Good morning.
Conservation of charge means the total electric charge of an isolated system never changes.
♪flipping physics♪
- What is an isolated system?
- An isolated system is one where charges can neither enter nor exit the system,
hence, it is isolated.
Let's start by taking the universe as our isolated system; conservation of charge means
the net electric charge of the universe never changes.
Add up all the positive charges and subtract all the negative charges in the universe and
you will always get the same number.
Or we could have a smaller isolated system, like the conductive metal pieces of the electroscope
we used in demonstrations in a previous lesson.
The conductive metal pieces of this electroscope are electrically isolated from the rest of
the universe by the rubber and glass insulators.
In other words, the net electric charge of the electroscope will remain constant as long
as it remains isolated.
- Seems pretty simple.
- Yeah, if no charges are allowed to go into or come out of a system, then the total charge
of the system does not change.
- Exactly. Let's do an example problem.
Bobby, please read and Billy please translate.
- Two charged conducting objects collide and separate.
Before colliding, the charges and the two objects are +3e and -6e.
Which of the following are possible values for the final charges on the two objects?
Choose all possible answers.
- Please stop.
Okay, well, two charged objects collide and bounce off of one another...
We know their initial charges and we are trying to determine what values their final charges
could be after the collision.
Let's say charge one equals +3e and charge two equals -6e...
This is a multiple choice problem and more than one answer could be correct.
Let's see what our choices are... Bobby.
- Choice (a) is +4e and -7e, choice (b) is +2e and -2e, choice (c) is -1.5e and -1.5e,
choice (d) is -3.5e and +2.5e and choice (e) is +e and -4e.
- Other than beginning to solve the problem,
I do not think there is anything more we need to write down.
May I solve the problem?
- Yes Billy, please solve the problem.
- Well we know the initial total charge equals the initial charge of object one plus the
initial charge of object two which equals positive +3e plus -6e which equals -3e and
we know the initial and final total charge of the system is the same, so the total final
charge of the system has to equal -3e.
Actually, it does not say the system is isolated, so, how do we know it is isolated?
- The problem does not mention the two objects touching anything else, therefore you may
assume the two objects are isolated from the rest of the universe.
- Okay, great. Now, all we have to do is determine the total final charge for each choice and if it equals
-3e, then that choice is a possible choice and is correct and if it's not equal -3e,
then that choice is not possible and is not correct.
For choice (a), charge 1 final plus charge 2 final equals +4e plus -7e which equals -3e,
so the total final charge for choice (a) equals -3 and is a possible combination of charges
for our two conducting objects.
The total final charge for choice (b) equals +2e plus +2e which equals 0, so choice (b)
is not possible.
The total final charge for choice (c) equals -1.5e plus -1.5e which equals -3e, so choice
(c) is a possible combination as well.
The total final charge for choice (d) equals -3.5e plus 2.5e which equals negative -e,
so choice (d) is not possible.
The total final charge for choice (e) equals +e plus negative -4e which equals -3e, so
choice (e) is a possible combination.
That means, the answer is that choices (a), (c) and (e) are all possible.
- I do not like it when he does not say anything and just waits.
- That usually means we did something wrong.
- "We did something wrong"?
I think you mean "you" did something wrong.
- No, I mean "we".
- Actually Billy is right.
It is our job to pay attention and make sure nobody makes mistakes.
So yes, "we" must have made a mistake.
I will fully admit that I do not always do a great job at it but however, that is what
we are supposed to be doing.
- Thank you Bo.
- Yeah.
- You are right um, but what is our mistake?
- What is e?
- That is exactly what do you need to be asking yourselves...
What is lowercase e?
- e is the elementary charge, it's the magnitude of the charge on a proton or an electron,
but why does that matter?
- Because charge is quantized.
- Right. An object cannot have anything but an integer multiple of the elementary charge.
- Because objects get their electric charge from adding or subtracting charged particles
which are usually electrons.
For example, half an electron is not possible.
- That means neither (c) nor (d) could be correct because they both have non integer
multiples of the elementary charge.
- Only (a) and (e) are possible.
Choice (c) is not possible.
- Yes, and please recognize that if all along you had been saying elementary charge instead
of e, there would have been a much higher chance you would have noticed your mistake.
This is an example of why I always ask you to say what the symbols mean rather than just
the letter names, because the letters represent something in the physics world we live in.
Please, say the words not just the letters.
Let's do another example problem.
Bo please read and Bobby please translate.
- Two identical, conducting spheres are held using insulating gloves a distance x apart.
Initially, the charges on each sphere are +3.0 nC.
