# (1 of 2) Electricity and Magnetism – Review of All Topics – AP Physics C 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
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.

## 73 thoughts on “(1 of 2) Electricity and Magnetism – Review of All Topics – AP Physics C”

1. Alison Thompson says:

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

2. Arlind Mara says:

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

3. Oshyrath says:

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?

4. captainwankbeard says:

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

5. varun009 says:

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

6. SHONSL says:

2 minutes in and i love this haha

7. Janoy Cresva says:

i am very thankful that you upload such videos 🙂

8. babu wanyeki says:

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

9. Caleb Hille says:

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")

10. Tyler Raco says:

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

11. Kele Shi says:

Great video I love it so much!!!

12. Andre Mendoza says:

Twinkle Twinkle little star, power equals I squared R…

13. Prodigy 1227 says:

gonna pass my test yay

14. Michael Olson says:

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!

15. Yes Please says:

You are awesome

16. cfafish says:

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

17. Lewis U. says:

This is far more complex than it needs to be.

18. Celeste Torres says:

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

19. ihonestytruthful says:

I love E&M ! thanks for the video

20. Dipendra Kunwar says:

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

21. Max Narvaez says:

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

22. GrotiusMaximus says:

This channel should have 1 million subscribers already

23. Reese Hagan says:

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.

24. Kirito96 says:

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.

25. Sahil Dhar says:

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

26. Charles C says:

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! 🙂

27. TheRoflcopterGod says:

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…

28. Electrician Dallas Tx says:

Thanks for the tips you have discussed here.

29. estlou says:

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

30. Juan Gallego says:

31. Qualu Nedakul says:

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.

32. Reason says:

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

33. Michael S. Green says:

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

34. Team Warriors Harsh says:

Your creep me out no offense

35. AybukeAkkoca says:

OMG! YOU'RE REALLY AWESOME!!!

36. jove hassan says:

Awesome job putting together

37. fbg00 says:

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?

38. Vladimir Putin says:

Test tmr……….. I am scared

39. King Koopa says:

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

40. CharlemagneXVII says:

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

41. David says:

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

42. TheOfficialMeezak says:

very helpful for college physics, thanks!

43. whoosht says:

You sir are awesome

44. ChewVodka says:

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

45. StereoSoundAgent says:

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.

46. sarah h says:

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.

47. Worried Bacteria says:

you suck idiot

48. ofer greenberg says:

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?

49. Nate says:

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

50. MinDetonator96 says:

51. Ducksfan101 says:

2018 Electricity and Magnetism anyone??

52. Saheth Edupuganti says:

Exam tomorrow

53. Annie Ho says:

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

54. Harshil Patel says:

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?

55. Sam Gilson says:

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

56. Ann Wang says:

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

57. Pablo Roman says:

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

58. Keaton Steuben says:

59. Simon bastin says:

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

60. Mark Cohen says:

stop tapping the board hombre

61. عبدالرحمن 2018 says:

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

62. T C says:

tips for everyone. Slow down the pace by 400%

63. Andy says:

Who's got a mid term tomorrow? 😅😅😂😂

64. Emily Fang says:

2019 E & M squad??? 🙂

65. Nico Reyes says:

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

66. Georgy Thayyil says:

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

67. Justin Vaughn Salvador says:

Why is this in my recommandations

68. SHICHO says:

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

69. Gigi Spence says:

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

70. ElectroShock says:

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.

71. Marefe Balagtas says:

72. Phumlani Fikeni says:
73. WWE collections says: