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(Anzar) Look at all that water.
Just think about the energy that is stored in there,
ready to do work.
That form of energy is called gravitational potential energy,
stored energy that gravity can turn into kinetic energy.
When it does become kinetic energy,
it can be converted to hydroelectric power
that can heat homes, restaurants and stores,
and run computers.
But gravity isn't the only force that can have potential energy.
In this segment, we're going to talk about
electric potential energy.
That's energy stored by electric charges.
When we know the amount of electric potential energy
we can store,
we also know the amount of electrical energy
we can generate.
When electrical engineers designed the circuits
that provide electrical power,
they need to know how much electric potential energy
they have to work with.
And that's essential for running everything
from electric toothbrushes
to lights in football stadiums.
Let's dig a little deeper into electric potential energy.
We know that it's the magnitude of the work
performed on a charged object
by an electric field.
In other words, electric potential energy
is the energy that a charge in an electric field possesses
which gives it the ability to do work.
Like all forms of energy,
electric potential energy is a scalar quantity,
but unlike other scale or quantities
like speed and temperature,
it can be positive or negative.
Now, it has nothing to do with direction,
like it would in a vector quantity,
but is determined by whether energy
is lost or gained in a system.
Electric potential energy depends on three things.
The type of charge,
whether it's positive or negative,
the amount of charge,
and the strength of the electric field it's in.
Electric potential energy uses the same units
as gravitational potential energy, Joules.
We can figure out how much energy a system has
by considering the electric charges
and fields that are involved.
Let's do a quick calculation to see how that works.
Say you have a charge of positive five
times ten to the negative twelve coulombs,
creating an electric field.
If a second point charge of negative three times
ten to the negative 15 coulombs is seven meters away,
what is the electric potential energy
stored by the second charge?
Electric potential energy equals a constant k
times a product of the charges
divided by the distance between them.
Now we plug in what we know.
K is nine times ten to the ninth
Newton meters squared per coulomb squared.
This is multiplied by the first charge,
positive five times ten to the negative twelve coulombs
times the second charge,
which is negative three times ten
to the negative fifteenth coulombs
divided by a distance of seven meters.
Plugging these values into the electric potential energy
equation gives us negative 1.9
times ten to the negative seventeen Newton meters.
Since a Newton meter equals one Joule,
our answer is that the electric potential energy
of the second point charge
equals negative 1.9
times ten to the negative 17 Joules.
Notice that the sine of each charge matters
and the answer is a negative number.
The negative sign tells us that work must be done
on the system to keep these charges apart,
so electric potential energy is the ability of a charge
to do work.
But how does that, well, work?
Let's say we have two charged plates.
The top plate is positively charged,
and the bottom plate is negatively charged.
You can see the electric field lines
going from the positive plate to the negative plate.
Let's put a positive charge
in the electric field.
Work must be done to push a positive charge
towards a positive plate
or away from the negative plate.
When the positive charge is moving
opposite the direction of the electric field,
we call that moving up the field.
the further up the field the positive charge goes,
the more work you have to do.
Like, if you were pushing a ball uphill.
When the positive charge is here,
near the positive plate,
what kind of electric potential energy
does it possess?
If you said it's high or strong,
that's right.
In fact, we can say that the charge
has maximum electric potential energy.
The charge doesn't want to be up here.
So if you let it start to move,
it will be repelled away
from the positive plate,
and attracted towards the negative plate.
It will accelerate all the way down.
While it's falling, what's happening?
Think back to gravitational potential energy
of the dam, because this works
in a very similar way.
If your answer was that the electric potential energy
is decreasing,
being converted into kinetic energy,
you're right.
When it reaches the negative plate
at maximum velocity,
how much electric potential energy is left?
If you said none, you got it right again.
It has no electric potential energy left.
It all changed to kinetic energy.
Another important characteristic
of electric potential energy
is that it is conservative.
Which means that it obeys the law of conservation of energy.
Whatever an object loses in potential energy
it gains in kinetic energy,
and vice versa.
Now let's look at what happens to electric potential energy
in different scenarios.
A positive charge near another positive charge
has high potential energy.
A positive charge near a negative charge
has low potential energy.
A positive charge gains electric potential energy
when it is moved in a direction
opposite the electric field.
