Download Outline: Allow me to put this unit in very basic terms. If I were to sum

Outline:
Allow me to put this unit in very basic terms. If I were to sum up this unit in four
words, it would be the following: Electricity is a force. If I had one more
word, that statement would be: Electricity
is a measurable force. And
if I had three MORE words (scary, isn’t it?), it would be Electricity is a
measureable force in many ways. Has your brain melted yet?
Okay, so we’re doing fine as of now. Now let’s begin to get into the real math and
science behind this unit. You see, all objects possess CHARGE1 in the object itself.
Just pick any object. Go ahead. I dare you. What’s that you say? You can’t think of
anything. Hmph. Allow me to demonstrate… Imagine a plate. You know, like the
ones you eat dinner on. Paper? Plastic? Porcelain? Doesn’t matter what it’s made out
of. Just any plate, like the following:
You see? Now, let me tell you this awesome Physics fact: This plate has
charge. But wait, there’s more! This plate has an even amount of
charge distributed throughout. And just pick any material you can find.
Machinery, turntables, vegetables, closets, even you and me, all have charge. Now,
what makes electricity interesting are the kinds of charges. To be frank: there are
two. They are:
Positive +
and
Negative –
These are just names. It’s like naming charges “Kelsey” charges and “Gavin”
charges. (Thank you, Mr. Wadness for that lovely example).
Now, here’s another key concept to learn. This one is what makes electricity
work. Opposite charges attract, like charges repel. Okay folks
bear with me. A positive and a negative charge with attract each other, while a pair
of positives and a pair of negatives will repel each other. That’s how it works in
electricity. And so, every object has positive and negative charges. That’s a fact. But
there’s one more state of charge to keep in mind. If an object has the same number
of positive and negative charges scattered evenly throughout, that object is part of
the third charge state, which is:
Neutral +/A neutral object doesn’t appear to feel an electric force, because the charges
when distributed throughout aren’t strong enough to produce a measurable force.
CHARGE: A property that exists in all normal matter that allows it to experience an
electrical force.
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Remember the plate from before? Now let me illustrate what it looks like with
charge in it:
The red pluses and the blue minuses each represent positive and negative
charges respectfully. They’re scattered throughout, so they don’t have enough
power to feel an electric attraction or repulsion, if say a positive point charge passed
by it. And even if you had a strong positive charge next to the plate, it still wouldn’t
move. That’s because the plate is ceramic, and ceramic is a NONCONDUCTOR2. The
plate can’t feel an attractive force, unless all the positives and negatives were
rearranged to opposite sides.
But what happens if the plate were made out of, say Copper? Well, Copper is a
CONDUCTOR3, which makes electrons travel through the material very easily. So, if a
positive test charge were right by it, the positives would shift away from the test
charge (repulsion) and the negatives would shift towards it. The Copper would then
be POLARIZED4 and feel electric force. Consider the following:
The copper plate on the left has no test charge near it. When a positive test
charge is added near one end on the right, the negatives align to try and meet the
positive charge. Now, imagine if instead of a plate, we had just two charges in open
space. I’ll illustrate:
The two charges will attract each other, because they apply force on each other.
It’s the same deal if the charges are the same, except that they’ll repel instead. So, big
question: How can we measure this force?
The answer: Coulomb already has. Charles Augustin de Coulomb studied charged
objects in the late 1700’s. After making his experiments, he discovered the
fundamental law to find the force on two charges. In 1783 he published his
discovery of what became known as COULOMB’S LAW5 as a fundamental law to find
the force between two charges, given that their charges and the distance between
them is known. It looks like this:
Felectric=Kq1q2
r
2
Okay, so the force is stated F=kq1q2/r2. “k” is a constant. Don’t worry. It’s
expressed as 8.98x109 Nm2/c2. The two q’s are the two charges involved in the
equation are the two charges in question. “r” is the distance in meters between the
two. (There’s a good reason why this looks like the universal gravity law).
But now there’s the million-dollar question (estimated to be worth $1,024,956
adjusted for inflation) where does that force come from? So let me briefly (and I
NONCONDUCTOR: Any material that does not allow the free passage of charge.
CONDUCTOTOR: Any material that allows for the passage of electrons (charge).
Opposite of nonconductor.
4 POLARIZATION: Formation of opposite sections of charge in an object.
5 COULOMB’S LAW: Formula for finding force between two charges.
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mean BRIEFLY) explain that it is caused by ELECTRIC FIELD6. The electric field is
what supplies force to all charged objects. All charged objects have one. It looks like
this:
Those arrows represent potential force that will someday affect an electrically
charged object. Once you know the electric force on an object, the field at that point
is easy to calculate:
E=F
Q
See? The electric field is equal to the force divided by the charge that’s causing it.
The field is measured in units of Newtons per coulomb (N/C) or volts per meter
(V/m). Extra credit for anybody who shows me a detailed unit conversion
explaining why the two are equal by the end of next week. (Do the conversion
backwards and forwards N/C to V/m and V/m to N/C. They’re different.)
