Bo: Hey, guys! Billy: Hey, Bo! Bobby: Hi, Bo! ♫ (lyrics) Flipping Physics ♫ Mr. P: Ladies and gentlepeople, the bell has rung,

therefore class has begun. Therefore, you should

be seated in your seat, ready and excited to review

everything we learned in electricity and

magnetism in AP Physics C. Here we go, are you excited? Billy: Yeah! Bobby: Oh, boy. Bo: Okay. Mr. P: All right, just like mechanics, I need you to just listen, okay? Billy: Maybe? Bobby: Oh, boy. Bo: Shh. Mr. P: All right, let’s get started. Coulomb’s Law, the electric force. The force between two charged particles, charged positive and negative, we have the law of charges unlike charges attract,

like charges repel. In this particular case, we

have the force between them. Kq1q2 over r² where K is Coulombs constant, 8.99

times 10 to the ninth. What is it? Newtons times meters squared over Coulombs squared, q1q2,

these are the two charges divided by r. Now, r, r² is the distance

between the center of charges to the two charges, not to

be confused with the radius, and this is especially confusing because sometimes it is the radius. So r is not the radius by definition. It is the distance between

the center of charges of the two charges, and it is sometimes the

radius, which can be confusing. One confusing piece about this as well is that you need two charges, and if you change the

charge of one of them, the electric force on

both the charges changes because in order to have

this electric force, you need two charges. The electric field is equal

to the electric force per unit charged, that’s a test

charge in the electric field is defined by a positive test

charge, a small one at that, a small positive test charge. If you plug in the

equation for Coulomb’s Law, one of the charges ends up canceling out, and you get for, the electric

field for a point charge is Kq over r². Bo: You guys do know that he posts all of his lecture notes at

flippingphysics.com, right? Billy: You do realize you said

the exact same thing last time. Bo: Oh. Mr. P: Some notes about

electric field lines. Electric field lines always

start at a positive charge and at a negative charge, unless there are more

positive or negative charges than the other, so they can

either start or end at infinity. Electric field lines are never loops, and they are always normal to the surface, right next to the surface,

they are always perpendicular or normal to that surface. Three different charge densities. Volumetric charge density, surface charge density and linear charge density. Rho, sigma, and lambda. Charge per unit volume,

charge per unit area, and charge per length. You need to know these charge densities. They’re going to come up quite a bit in electricity and magnetism. Electric flux. The symbol is an uppercase Phi, looks like an eye with a

circle in the middle of it with a lower case, I’m sorry, with a subscript of an

uppercase E for electric field, so this is the electric flux. It is the integral of the

electric field with a dot product with respect to the

area, therefore we have EA cosine theta, if there is a constant

area electric field and angle. The electric flux leads us to Gauss’ Law. Gauss’ Law, the electric flux. Now this Gauss’ Law. It has to do with the Gaussian surface. Whenever using Gauss’

Law, you have to draw and identify your

Gaussian surface, please. Gauss’ Law is the closed surface integral E dot dA is equal to the charge

inside the Gaussian surface divided by E not. Usually we use Gauss’ law to

figure out the electric field on something that electric field, that in order to use Gauss’ Law, you choose a Gaussian surface

such that the electric field is constant on the Gaussian surface. The dot product, so we have

the cosine of the angle. Therefore, the angle needs

to either be 0 or 90 degrees in order to use Gauss’ Law,

at least in this class. That’s why we choose our Gaussian surface such that the theta is equal

to either 0 or 90 degrees, so please be very careful

with Gauss’ Law. Make sure the electric field is constant on your Gaussian surface, and the angle between the electric field and the area vector is either

0 or 90 degrees, please. Remember to use Gauss’ Law to figure out the electric field around

a point particle or a … We use it to show that

the electric field around any spherical object is

equal to the electric field caused by our point particle. That is something that’s

important to know. You need to know how to derive it, and sometimes it’ll just ask

you what is the electric field around this particular spherical object. And if they say “what is?”, don’t derive it because you don’t want to

waste time on the AP test. That’s the last thing you want to do. Simply if they ask what

is the electric field around this particular spherical object, then you can simply say it

acts like a point charge, and it’s Kq over r². Certainly, if they ask you to derive it, you’re going to have to use Gauss’ Law. Electric potential energy, we have Kq1q2 over r. Electric potential energy, again, in order to have electric

