♪♪
(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.