A negative charge gains electric potential energy
when it is moved in the same direction
as the electric field.
Those are the basics of electric potential energy,
which has a strong resemblance
to gravitational potential energy.
Both depend on the position of an object in a field,
and both can be positive or negative.
To understand the equation for electric potential energy
stored by a charge between two charged plates,
let's look at the equation for gravitational potential energy
and compare it to electric potential energy.
The potential energy of an object
due to gravity equals its mass
times gravitational field strength
times its height.
So, the electrical equivalent of mass
is charge, which is q,
where g represents
the strength of the gravitational field,
we replace it with electric field, e.
And the height above ground becomes the distance
above the bottom plate.
So we can write the equation for electric potential energy
stored by a charge between two charged plates
as the charge q,
times the electric field e,
times the distance the charge has moved
within the field, d.
We've seen what electric potential energy is,
and that it is equal to the work
a charge in a field can do,
but how can we talk about it
in a way that makes it useful to us.
One way to describe it is per unit charge,
which we call electric potential.
Be careful not to confuse the two.
I know the names are similar,
but when we have a system with many charges,
electric potential energy
tells us the energy of all the charges
we're working with.
Electric potential tells us the energy of a single unit
of charge.
Electric potential, represented by a v,
is the electric potential energy per unit charge.
Let's talk about units,
and that will make the difference between
electric potential energy
and electric potential easier to understand.
Energy is measured in units of Joules, right?
A volt is defined as a Joule per coulomb.
When we calculate electric potential,
we can simplify the units to volts.
Electric potential is also called voltage.
This term connects electric potential
to the electricity we harness everyday.
Electric potential at a point in space
depends on two main factors;
the amount of charge creating the potential,
and the distance from that charge.
We can write this out as another type of equation
that looks like this.
Electric potential, v,
equals Coulomb's Constant, k,
times a charge responsible for the potential, q,
divided by the distance, r,
from q.
What if we want to solve for electric potential
at a point at which potential
is created by more than one charge.
The electric potential of multiple charges equals
the sum of the potential of each individual charge
at a point in space.
Like electric potential energy,
electric potential is a scalar quantity,
so it's easy to add together.
Now, how does that work?
Say we have two charges; q sub 1,
and q sub 2,
and a point in space we'll call point A.
Q sub 1 is one meter from point A,
and q sub 2 is three meters from point A.
Q sub 1's charge is negative five times ten
to the negative six coulombs,
and q sub 2's is positive five
times ten to the negative six coulombs.
We want to know what is the electric potential
at point A.
Recall that electric potential V
equals k times q,
divided by r.
The potential at point A from q sub 1
equals k times q sub 1
divided by the distance between q sub 1
and point A.
K equals nine times ten to the ninth
Newton meters squared per coulomb squared.
Q sub 1 equals negative five time ten
to the negative sixth coulombs,
and r equals one meter.
Plugging these numbers into the equation,
we find that the potential at point A
due to q sub 1
equals negative 45,000 Newton meters
per coulomb, or volts.
There's still one more thing that effects the potential
at point A, and that's q sub 2.
The electric potential at point A
equals the potential at point A
due to q sub 1, plus the potential
at point A due to q sub 2.
So to solve for the total potential at point A,
we'll need to know the potential at A
from q sub 2 as well.
The potential at point A from q sub 2
equals k times q sub 2
divided by the distance between them.
Q sub 2 is positive five times ten
to the negative six coulombs,
and the distance, r, is three meters.
Plugging these numbers into the equation,
we see that the potential at point A
from q sub 2 equals 15,000 volts.
That means the total potential at point A
is negative 45,000 volts,
plus 15,000 volts,
which equals negative 30,000 volts.
That's the total electric potential at point A
due to q sub 1 and q sub 2.
Now, I know we've covered a lot here,
but these are key concepts for you to understand
energy contained in electric charges
and how we measure it.
We went over two terms with similar names.
Electric potential energy,
or energy stored by electric charges,
and electric potential,
which is the measure of electric potential energy
per single unit of charge.
We can use both to help harness the electric power
that we use everyday.
That's it for this segment of "Physics in Motion,"
and we'll see you next time.
(announcer) For more practice problems,
lab activities and note-taking guides,
check out the "Physics in Motion" toolkit.