Oh, that's Nanocoulombs.
+3.0 nC and +6.0 nC.
- Stop... Initial distance equals x, charge one initial equals +3.0 nC
and charge two initial equals +6.0 nC. Bo...
- The two spheres are touched together and returns to the same distance x apart.
You may assume x is the distance between their centers of charge.
Part a, what is the final charge on each sphere?
Part b, is the final electric force between the two spheres increased, decreased, or the
same when compared to the initial electric force?
- Final distance equals x.
Part a, charge final for each sphere equals question mark, Part b, write, final electric
force question mark initial electric force...
Actually, both distances are the value of r in the electric force equation, but this
is between centers of charge, so add r initial equals r final equals x instead of what I
said about distance before.
- Bo, this problem is yours.
- We know the two spheres form an isolated system because the insulating gloves prevent
charges from entering or leaving the two spheres system.
Therefore, the total final charge equals the total initial charge which equals charge one
initial plus charge two initial or +3 nC plus +6 nC or +9 nC.
And I don't know from there.
- You may not be aware of this, however, because the two conducting spheres are identical,
after touching, the excess charges will be evenly distributed between the two spheres.
- Yeah, that is useful information.
Now that we know that, we know charge one final equals charge two final and we can just
call them charge final.
Therefore, the total charge final equals 2 times charge final and the final charge on
both spheres equals the total final charge divided by 2 or 4.5 nC.
So, both charges end with 4.5 nC of charge.
- That cannot be correct.
- Why not?
- We just went through how the charge has to be an integer multiple of the elementary
charge, so it can't be 4.5 nC.
- Oh Nanocoulombs is not the elementary charge, the elementary charge is 1.6 x 10^-19 C.
This is totally different than the previous example.
Before we had only like three or four or six excess charge carriers.
With 4.5 nC, we have a lot more than that.
Actually, we can determine the total excess number of charge carriers on each of the spheres,
the charge quantization equation for our final charge is charge final equals the number of
excess charge carriers final times the elementary charge.
That means the final number of excess charge carriers equals charge final divided by the
elementary charge which equals 4.5 nC divided by...
Actually, we need the charge in Coulombs.
- Nano means times 10^-9.
- Nice. So, 4.5 x 10^-9 C divided by 1.60 x 10^-19 C per charge carrier and that equals
2.8125 x 10^10 or 2.8 x 10^10 excess charge carriers with two significant digits.
- Okay, so that means because the excess charge
is positive, those excess charge carriers are protons.
In other words, each of the spheres has 28 billion more protons than electrons on it.
- 2.8 billion is a lot!
- Very small.
- That is correct...
Each sphere has 28 billion more protons than electrons.
But realize, each sphere has a whole heck of a lot more total protons and electrons.
It is just that each sphere has 28 billion fewer electrons than protons.
Bobby, could you please do Part (b).
- Part (b) is where we compare the electric force after contact to the electric force
before contact between the two spheres.
Let's start with the equation for the electric force.
It equals the Coulomb constant times charge 1 times charge 2 divided by the square of
r, the distance between the centres of charge of the two charges.
For the initial electric force, we can add a subscript for initial to all of the variables
except the Coulomb constant.
So, the initial electric force equals the Coulomb constant times (3 x 10^-9)(6 x 10^-9)
all divided by x^2 because x is both the initial and final distance between centers of charge
for the two charges.
That means, the initial electric force equals...
- I think we need to substitute 8.99 x 10^9 N times m^2 over C^2 for the Coulomb constant.
- Actually, we do not have a value for x and we are just determining which electric force
is larger, initial or final, so we do not need to substitute that in.
- Okay.
- The initial electric force equals 1.8 x 10^-17 times the Coulomb constant over x^2.
We can also do the same thing for the final electric force, only we substitute it for
4.5 x 10^-9 for both charges and the distance between the centres of charge is again x.
And we get 2.025 or 2.0 x 10^-17 times the Coulomb constant over x^2 with two sig figs.
Both numbers are to the power of 10^-17, so 2.0 is greater than 1.8 and therefore we know
the final electric force is greater than the initial electric force.
- I feel like we could have just said 4.5^2 is greater than
3 x 6 and to determine to the answer.
- Really?
- You have to show your work.
- The solution is much more important than the answer.
- And I want to understand why, not just get an answer.
- Darn right. - Yeah, OK.
- Yeah.
- Sure Mr. P, that was [?].
- Yes, please, always show your work and understand your solution.
It is much better for your learning long-term.
I hope I have made that clear after all these lessons.
Thank you very much for learning with me today, I enjoyed learning with you.