit
as that delta-t goes to 0.
And it becomes defy dt.
Now let's look at this equation
a little bit more carefully.
So again over here on my left,
I've got the symbol, epsilon.
And that represents
my induced emf.
It's not the
average emf anymore.
It's the actual induced emf at
a particular moment in time.
I still have my
minus sign referring
to the direction and
the N representing
the number of loops.
But now I want to take
this whole quantity
and represent it as one
thing, defy dt, which
is the rate of flux change.
Now another way you
could write this equation
to kind of emphasize
this is to look
at the derivative with respect
to time of the magnetic flux,
emphasizing, again, that I'm
looking at the magnetic flux,
and I have to take the
derivative with respect
to time.
This is one
mathematical operation
that operates on my flux.
So there's no dividing by time
or anything like that on this.
You're simply looking at
the rate of change of flux.
So that's our Faraday's law
in our Calculus based version.
