We now discuss the basics of electricity
as well as the circuits on how electricity flows in circuits.
So we're ready to move to magnetism.
Again as an overview we've already discussed our basic mechanics.
As well as the laws governing fluids and gases.
So now we're finishing up our section on electricity, circuits, and magnetism.
Before we move on to a wave phenomenon
and then the microscopic structures.
So I'll finish now with magnetism.
This discussion of magnetism, we'll start with magnetic fields
and how magnetic fields work
and then we'll discuss the forces that charges experience
when they are in the presence of magnetic fields.
But first let’s introduce magnetic fields.
Magnetic fields come from the motion of electric charges.
So if we have a charge for example moving through a wire like this one.
We have the current moving through the wire.
It creates a magnetic field in the circle around the entirety of the wire.
The strength of this magnetic field
is proportional to the current flowing in the wire, I
so that’s not the number one.
It's the current I, divided by the distance you are away from the wire.
The actual expression for the amount of magnetic field
you experience when you're in a certain distance from a wire like this one
is a much more complicated expression.
So the important thing to know for us right now
is that it is simply proportional to the amount of current flowing in the wire
and the distance you are away from the wire.
The units of the magnetic field are force per charge times velocity
or Newton’s per amp times meters.
We call these units Teslas and we symbolize this with the letter T.
The way you find the magnetic field as produced by wire
is by using something we call the right-hand rule.
What you do is just like you see in the picture here.
First, put your thumb in the direction of the current as it's flowing
and then curl your fingers in the direction
that the magnetic field will be created.
So if you put your thumb in the direction of the current,
you would simply curl your fingers in the direction
wrapping around your thumb to the direction of the current.
And you'll find the direction, circular direction of the magnetic field.
Sometimes we discuss the magnetic field going into a surface
or coming out of a surface because current and magnetic fields
are always related in a very sort of three dimensional way.
It's hard to think about a current flowing linearly
and then the magnetic fields wrapping around it.
So we'll often find it useful to be able to use this third dimension
going sort of into or out of the page if you will.
By convention, when we're talking about any vector
of whether it's the current or the magnetic field going into the page.
We mark it with an X like this.
If it's coming out of the page at us we instead mark it with a dot.
So using our right-hand rule as we've already discussed
we could talk about the current going into the page
by again doing the same thing.
We put our thumb in the direction of the current
which is going into the page.
Our fingers will wrap around the direction of our thumb’s motion
and that will show us the direction of the magnetic field.
We can do the exact same thing for the current
that’s going into the page or sorry,
out of the page and then wrap our thumbs one more time,
fingers one more time around the direction of the current
which is represented by our thumb
and again get the direction of the curling of the magnetic field.
Sometimes we might not want
our magnetic field to be going in a circle though.
We might just want a straight line of the magnetic field.
But we can be very clever and wrap a wire into a loop over and over and over again
and if you use your right-hand rule enough times,
you could put your thumb on the direction of the current
as shown by this looping wire
and convince yourself if you spend enough time looking at it.
That in fact yes you will get a linear magnetic field
going in the same direction
as the current is flowing through this particular wire.
You can be sure to find the direction of this magnetic field
by again using the right-hand rule,
but you can use it in a slightly different way this time
if you know the direction of your current
you know trying to find the direction of your magnetic field
through this looped coil which we call a solenoid.
When you're doing this case it's something slightly different.
You curl you fingers in the direction of the curling wire
and then your thumb will give you the direction of the magnetic field.
One more phenomenon that we should definitely touch on
with regard to magnets is the idea of a bar magnet.
We usually are somewhat familiar with the idea of a bar magnet
as well as the fact that a bar magnet has both a north and a south pole
and the idea that the north and south poles
were usually want to repel each other.
But we should also know our conventions with how magnetic fields flow
in a given bar magnet and the magnetic fields
always go for a bar magnet like this one from north to south.
It's also important to know that for a magnetic fields,
unlike charges, there is no such thing as a source for magnetic fields
from which a magnetic field emanates very simply.
So for example, we couldn’t have something equivalent to a,
for example magnetic charge,
nothing like this has ever been discovered in nature despite
many searches which are still ongoing
but again we've never found and there's no reason to think
that there are such things as a single magnetic charge
equivalent to something like a single electric charge
from which we have a source of magnetic fields.
In other words, as it's often stated,
there is no such thing as a magnetic monopole.
So this bar magnet that you see is often called a magnetic dipole
because it has a north and a south pole
but there is no such thing for example as an isolated north pole
with simple magnetic fields emanating straight from it
without a corresponding south pole.
It is also important to know how a bar magnet
or any magnetic object behaves in the presence of other magnetic fields
and what it will always do is try to twist to orient itself
with the magnetic field that is present.
Twisting itself in response to the magnetic field
to try to align north to south and south of north
in order to make the magnetic field lines
all be pointing in the same direction.
When we're talking about magnetic fields for example
this one's produced by these two wires.
We should also be aware that these fields
also follow the idea of superposition.
In other words, if I know that magnetic field from this upper wire
and I know that magnetic field from the lower wire
using both the current and the right-hand rule as we've already discussed,
to find the total magnetic field for example
anywhere between them or anywhere outside of them
I simply have to add the magnetic field from each wire.
Again to find the direction of the magnetic fields from these wires
you would simply use your right-hand rule.
So for this lower wire we have the current flowing to our left
and so we have the magnetic field going into the page on the one side
and then out of the page on the other side.
By the same token on the upper wire that we have here
we could do the exact same sort of analysis.
Again, using our right-hand rule
watching the direction of the current
and curling our fingers around the thumb
to see which direction your magnetic field is going.
Again remembering that the dots represent magnetic fields going out of the page
and the X’s represent magnetic fields going into the page.