0:00:00.000,0:00:00.830


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Before we move on, I want to[br]clarify something that I've

0:00:03.510,0:00:04.490
inadvertently done.

0:00:04.490,0:00:06.660
I think I was not exact[br]with some of the

0:00:06.660,0:00:07.550
terminology I used.

0:00:07.550,0:00:10.920
So I want to highlight the[br]difference between two things

0:00:10.920,0:00:12.590
that I've used almost[br]interchangeably up to this

0:00:12.590,0:00:15.100
point, but now that we are about[br]to embark on learning

0:00:15.100,0:00:18.260
what voltage is, I think it's[br]important that I highlight the

0:00:18.260,0:00:20.200
difference, because initially,[br]this can be very confusing.

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I remember when I first learned[br]this, I found I often

0:00:23.430,0:00:26.680
mixed up these words and didn't[br]quite understand why

0:00:26.680,0:00:27.540
there was a difference.

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So the two words are[br]electrical-- or sometimes

0:00:31.280,0:00:33.580
you'll see electric instead[br]of electrical.

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So "electric potential energy"[br]and "electric potential." I

0:00:49.110,0:00:51.380
think even in the last video,[br]I used these almost

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interchangeably, and I shouldn't[br]have. I really

0:00:53.630,0:00:56.500
should have always used[br]electrical or electric

0:00:56.500,0:00:57.390
potential energy.

0:00:57.390,0:00:58.850
And what's the difference?

0:00:58.850,0:01:05.379
Electrical potential energy is[br]associated with a charge.

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It's associated with a particle[br]that has some charge.

0:01:08.830,0:01:12.390
Only that particle[br]can have energy.

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Electrical potential, or[br]electric potential, this is

0:01:16.520,0:01:18.860
associated with a position.

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So, for example, if I have a[br]charge and I know that it's at

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some point with a given electric[br]potential, I can

0:01:26.720,0:01:29.590
figure out the electric[br]potential energy at that point

0:01:29.590,0:01:32.710
by just multiplying actually[br]this value by the charge.

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Let me give you some examples.

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Let's say that I have[br]an infinite

0:01:38.380,0:01:39.740
uniformly charged plate.

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So that we don't have to do[br]calculus, we can have a

0:01:41.290,0:01:43.050
uniform electric field.

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Let's say that this[br]is the plate.

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I'll make it vertical just so we[br]get a little bit of change

0:01:47.130,0:01:55.760
of pace, and let's say it's[br]positively charged plate.

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And let's say that the[br]electric field

0:01:57.170,0:01:59.010
is constant, right?

0:01:59.010,0:02:00.060
It's constant.

0:02:00.060,0:02:05.580
No matter what point we pick,[br]these field vectors should all

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be the same length because the[br]electric field does not change

0:02:08.156,0:02:12.290
in magnitude it's pushing out,[br]because we assume when we draw

0:02:12.290,0:02:14.810
field lines that we're using a[br]test charge with a positive

0:02:14.810,0:02:16.060
charge so it's pushing[br]outward.

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Let's say I have a[br]1-coulomb charge.

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Actually, let me make[br]it 2 coulombs just

0:02:24.420,0:02:26.320
to hit a point home.

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Say I have a 2-coulomb charge[br]right here, and it's positive.

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A positive 2-coulomb charge, and[br]it starts off at 3 meters

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away, and I want to bring[br]it in 2 meters.

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I want to bring it in 2 meters,[br]so it's 1 meter away.

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0:02:51.800,0:02:56.250
So what is the electric-- or[br]electrical-- potential energy

0:02:56.250,0:03:00.600
difference between the particle[br]at this point and at

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this point?

0:03:02.200,0:03:05.270
Well, the electrical potential[br]energy difference is the

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amount of work, as we've learned[br]in the previous two

0:03:07.860,0:03:11.390
videos, we need to apply to this[br]particle to take it from

0:03:11.390,0:03:12.770
here to here.

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So how much work do[br]we have to apply?

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We have to apply a force that[br]directly-- that exactly-- we

0:03:21.290,0:03:22.990
assume that maybe this is[br]already moving with a constant

0:03:22.990,0:03:24.840
velocity, or maybe we have to[br]start with a slightly higher

0:03:24.840,0:03:27.210
force just to get it moving, but[br]we have to apply a force

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that's exactly opposite the[br]force provided by Coulomb's

0:03:34.000,0:03:37.570
Law, the electrostatic force.

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And so what is that force we're[br]going to have to apply?

0:03:40.030,0:03:42.620
Well, we actually have to know[br]what the electric field is,

0:03:42.620,0:03:44.650
which I have not told you yet.

0:03:44.650,0:03:46.220
I just realized that,[br]as you can tell.

0:03:46.220,0:03:54.330
So let's say all of these[br]electric field lines are 3

0:03:54.330,0:03:57.100
newtons per coulomb.

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So at any point, what is the[br]force being exerted from this

0:04:01.260,0:04:02.940
field onto this particle?

0:04:02.940,0:04:07.630
Well, the electrostatic force[br]on this particle is equal to

0:04:07.630,0:04:16.269
the electric field times the[br]charge, which is equal to-- I

0:04:16.269,0:04:19.829
just defined the electric field[br]as being 3 newtons per

0:04:19.829,0:04:25.220
coulomb times 2 coulombs.

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It equals 6 newtons.

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So at any point, the electric[br]field is pushing this way 6

0:04:30.940,0:04:33.416
newtons, so in order to push the[br]particle this way, I have

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to completely offset that, and[br]actually, I have to get it

0:04:35.930,0:04:37.170
moving initially, and I'll[br]keep saying that.

