We know from Faraday's law of induction 
the strength of the voltage induced in a
loop. We know that's proportional to the
rate of change of magnetic flux through
that loop and it's also proportional to
the number of turns that you apply to
that loop. But we haven't yet discussed
the direction - does it go clockwise or
anti-clockwise? And there are so many
right-hand rules in electromagnetism, it
would be very confusing if we were to add
yet another and there are so many
different things you'd have to add into
your mind to get this correct, but it
turns out there's a really simple way of
figuring it out using the conservation of
energy. Using the conservation of energy
when you're talking about induction is
usually described as following Lenz's
law.
It was developed by Heinrich Lenz in 1834
before the ideas of energy and
conservation of energy had really
reached their final form though these
days we can see that they are one in the
same.
So Lenz's law states: (...)
that you can't get something for nothing.
If I have a coil making a magnetic field
and then I have another coil that's
going to have a magnetic field induced
in it. Now if I'm putting current in that
first coil it's gonna make a magnetic
field that reaches right down into the
second coil and remember that this is often
helped by having a bar or some
ferromagnetic material running through
the two of them. However the key point is: 
when we change the current, we're going
to change the magnetic field. And when we change the magnetic field in the first
coil, we change the magnetic field in the
second coil and that changes the flux
flowing through it. And that's going to
induce some kind of current in the second
coil. And the question is: which way
should it go? So if we take an example
that this current increases. If that
current increases that's going  to
increase the strength of the magnetic
field, which means it's going to increase
the amount of magnetic flux going to the
second coil. Now if an increasing
magnetic flux going through that coil caused a voltage that would increase the magnet
field, even more, then you would have a
runaway effect. We'd have more flux, so we'd
would get more of that voltage and so we
get more current, so we get more magnetic
field and then so we get more of that voltage
and it will go on to infinity. And so
that obviously can't be the way it works.
And so the voltage that's induced has to
make a current that resists that
magnetic field change. So to resist the
flux going up, we need some magnetic
field made that way and if I look at
that and that wire I see that I need the
current to be going out of the page here,
and that will make a magnetic field that
goes up, and so I'm going to need the
current to be flowing in that direction
around this loop and so we're going to
have to have a potential going in that
direction. And so if the magnetic flux is
increasing we know that the potential
has to be going that way and if the magnetic
flux is decreasing then it would go
the other way.