ONE MORE IMPORTANT THING: The electric field is defined by which way a
POSITIVE (+) charge would move in it. So, for the above picture, if the point charge
were negative, the lines would be drawn into the charge, because that’s how a
positive charge would move.
So essentially, electric field provides force. So, vectorally, the electric field
applies force and moves a charge. Add the resultant vectors, and you’ve calculated
yourself one awesome force!
(Isn’t physics just lovely?)
Another equation ofr electric field (derived by adding coulomb’s law to the
aforementioned one and doing calculus:
E=q/40r2
So we get it? Electric field can be solved for multiple ways, depending on what
we know.
Okay so let’s see what we’ve gone through. Charge? Check. Coulomb’s law?
Check. Electric Field? Check-a-roo. But suppose we want to calculate the electric
field for something that’s not as simple as a point charge? Hm? Who do we call for
that? WAIT! I know who we call! Mr. Carl Friedrich Gauss! Recognize the name? Of
course you do. He’s the discoverer of a little function we call GAUSS’ LAW7. Gauss
stated that the electric flux that passed through any surface
was proportional to the charge inside it.
Did I lose you? Nuts. Let me explain. When we drew the electric field earlier,
remember how all those lines surrounded the charge? Well those lines are actually
called “electric flux”, and they have a value. In Gauss’ law, the flux is defined by the
ELECTRIC FIELD: An invisible field that surrounds charged objects and provides
electric force to other charges nearby.
7 GAUSS’ LAW: For determining the electric field of an object that isn’t as simple as a
point-charge.
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amount of charge that’s enclosed in a certain area. That law can be expressed
mathematically:
EdA=Qenclosed/0
(I know that’s not actually the sign for “closed integral” and is instead the Greek
lowercase letter “Iota”. Just keep it on the DL and maybe Mr. Wadness won’t notice.)
Okay, so this is Gauss’ law. It’s all pretty straightforward, except for the dA, which is
just the surface area of what you’re measuring. (The area that the flux passes
through. We’ll learn why this is important later). So say for a sphere it would be
4r2. For a cylinder it would be 2rl (we’ll learn why we use half the formula for a
cylinder later).
So, let’s say we have a metal conducting sphere. Like this picture:
The sphere has a positive charge of, let’s say +Q. Because it’s a sphere, we want
to plug in the correct surface area formula, which is 4r2. The yellow circle on the
inside is r1. As you can see, because in a conductor, the charge is located on the edge,
r1 encloses no charge. Q is zero, and consequently, E is zero. But the pink circle,
which is r2 fully encloses the sphere, contains the entire charge for the sphere.
Therefore Qenc=+Q. dA, is 4r2 as mentioned earlier, and everything else stays the
same. So our equation is (drumroll please)
E(4r2)=+Q/0
Or
E=+Q/4r20
It’s so simple you can do it at home! (If you haven’t already you most likely failed
physics for the third quarter.)
Now, in a cylinder things get tricky. If a cylinder has charge, we want to use dA,
right? So we plug in the surface are formula for a cylinder, right? That formula is
2rl+2(r2). But it’s tricky. Get this: we only want to include the parts of the formula
that the flux goes through. Okay, so in a cylinder the charge resides in the middle,
producing only flux that goes through the CURVED part of the cylinder. No flux goes
through the ends! Therefore the calculation for the surface area of the ends, which is
2(r2), can go. We are left with 2rl for the dA of a cylinder. The rest is algebra. For a
flat sheet of charge, dA would be just length times width. For a thick sheet of charge
dA would be 2(length times width), because the flux only goes through two sides.
Get it? I hope so.
What happens when a nonconductor is used for Gauss’ law? Keep in mind, the
charges don’t flow to the end like they would in a conductor. Given the charge
density, and the amount of area enclosed, you should be able to find the amount of
charge enclosed. Just multiply the two values together, and you’ll get the total
charge enclosed by whatever radius is made.
Is that it? I think that’s it. Wow, I am long-winded. So congratulations, you now
know about electric force and fields! Wait, you didn’t just skip to the last paragraph,
did you? DID YOU?! Wow, that’s cheap man, that’s real cheap. Do you read the last
page of a mystery book first, too? Wow, I hope you have a crushing feeling of guilt
now. I mean, think about all the wonderful PHYSICS8 you could have learned by
reading through. You could have learned all about Coulomb’s law, charges, the
electric field, electric forces, and Gaussian surfaces, but no, Mr. Hotshot has to skip
to the end I order to feign accomplishment to add excitement to his drab wretched
life! Well, listen here Mr. Hotshot, I have better things to do than waste my time with
inconsiderate people who have no regard for what person has to offer intellectually,
especially when its as valuable as this! God, I hope you’re crushed with shame now.
For those of you who did read through, good job. It’s not easy to get at first, but you
did really well. Let’s go on to see what other physics marvels await us!
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PHYSICS: Sheer bliss, believe me.