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>> In this video,
we're going to take a closer
look at Coulomb's Law.
Remember that Coulomb's Law
says the magnitude of
the electric force between
two charges, q1 and q2,
equals a constant number--
we'll call it k,
times the absolute value
of the charge q1
times the charge of q2,
all divided by the distance
between q1 and q2,
we'll call it r, squared.
The constant number k
equals 9 times 10 to the ninth
Newton meters squared
per Coulombs squared.
Our first exercise involves
calculating the force
between two point charges.
The exercise states that
we have two point charges.
q1 equals positive 5.2
times 10 to the negative ninth
Coulombs, and q2 equals
negative 4.6 times 10 to
the negative ninth Coulombs.
They are separated by a
distance of 7 centimeters.
Find the magnitude
and direction of the force
of q1 on q2,
and the magnitude and direction
of the force q2 on q1.
This is a two-part problem,
so let's start with part one.
Finding the force of q1 on q2.
We need to figure out
force direction,
which way the force points,
and magnitude, how strong it is.
Since the two charges
have opposite signs,
the force between them
will attract.
It will pull the charges
closer together.
We can draw an arrow
on the diagram to show
which way the force of q1 on q2
will point.
To the left in the
negative x direction.
To solve for force magnitude,
we'll use Coulomb's Law.
The problem states that q1
is positive 5.2 times 10
to the negative ninth Coulombs.
q2 is negative 4.6
times 10 to the negative
ninth Coulombs,
and r is 7 centimeters,
or 0.07 meters.
Let's put all these values
into Coulomb's Law
and see what we find.
We'll insert our charges,
then our constant k,
and divide by the distance
between the charges squared.
5.2 times 10 to the negative
ninth Coulombs,
times negative 4.6,
times 10 to the negative
ninth Coulombs,
times our constant k,
which is 9 times 10
to the ninth Newton meters
squared per Coulomb squared,
all divided by the radius,
which is 0.07 meters squared.
We find that the magnitude
of the force of q1 on q2
is 4.4 times 10 to
the negative fifth Newtons.
Since we're solving for
force magnitude, even though
one of the charges is negative,
our answer is a positive number.
So that's the electric force
of q1 on q2.
How about q2 on q1?
We can figure it out
without using Coulomb's Law.
Newton's third law says
that for every action,
there is an equal
and opposite reaction.
So when q1 pulls on q2
in the negative x direction,
q2 pulls on q1
in the positive x direction,
with the same strength.
On the diagram,
the force vector
should look like this.
So the force of q2 on q1
is 4.4 times 10
to the negative fifth Newtons
in the positive x direction.
Now, let's do an example
using Coulomb's Law
to solve for distance
between two electric charges.
Here's our situation.
Two identical charges,
q equals positive 2 times 10
to the negative tenth Coulombs,
experience an electric force
between them of 6 times 10 to
the negative fourth Newtons.
How far apart are the charges
from one another?
Solving this challenge
involves rearranging
the Coulomb's Law equation.
We want to solve for r,
the distance between charges
that corresponds to a force
between the charges
of 6 times 10 to
the negative fourth Newtons.
We start with Coulomb's Law,
as we usually see it.
We want to algebraically
arrange this equation
so it reads r equals something.
Our first step is to multiply
both sides of the equation
by r squared.
We'll then divide both sides
by f electric.
Our last step is to take
the square root of both
the left and the right side.
This gives us the form of
Coulomb's Law we wanted,
the one that lets us
solve for r.
When we insert the values
of q1 and q2,
which are identical,
and the electric force strength,
we find that r, the distance
between the identical charges,
equals the square root of
9 times 10 to the ninth
Newton meters squared
per Coulomb squared,
times 2 times 10
to the negative ninth
Coulombs squared,
divided by 6 times 10
to the negative fourth Newtons,
which equals 7.7 times 10
to the negative fourth meters,
or 0.77 millimeters.
Solving problems using
Coulomb's Law often
involves two things.
Figuring out electric force
direction and magnitude.
You can rely on your knowledge
of vectors and charge repulsion
and attraction
to arrive at direction.
And force magnitude,
or any other variable
in Coulomb's Law equation,
can be solved for using given
quantities and rearranging
the equation when needed.
Here's another Coulomb's Law
problem to try.
Two electric point charges,
q1 and q2, are separated
by two centimeters.
The electric force magnitude
between them is 3.8 times 10
to the negative sixth Newtons.
q1 is an electron.
What is the magnitude
of the charge q2?
Go ahead and press pause,
give it a try, and when
you think you have the answer,
come back and check your work.
Did you get 1.1 Coulombs?
If so, that's great.
If not, let's take a look
at it together.
The first thing we wanna do
is write down Coulomb's Law,
and all the parts we were given.
We know that k,
the Coulomb's Law constant,
is 9 times 10 to the ninth
Newton meters squared
per Coulombs squared.
We also know from the problem
that the electric force between
the charges is 3.8 times 10
to negative six Newtons.
And we're told that
one of the charges, q1,
is an electron, which means
it has a charge of negative 1.6
times 10 to the negative
nineteenth Coulombs.
We needed to solve
for the magnitude
of the second charge, q2.
That means our answer
will be a positive number.
We know we'll need to use
Coulomb's Law and that we
need to rearrange the equation
so that we can solve for q2.
If we rearrange the equation
to solve for q2
by first multiplying
both sides of the equation
by the distance squared,
then dividing both sides of
the equation by Coulomb's Law
constant and q1,
we will have q2 isolated
on one side of the equation.
Now we can plug in our values
for force, distance,
the constant k,
and the charge q1.
We find that q2
equals 3.8 times 10
to the negative six Newtons,
times 0.02 meters squared,
divided by 9 times 10
to the ninth Newton meters
squared per Coulomb squared,
times the absolute value of
negative 1.6 times 10 to the
negative nineteenth Coulombs,
which equals 1.1 Coulombs.
That's a closer look
at Coulomb's Law.
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