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I just want to hit[br]that point home.

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So I have to apply a force of[br]6 newtons in the leftward

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direction and I have to apply[br]it for 2 meters to get the

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point here.

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So the total work is equal to[br]6 newtons times 2 meters,

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which is equal to 12[br]newton-meters or 12 joules.

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So we could say that the[br]electrical potential energy--

0:05:04.200,0:05:05.570
and energy is always joules.

0:05:05.570,0:05:07.950
The electrical potential energy[br]difference between this

0:05:07.950,0:05:10.850
point and this point[br]is 12 joules.

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Or another way to say it[br]is-- and which one

0:05:13.520,0:05:14.530
has a higher potential?

0:05:14.530,0:05:16.140
Well, this one does, right?

0:05:16.140,0:05:19.610
Because at this point, we're[br]closer to the thing that's

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trying to repel it, so if we[br]were to just let go, it would

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start accelerating in this[br]direction, and a lot of that

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energy would be converted to[br]kinetic energy by the time we

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get to this point, right?

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So we could also say that the[br]electric potential energy at

0:05:33.520,0:05:38.400
this point right here is 12[br]joules higher than the

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electric potential energy[br]at this point.

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Now that's potential energy.

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What is electric potential?

0:05:46.300,0:05:51.330
Well, electric potential tells[br]us essentially how much work

0:05:51.330,0:05:55.550
is necessary per unit[br]of charge, right?

0:05:55.550,0:05:58.220
Electric potential energy was[br]just how much total work is

0:05:58.220,0:06:01.650
needed to move it from[br]here to here.

0:06:01.650,0:06:05.890
Electric potential says, per[br]unit charge, how much work

0:06:05.890,0:06:09.340
does it take to move any charge[br]per unit charge from

0:06:09.340,0:06:11.010
here to here?

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Well, in our example we just[br]did, the total work to move it

0:06:14.070,0:06:15.780
from here to here[br]was 12 joules.

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But how much work did it take to[br]move it from there to there

0:06:20.130,0:06:21.500
per charge?

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Well, work per charge is equal[br]to 12 joules for what?

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What was the charge[br]that we moved?

0:06:32.280,0:06:35.040
Well, it was 2 coulombs.

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It equals 6 joules[br]per coulomb.

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That is the electric potential[br]difference between this point

0:06:48.930,0:06:49.760
and this point.

0:06:49.760,0:06:51.180
So what is the distinction?

0:06:51.180,0:06:54.150
Electric potential energy was[br]associated with a particle.

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How much more energy did the[br]particle have here than here?

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When we say electric potential,[br]because we

0:07:00.140,0:07:03.490
essentially divide by the[br]size of the particle, it

0:07:03.490,0:07:05.720
essentially is independent of[br]the size of the particle.

0:07:05.720,0:07:07.960
It actually just depends[br]on our position.

0:07:07.960,0:07:12.130
So electric potential, we're[br]just saying how much more

0:07:12.130,0:07:15.180
potential, irrespective of the[br]charge we're using, does this

0:07:15.180,0:07:18.240
position have relative[br]to this position?

0:07:18.240,0:07:21.960
And this electric potential,[br]that's just another way of

0:07:21.960,0:07:27.980
saying voltage, and the unit[br]for voltage is volts.

0:07:27.980,0:07:30.600
So 6 joules per coulomb,[br]that's the

0:07:30.600,0:07:34.030
same thing as 6 volts.

0:07:34.030,0:07:42.060
And so if we think of the[br]analogy to gravitation, we

0:07:42.060,0:07:46.170
said gravitational potential[br]energy was mgh, right?

0:07:46.170,0:07:46.860
This was force.

0:07:46.860,0:07:49.040
This was distance, right?

0:07:49.040,0:07:52.970
Electric potential is[br]essentially the amount of

0:07:52.970,0:07:55.820
gravitational-- if we extend[br]the analogy, the amount of

0:07:55.820,0:07:58.890
gravitational potential energy[br]per mass, right?

0:07:58.890,0:08:04.500
So if we wanted a quick way of[br]knowing what the gravitational

0:08:04.500,0:08:06.640
potential is at any point[br]without having to care about

0:08:06.640,0:08:09.340
the mass, we divide by the[br]mass, and it would be the

0:08:09.340,0:08:11.130
acceleration of gravity[br]times height.

0:08:11.130,0:08:13.750
Ignore that if it[br]confused you.

0:08:13.750,0:08:15.590
So what is useful[br]about voltage?

0:08:15.590,0:08:19.650
It tells us regardless of how[br]small or big or actually

0:08:19.650,0:08:23.170
positive or negative a charge[br]is, what the difference in

0:08:23.170,0:08:26.980
potential energy would be if[br]we're at two different points.

0:08:26.980,0:08:31.390
So electric potential, we're[br]comparing points in space.

0:08:31.390,0:08:37.760
Electric potential energy, we're[br]comparing charges at

0:08:37.760,0:08:39.330
points in space.

0:08:39.330,0:08:40.789
Hopefully, I didn't[br]confuse you.

0:08:40.789,0:08:43.059
In the next video, we'll[br]actually do a couple of

0:08:43.059,0:08:45.690
problems where we figure out[br]the electric potential

0:08:45.690,0:08:48.960
difference or the voltage[br]difference between two points

0:08:48.960,0:08:51.050
in space as opposed[br]to a charge at two

0:08:51.050,0:08:52.190
different points in space.

0:08:52.190,0:08:54.760
I will see you in[br]the next video.

0:08:54.760,0:08:54.900