potential energy, you have to have 2 charges, Kq1q2 over r. Electric potential difference. Notice the relationship here between electric potential difference and electric potential energy and the electric field,

and the electric force. The electric potential difference is the change in the

electric potential energy per unit charge, just

like the electric field is the electric force per unit charge. It’s a way to get rid of that test charge and just talk about the energy that exists in a particular space without the charge that could be there. When you add the charge, then you would have the energy, but it’s an energy that exists

in a field, if you will, just like we have an electric field. We have the same thing. We can talk about the

electric potential difference caused by a point charge, so the electric potential difference is, again, all we do is

substitute in the equation for the electric potential energy, and we end up with Kq over r. That is the electric potential difference for a point charge, but the electric potential difference between a point infinitely far

away and a point r distance from our point of charge. We can use that to figure out

the electric potential difference between a point infinitely far away and a continuous charge distribution of distance r from a

continuous charge distribution by simply taking our

continuous charge distribution and breaking it up into little pieces, dq, which is all going to have an

electric potential difference, dV, which is Kdq over r. In other words, you end up

having to take the integral for a continuous charge distribution. Please remember that

electric potential difference is a scalar because it comes

from energy, which is a scalar, unlike electric field, which is a vector because electric force is a vector. The electric potential

difference by definition is the negative of the integral

of electric field dot product with dr, with respect to position. In a constant electric field,

that actually works out to be the negative times

the electric fields times the change in position. Electric potential differences

is an important one and the constant electric

field is equal to negative E delta d. A unit that often gets used on the AP test is one electron volt,

and the one electron volt is defined as 1.6 times 10

to the negative 19 Joules. Notice that electron volt

sounds like it is a volt like the electric potential difference, but it is not. It is simply a measurement of energy. It’s just a very small amount of energy and we use that for describing very small amounts of energy. Capacitance is defined as the charge that can be carried, that

can be stored on a capacitor per electric potential

difference for that capacitor. For a parallel plate capacitor, we have an equation which we derived, which is the dielectric

constant times E-not times the area of the

two plates divided by d, the distance between the 2 plates. An important thing to

realize about capacitance is it is always positive and this charge is the

charge on 1 of the 2 plates. If we were to talk about the

total charge in a capacitor, it’s actually going to be 0 because the 2 plates are going to carry

the same amount of charge. Therefore, this charge is the charge either on the positive or negative plate depending on whether you’re

talking about a negative or positive electric potential difference, but the capacitance by

definition has to be positive. You have equations for

capacitors in series and capacitors in parallel. We’ll start with capacitors in series. A capacitor in series is simply equal to the inverse of the sum of the

inverses of the capacitances of the various capacitors and when you have capacitors in series, charge is the same, and the

electrical potential differences add. When you have capacitors in parallel, it is simply adding the capacitors. You simply add the sum of the capacitors to get the equivalent capacitance. For capacitors in parallel, the electric potential

difference is the same, and the charges add, again, for capacitors in parallel. We’ve derived the equation for the energy stored in a capacitor. The energy stored in a

capacitor can be defined. We have, actually, three

different equations, but it all has to do with

whether you have charge, capacitance, and electric

potential difference, which two of those you have. We have three different equations, and you should really know all three. Current. Current is defined as

the derivative of charge as a function of time. Literally, the charge of the current is if you could count the

charges as they go by in time, how long it would take, it is literally the charge per unit time. That is what current is. That is one of the two

equations we have for current. We also have another equation for current. Another equation we

have for current is that it is equal to the charged carrier density multiplied by the charge per carrier multiplied by the drift velocity times the cross-sectional area. Where n, the charge carrier density, is the number of charges

per unit of volume. q is the charge on those charge carriers. V sub d, the drift velocity,

is actually very small. It’s an important piece to realize that the overall change in

motion of the charges themselves is actually very small and in general, and the cross-sectional area is the area normal to

the direction of travel, of net travel of the drift velocity. Resistance. Electric potential

difference equals the current time to resistance is

usually how you see it, but if you were to rearrange

it solve for the resistance, resistance equals the

electric potential difference divided by the current. Not to be confused with resistivity. Resistance in terms of resistivity, resistivity would be rho. Resistance is equal to rho, the

resistivity times the length divided by the cross-sectional area. Resistance is the resistance

of a specific geometric object which includes both the

resistivity of the object to the length and the

cross-sectional area, whereas resistivity is

simply a material property. Three different equations

for electric power. Current times electric

potential difference, current squared times resistance and electric potential difference squared divided by the resistance. Just like the energy

stored in a capacitor, we have three different equations, but it really just depends

on which two you have. This is the rate at which

electric potential energy is being converted to heat

and sound and light, depending on exactly what

you are talking about in a specific case. EMF, or electromotive force

versus terminal voltage. Electromotive force, again, a misnomer, sounds like a force. It is not. The electromotive force is the ideal electric potential

difference across a battery, whereas delta V sub t, the terminal voltage is the

actual potential difference you get from a battery,

what you would measure at the terminals of the battery. The only way to get the

emf out of a battery actually is to have a

current equal to zero. If you look at the equation

for the terminal voltage, it’s equal to the emf across a battery minus the current through the battery times the internal resistance, lowercase r for the internal resistance. Again, the only way to

get the terminal voltage equal to the emf is if that

current is equal to zero and what’s the point in that? you’re not actually

getting anything out of it. We can have resistors in parallel and resistors in series. When you have resistors in parallel, you have the equivalent

resistance is equal to the inverse of the sum of the inverse of the resistances, where the electric potential difference is going to be the same

and the currents add, again, when you have

resistors in parallel. If you have resistors in series, that means that the resistances

are simply going to add. you’re going to have the

sum of the resistances, and when you have resistors in series, the currents are going to be the same and the electric

potential differences add, so it’s reversed. Kirchhoff’s Rules. An example of when we would

need to use Kirchhoff’s Rules, are when we have two batteries in a circuit,

and it’s hard to identify what the current directiion

you’re going to be, so on and so forth. When you use Kirchhoff’s

Rules, it’s the basic idea that … at a junction, for example, at point A, that the currents into

the loop are equal to the currents going out of the loop. when you add up all the currents going in, those are going to be equal

to the currents going out, and the electrical potential

difference around a loop, the other Kirchhoff’s rule is equal to 0. The electrical potential

difference around a loop is going to be equal to 0. What that’s going to look like

in this particular case is … When you’re using Kirchhoff’s rules, you have to pick a loop direction. Pick your loop directions and

you have to pick a junction. You’re always going to have

one more loop than you need and one more junction than you need. You’ll notice there’s

actually a loop that goes all the way around the outside, which I have yet to define and we only need one of the junctions. Let’s start with one of the loops. Let’s start with loop A. As you go around loop A, we’ll start at emf 1. That’s going to be positive

because we’re going in the direction of the loop. As you go in the direction of the loop, in the same direction of the current, as you go across a resistor, the electric potential

is going to go down, so we have the negative

electric potential difference across the resistor. Now, notice that we’re

going opposite the direction of the positive versus

negative of the emf of 2, therefore, going in that loop direction, the emf is going to be equal to, we’re going to have a negative emf. Note the current is independent. It’s irrelevant when we’re talking about whether we’re going positive

or negative for the emf. It only has to do with

the direction of the loop verses the positive and negative

terminals of the battery. Because for resistor

3, we’re going opposite the direction of the current for our loop, then the electric potential difference is actually going to go up, and we have the positive

electric potential difference across resistor 3. Then I just substitute in

current times resistance for each of those, and that

is our equation for loop A. Somehow, I neglected to mention the main really important piece there is that the electric potential

difference around loop A is also equal to 0. Important but I skipped

it there, I’m sorry. The electric potential

difference around loop B is also equal to 0, so

as we go around loop B, now, notice we’re doing

in the same direction as going from negative to positive across terminals and battery emf 2, so that’s going to be positive

as we go around loop B. (whistles) And, we are going in the direction

of the current in the loop, and the current direction of the same, so the electric potential

is going to go down for both resistor 2 and resistor 3, so we end up with 0 is equal to the emf 2 minus current 2 times resistor 2, minus current 3 times resistor 3. If we look at the first rule here with some of the currents

into and out of a junction are the same. If we look at junction A, we have current 1 going into junction A, current 3 going into junction A, and current 2 going out of junction A. In other words, current 1 plus current 3 is equal to current 2. Notice now that we actually

have three equations that we need to solve simultaneously. Usually the way I will end up solving that is using row-reduced echelon form on my calculator. And creating that matrix is, as far as I am concerned, the easiest way to solve

a problem like this. Next, we have a concept of an RC Circuit, a circuit where we have both a resistor and a capacitor, and usually a battery, but that would be charging a

capacitor through a resistor in an RC Circuit. You can also have discharging a capacitor through a resistor. Let’s write down some of the equations. Charging a capacitor through a resistor, we end up with the charge as a function of time on the capacitor

is equal to the capacitance times the emf times the quantity 1 minus E to the negative t over RC. You can also derive that the

current is a function of time is equal to the emf

divided by the resistance times the E to the negative t over RC. Again, this is charging a

capacitor through a resistor, and it’s important that you know how to derive these equations, but it is almost more important that you understand the limits because the limits come

up very often in problems. For example, when you’re

charging a capacitor through a resistor, at

time t is equal to 0, the initial charge on the capacitor is going to be equal to 0, and the current is going

to be at a maximum. You could see that in the equations, but that also should make sense to you because initially, there’s

no charge on the capacitor. Therefore, the electric potential difference, across the capacitor, is going to be equal to 0, therefore the electric potential difference,

across the resistor is going to be at a maximum. Therefore the current across the resistor is going to be at a maximum. On the other end, at time is

approximately equal to infinity, we have fully charged the capacitor, therefore the charge is equal to q max, and therefore, the electric potential difference, across the capacitor is going to be pretty much equal to, potentially difference across the battery, therefore there’s going to be

no current across the resistor because there’s none left. The electric potential difference

across the resistor is equal to 0. you could also talk about

discharging a capacitor through the resistor. Discharging a capacitor

through a resistor, we end up with our equations for the charge as a function of time, which can be equal to charge initial times E to the quantity

of negative t over RC, and the charge is, our current

is a function of the time, is going to be equal to

negative of the charge current inital times E to

the negative t over RC. Negative simply because the

current has changed directions when we’re discharging

versus charging a capacitor. now, again, the limits are very important. To add time t equals 0, we’re going to have the maximum current and the maximum charge because we start out with the most amount of

charge on the capacitor, we’re going to be releasing

that through the circuit, therefore, the current is

going to be at a maximum, and it’s going to decrease

as a function of time. the charge is going to be at a maximum, and decrease as a function of time. Both are going to end at zero at the end. You should be aware of how to

derive all these equations, you should know the limits

of all these equations, and you should also be

familiar with the shapes of these different graphs, please. Another thing, the time constant. One other thing that we need to talk about is the time constant. Time constant for an RC circuit is the resistance times the capacitance. It is literally the time it

takes to get a 63.2% change in whatever we were

talking about right here. Unfortunately, this number,

63.2% is a very important number and one that you should memorize. I’m not a fan of memorization, but it is an important one. The idea of I’m not a fan of memorization, here is it where it comes from. If you plug in the time

constant RC in for your time, you’ll get 1 minus E to the negative 1, which is 0.632, or 63.2%. That’s where it comes from. If you forget, you can just

do that in your calculator and use your brain. Lecture notes are available

at FlippingPhysics.com. Please enjoy lecture notes responsibly.

Why couldn't you have been MY physics teacher???

your four videos for the ap exams saved me. Thanks man

How screwed am I if I only answered 2 out of 3 questions on the free response and guessed on 4 on the multiple choice?

you're good man. a 70% (or maybe 75? not sure) is a 5.

Moriarty? Can't wait to see you in the next season of sherlock!

2 minutes in and i love this haha

i am very thankful that you upload such videos 🙂

I'm a freshman in high school and i got a 5 on this test.

thank you, this video was unbelievably helpful, it reviewed all important topics and reminded me exactly what I need to review for the test. your a saint.( "immediately subscribes and likes this page")

If it wasn't for this video I would have know nothing on my physics 212 final

Great video I love it so much!!!

Twinkle Twinkle little star, power equals I squared R…gonna pass my test yay

Extremely helpful even for college-level physics. I take the excellent explanation of formula's from you, and the deeper derivation of some of them from my college lectures. Thank you so much!

You are awesome

You sir, are awesome! Thanks for posting this!!!

This is far more complex than it needs to be.

I wish you were my Physics teacher. You're more interesting to listen to and make more sense at the same time.

I love E&M ! thanks for the video

This is the way to flip physics, amazing trick to teach 🙂

Definitely a great find the night before the AP Test. Thanks!

