in this video we introduced the idea of electromagnetic induction then we introduced
lenses law and the idea of magnetic flux as a way to talk about induction more precisely
finally we work a couple qualitative examples of induced current in order to clarify lens's law
we start with a simple experiment with a bar magnet and a coil of wire on the left in the
top picture we're approaching a coil of wire with the north pole of a magnet and what we
observe in the coil assuming that its terminals are connected so current is allowed to flow
what we observe is a current flowing in the shown direction
then if we allow things to settle down for a second and we suddenly remove that north pole
of the magnet we'll see current induced in the opposite direction in the coil
so what's going on here to clarify this behavior we first introduced the idea of magnetic flux
magnetic flux is a way of talking about how many magnetic field lines are penetrating a loop
and we're going to quantify this in the next video when we talk about the change in flux and
faraday's law for now we're just trying to cover it qualitatively so what i have in the picture is
just some arbitrary surface and i call that a and the perimeter of that is a conductive loop
and i have this green vector called a normal vector that's perpendicular to the surface element
that's how we talk about the orientation of surfaces because it's so much easier than talking
about the actual angle of the surface so this normal vector is just perpendicular to the surface
i've also shown three magnetic field lines that are penetrating the loop so these are the points
where they actually cross the surface right here where the color changes here here and here
so in this picture i have three magnetic field lines penetrating the surface
and when we quantify that appropriately that's called the magnetic flux through
the loop notice that the magnetic field isn't coming in exactly perpendicular to the surface
and we talk about that degree of alignment with this angle theta between the magnetic field
and the normal vector so i have some magnetic field coming through with a component in the same
direction as the normal vector in this picture so flux is the amount of magnetic field poking
through a loop and lenses law tells us that the induced current or possibly just the emf
if the circuit isn't completed will act in the direction that opposes the change in flux
so when i go back to our experiment the reason the current is induced in this direction
is because the loop has been exposed to new flux pointing rightward through the loop so the current
is induced in the direction that will reduce that change in other words the direction that creates
leftward magnetic field lines coming through the loop if i point my thumb in the direction
of current and loop my hands around using the ampere's law right hand rule i see that this
current is in exactly the right direction to oppose the change in flux coming through the loop
likewise in the second picture we allowed everything to settle down with a bunch of
rightward magnetic fields poking through the loop due to the magnet but then when we remove
the magnet the loop is going to try to sustain that rightward flux through its interior
again using the ampere's law right hand rule i see that this current direction gives me
magnetic field lines pointing rightward through the loop as the loop struggles to
maintain the original magnetic field let's wrap things up with a couple qualitative examples
in the first example i have a loop sitting in the plane of the page and a magnetic field is suddenly
turned on pointing out of the page i'm asked to draw the direction of the induced current here
well this is a bunch of new outward flux through the interior of the loop and the loop is going to
respond by creating inward flux to try to keep that original flux of zero through its interior
using the ampere's law right hand rule i can kind of guess and check with my thumb in one direction
in the other direction and the way that gets it done is by using a clockwise current so i stick
my thumb in that direction my fingers loop inward through the interior of the loop and this loop is
now opposing the change in flux in my second example i have a loop sitting in the plane of
the page and it's experiencing an outward magnetic field now just to keep track of the orientation
of the loop we're using a normal vector so this is a vector perpendicular to the area
captured by the loop it's pointing out of the page as well so i have a bunch of field lines poking
out through the loop at this moment then i quickly rotate the loop by 90 degrees making the normal
vector perpendicular to the magnetic field in other words the face of the loop is now parallel
with the magnetic field so in my initial state there's a bunch of field lines coming out in
the same direction as the normal vector in the final state there are no magnetic field lines
penetrating the surface of the loop because the surface is parallel to the magnetic field
so the loop is going to respond by trying to generate magnetic field lines pointing in the same
direction as the normal vector in order to sustain that original magnetic field that agreed with the
normal vector direction so i could call that the induced magnetic field then i just have to figure
out which way is the current going to run in order to create those induced magnetic field lines it's
a little hard to see perspective in this picture but where my pen is right now is the near side of
this loop and if i run the current down on that near side face i put my thumb in the direction
of the current wrap the fingers of my right hand around through the loop that's going to generate
the correct induced field on the far side of the loop that current will be moving upward
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