Good morning.
We've already learned about the law of charges which governs the directions of the forces
on pairs of charges.
Today we'll learn about the magnitude of that force.
♪flipping physics♪
This equation is called Coulomb's Law and is named for Charles Augustin de Coulomb,
a French physicist who in 1785 published several papers which detailed his experimental determination
of this equation.
So, capital F sub e is the magnitude of the electric force which exists between two charged particles.
- I thought it was called Coulomb's force because it is Coulomb's Law.
- I thought it was called the electrostatic force.
- Yeah.
- It is sometimes called Coulomb's Force or the Electrostatic Force.
I will simply call it the electric force and I hope that is okay.
- Okay.
- Okay. The magnitude of the electric force equals the Coulomb constant k times the electric
charge of the first object, q1, times the electric charge of the second object, q2, all divided
by r squared.
Before we specifically define r, I want to know what the general form of this equation
reminds you of.
- Newton's universal law of gravitation, the big G equation.
- Right. The force of gravity which exists between any two masses.
- The force of gravity equals the universal gravitational constant or big G times mass
1 times mass 2 all divided by r squared.
Yeah, I can see how the forms of those two equations are similar.
- And class, in the Newton's universal law of gravitation, r is not...
- The radius.
- r is...
- The distance between the centers of mass of the two objects.
- This can be confusing because sometimes r is...
- The radius.
- Correct.
So, notice the similarity here with Coulomb's law; in that equation, r is not...
- The radius.
- R is...
- The distance between the centers of charge - mass of the two objects.
- Clearly it is between the centers of charge not the centers of mass.
- Clearly.
- This can be confusing because sometimes r is...
- The radius.
- Again.
- Right.
By definition, r is the distance between the centers of charge of the two objects.
However, sometimes r is also a radius.
Now let's talk about the two constants in the equations.
The universal gravitational constant equals 6.67 times 10 to the negative 11 Newton's
times meters squared divided by kilograms squared.
The Coulomb constant equals 8.99 times 10 to the nine Newton's times meters squared
divided by Coulomb's squared.
So class, which constant is larger?
- The Coulomb constant because times 10 to the 9th power is larger than times 10 to the
negative 11th power.
- That is true but think about how much larger the Coulomb constant is... 8.99 times 10 to
the 9th divided by 6.67 times 10 to the negative 11th means the Coulomb constant is 1.35 times
10 to the 20th power larger than the universal gravitational constant.
- I guess the electric force usually wins.
- Yes it does.
Going back to the example from last time, rubbing the balloon on my hair gives the balloon
a net negative charge and my hair a net positive charge.
That causes an attractive electric force between the balloon and my hair.
However, there is still a force of gravity pulling the balloon down, right?
But the magnitude of the electric force acting on the balloon is so much larger than the
force of gravity acting on the balloon that the balloon sticks to my hair and does not
accelerate toward the ground.
- Sure.
- All right.
Let's do a basic example problem.
Bo, please read the problem and Bobby please translate.
- Two equal magnitude point charges are located 2.0 meters apart.
If the magnitudes of their charges are both 5.0 μC, and one is positive and one is negative,
what is the electric force acting on each charge caused by the other charge?
- I'm sorry, but what is a point charge?
- And what are in what are Mu coulombs?
- Right, okay.
Point charges are just like point masses only the description has to do with charge rather than mass.
In other words, a point charge is an object which has zero size and carries an electric charge.
- How can an object have zero size?
- Yeah, think of it this way; remember how much larger the Coulomb constant is than the
universal gravitational constant?
- Yes.
- Yeah.
- Then a point charge is an object whose mass is small enough that its mass is negligible
when compared to its charge.
Which is reasonable, correct?
- Absolutely.
- Yeah.
- And the Mu in front of the letter C means microcoulombs, which clearly we need to go over.
- Clearly.
- Yeah.
- So, three prefixes you should now be aware of because they will come up often are micro,
nano and pico.
Lowercase mu is the letter we use for micro and micro means one millionth or times ten
to the negative sixth.
In other words, one microcoulomb equals one times ten to the negative sixth coulomb.
Lowercase n is the letter we use for nano and nano means one billionth or times 10 to
the negative ninth.
In other words, one nanocoulomb equals one times 10 to the negative ninth coulombs.
Lowercase p is the letter we use for pico and pico means one trillionth or times 10
to the negative 12.
In other words, 1 pico Coulomb equals 1 times 10 to the negative 12th Coulomb's.
Those are all prefixes you should familiarize yourself with now that we are working with Coulomb's.
Bobby, please translate.