This channel should have 1 million subscribers already

Very quality video. Great to learn and review equations. But to be honest, this video will not help if you don't know how to use the equations with the problems you're given.

If only that intellect of yours could help you realize that it would have been better if you had a better handwriting, at least for the sake of the efficiency of this video at teaching/helping.

sir where can i find your lectures of capacitor and capacitance??

I just received word that I scored a 5 on this exam! This video along with all your others definitely helped. Thank you so much! 🙂

Why is Physics II so focused on calculations and values, over explaining concepts? I took Physics II during the Spring, and while I could calculate all these different things, I still felt fundamentally confused about some concepts. Oh well.. Maybe I should just watch a documentary…

Thanks for the tips you have discussed here.

I am trying to learn fundamentals of physics with electricity and magnatism and I am very thankful I have found your channel.

Dude Your lit !

Watched these videos before both of my ap tests (mechanics and E&M); got a 5 on both of them :D. srsly grateful to you Mr. P.

I see a line integral there and a flux integral? Aren't they double integrals?

God based magnetism on YouTube explains and demonstrates magnetism correctly. Check it out and stop making lame videos, jackass.

Your creep me out no offense

OMG! YOU'RE REALLY AWESOME!!!

Awesome job putting together

Thanks for making these fantastic videos. One remark: electric force should be a vector, and you state that it is a vector, but you give a scalar expression. Do you agree? Is there some correction you would make to the formula in the video?

Test tmr……….. I am scared

Studying for my Physics final and I found this extremely helpful. Thanks!

The AP exam is tomorrow. I'm going to engineering school so this course is required… Thank you for this lol

E&M is causing me to stress out so thanks for the help and review. Should go smoother tomorrow.

very helpful for college physics, thanks!

You sir are awesome

If the distance between two charges go from 2m to 1m, what would be the net charge? Both have a charge of +q

Every decent student often carries these 3 facets of their personality with them at all times, which side they chose to suppress and chose to entertain is a different matter. Nice use of parody, solid shit.

I want to take ap physics c next year but my math has always been behind. I am taking ap physics b right now while concurrently taking algebra 2. At first it was overwhelming, but I got used to everything and I now have a 99 in physics. I was wondering if I could somehow learn the calculus required for this course during the summer or would that be too difficult? I plan on going to georgia tech and majoring in physics/astronomy.

you suck idiot

Online we can allways stop and rewind. That being said, when you talk this fast the information doesn't stick that well. What's the hurry?

Hey man you are the only online physics professor that I cannot watch at 2.0 speed and understand. you are quick and engaging at regular speed and it's awesome. Props to you. I love the videos haha

Lord Faarquad looking ass

2018 Electricity and Magnetism anyone??

Exam tomorrow

Holy crap physics c exam is tomorrow. I am done for for FRQs, but wish me luck this is a pretty good review !!!

I feel pretty confident in getting a 5 in mechanics tomorrow, but I'm feeling shaky on e and m,especially gauss law, any tips?

psh all you people watching this the day before the exam i’m watching it the morning of

Watching these videos on 2x in my history class… Have mercy college board

it is a great review of the equations but many remain insufficiently explained.

this is dude is rad.

It's when I decide to watch videos like these that I know I will get pounded by the final. Thanks anyways!

stop tapping the board hombre

Good but there is icons if he talk about him what mean it

tips for everyone. Slow down the pace by 400%

Who's got a mid term tomorrow? 😅😅😂😂

2019 E & M squad??? 🙂

Who else is here for tomorrow? Good luck everybody. FRQs will be the death of me.

Wait a second, how does the change in electric potential increase when going through the 3rd resistor? I mean I see how the current is going the opposite direction, but how did the current reverse direction? look @ 14:27

Why is this in my recommandations

I’m here 30 minutes before my exam let’s go

If it wasn't for this video, I would know quite literally nothing going into my physics 1602 final tomorrow

Thanks for this. I can use this as an accelerated refresher course so I can dive into reviewing circuit analysis concepts and then go onto learning digital circuits, electronics, signals/systems, etc.

you are helpful!

It's so cool finding out that we do the exact same Physics😃

Sir why do dont have videos on charge, coluombs law,electric potential and field,gauss's law,capacitor and combination of capacitor etc.if you already uploaded please tell me