- Okay. Charge 1 equals positive 5.0 microcoulombs, charge 2 equals negative 5.0 microcoulombs,
r, the distance between the centers of charge of the two charges equals 2.0 meters and the
electric force equals question mark.
Actually, this is pretty simple.
Do you mind if I just solve the problem?
- No Bobby, I do not mind.
Please go ahead.
- So, electric force equals Coulomb constant times charge 1 times charge 2 divided by r squared.
That is 8.99 times 10 to the 9th, times 5 times negative 5 divided by 2 squared or -5.61875
times 10 to the 10th or -5.6 times 10 to the tenth Newton's with two significant digits.
- So 56 billion Newtons.
- Right that's probably not right.
- We need to convert the charges to coulombs and not microcoulombs.
- How do we know that?
- The Coulomb constant is in Newton's times meters squared per Coulomb squared.
The units need to play well together.
- Right, the units need to match.
- Okay, yeah.
Both charges have a magnitude of 5 microcoulombs or 5 times 10 to the negative sixth coulombs,
so substitute those charges into our equation and we get -0.0561875 or -0.056N with two
significant digits.
- Why is the force negative?
- Because it's to the left.
- I do not think that is correct.
- Okay, our math is correct but we clearly need to talk about the negative.
I'll start with the fact that this negative does not mean to the left, down, west or south.
I'll explain what the negative means in a moment but first, realize there are three
different ways I've seen this equation written.
The first being the form we have discussed so far, the second is the magnitude of the
force vector and the third is the vector form of the equation using the unit vector r.
This would be the electric force by charge 1 on charge 2 and the unit vector directed
from charge 1 toward charge 2.
We've not really worked with unit vectors in this class so far, so we are not using
the third equation and I feel that taking the absolute value of the equation loses a
bit of information.
So, I will use the first form of the equation and if you get a negative force, that means
the electric force is an attractive force, and if you get a positive force, that means
the electric force is a repulsive force.
- That makes sense...
If one of the charges is positive and one is negative, the electric force ends up being
negative regardless of which charges which, and we know opposite charges attract.
- And if both charges are positive or both charges are negative, the electric force will
be positive and a repulsive force.
And we know like charges repel, so the equation will show us if the electric force is repulsive
or attractive.
Thanks Mr. P.
- You are very welcome Bobby.
- In other words, we need to be smarter than our calculator.
- Alright, just like when we take the square root, we have to decide if the number is positive
or negative by thinking about direction.
When we get a positive or negative number using Coulomb's law, we need to remember negative
is an attractive force and positive is a repulsive force and be smarter than our calculator.
- But you do not ever use a calculator...
- You know, looking back at Newton's universal law of gravitation, it is interesting that
the force of gravity in that equation is always an attractive force.
However, Coulomb's law gives either an attractive or repulsive electric force.
I bet that is important to realize.
- Bo, that is important.
There are a lot of similarities between the two equations.
However, you are correct that the gravitational force always pulls masses together whereas
the electric force can pull charges together or push them apart as described by the law of charges.
But we have not quite answered the question which was "what is the electric force acting
on each charge caused by the other charge"?
Billy, what is the answer to this question...
Which charge did we just determine the electric force on?
- The equation gives us the electric force on both charges.
The two forces are equal and opposite and form a Newton's third law force pair.
For every force from charged one and charged two, there exists an equal but opposite force
from charge two on charge one.
So I guess the answer to the question is, the force on each charge equals 0.056N toward
the other charge.
- Absolutely Billy thanks.
I think we should do one more thing, just to solidify our understanding of the electrostatic force.
I think it is best described by this diagram, but here is what we are doing; if we place
a third charge, charge three with the same charge as the positively charged object, charge
one, only now 2.0m on the opposite side from the other negative charge, charge two, what
is the net force acting on charge one, the positive charge in the middle.
Bo, this one is for you.
- Well, first off, adding the third charge does not affect the electric force of 0.056N
which is from charge to on charge 1 and acting to the right.
We just need the - we need to add the electric force from charge 3 on charge 1
because both charge 1 and charge 3 are positive, the force from charge 3 on charge 1 will be
positive, will be a positive repulsive force on charge 1 and that would be to the right.
All the values in the electric force equation are actually the same as before - well, with
one exception, both charges are positive this time, but that means the electric force from
charge 3 on charge 1 will also be 0.0561875N and to the right.
So, the net force on charge 1 from both charge 2 and charge 3 will be 0.561875 times 2 because
both forces are in the same direction which equals 0.112375 or 0.11N to the right with
two significant digits.
- Very nice everybody.
Thank you very much for learning with me today, I enjoyed learning with you.