1
00:00:00,000 --> 00:00:00,930


2
00:00:00,930 --> 00:00:02,930
Let's imagine that instead of
having two charges, we just

3
00:00:02,930 --> 00:00:05,210
have one charge by itself,
sitting in a

4
00:00:05,210 --> 00:00:07,210
vacuum, sitting in space.

5
00:00:07,210 --> 00:00:12,650
So that's this charge here, and
let's say its charge is Q.

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00:00:12,650 --> 00:00:14,950
That's some number,
whatever it is.

7
00:00:14,950 --> 00:00:16,390
That's it's charge.

8
00:00:16,390 --> 00:00:21,850
And I want to know, if I were to
place another charge close

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00:00:21,850 --> 00:00:26,720
to this Q, within its sphere of
influence, what's going to

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00:00:26,720 --> 00:00:27,880
happen to that other charge?

11
00:00:27,880 --> 00:00:30,820
What's going to be the
net impact on it?

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00:00:30,820 --> 00:00:33,540
And we know if this has some
charge, if we put another

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00:00:33,540 --> 00:00:37,130
charge here, if this is 1
coulomb and we put another

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00:00:37,130 --> 00:00:40,720
charge here that's 1 coulomb,
that they're both positive,

15
00:00:40,720 --> 00:00:42,550
they're going to repel each
other, so there will be some

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00:00:42,550 --> 00:00:45,310
force that pushes the
next charge away.

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00:00:45,310 --> 00:00:47,920
If it's a negative charge and I
put it here, it'll be even a

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00:00:47,920 --> 00:00:50,580
stronger force that pulls it
in because it'll be closer.

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So in general, there's this
notion of what we can call an

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00:00:53,550 --> 00:00:56,070
electric field around
this charge.

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And what's an electric field?

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00:00:57,320 --> 00:00:59,960


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00:00:59,960 --> 00:01:04,019
We can debate whether it really
exists, but what it

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allows us to do is imagine that
somehow this charge is

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00:01:09,880 --> 00:01:13,280
affecting the space around it
in some way that whenever I

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put-- it's creating a field that
whenever I put another

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charge in that field, I can
predict how the field will

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affect that charge.

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So let's put it in a little more
quantitative term so I

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00:01:23,350 --> 00:01:24,990
stop confusing you.

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So Coulomb's Law told us that
the force between two charges

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is going to be equal to
Coulomb's constant times-- and

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00:01:33,945 --> 00:01:37,090
in this case, the first
charge is big Q.

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00:01:37,090 --> 00:01:39,890
And let's say that the second
notional charge that I

35
00:01:39,890 --> 00:01:43,170
eventually put in this field
is small q, and then you

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00:01:43,170 --> 00:01:44,600
divide by the distance
between them.

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00:01:44,600 --> 00:01:47,810
Sometimes it's called r because
you can kind of view

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the distance as the
radial distance

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between the two charges.

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So sometimes it says r squared,
but it's the distance

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between them.

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So what we want to do if we want
to calculate the field,

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00:01:56,890 --> 00:02:00,260
we want to figure out how much
force is there placed per

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00:02:00,260 --> 00:02:03,710
charge at any point around this
Q, so, say, at a given

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00:02:03,710 --> 00:02:05,460
distance out here.

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00:02:05,460 --> 00:02:09,070
At this distance, we want to
know, for a given Q, what is

47
00:02:09,070 --> 00:02:10,460
the force going to be?

48
00:02:10,460 --> 00:02:12,390
So what we can do is we could
take this equation up here and

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00:02:12,390 --> 00:02:14,890
divide both sides by this small
1, and say, OK, the

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00:02:14,890 --> 00:02:18,470
force-- and I will arbitrarily
switch colors.

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00:02:18,470 --> 00:02:27,100
The force per charge at this
point-- let's call that d1--

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00:02:27,100 --> 00:02:32,110
is equal to Coulomb's constant
times the charge of the

53
00:02:32,110 --> 00:02:37,440
particle that's creating the
field divided by-- well, in

54
00:02:37,440 --> 00:02:41,360
this case, it's d1--
d1 squared, right?

55
00:02:41,360 --> 00:02:45,280
Or we could say, in general--
and this is the definition of

56
00:02:45,280 --> 00:02:47,860
the electric field, right?

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00:02:47,860 --> 00:02:51,310
Well, this is the electric field
at the point d1, and if

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00:02:51,310 --> 00:02:53,400
we wanted a more general
definition of the electric

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00:02:53,400 --> 00:02:57,260
field, we'll just make this a
general variable, so instead

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00:02:57,260 --> 00:02:59,590
of having a particular distance,
we'll define the

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00:02:59,590 --> 00:03:03,870
field for all distances
away from the point Q.

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00:03:03,870 --> 00:03:08,100
So the electric field could be
defined as Coulomb's constant

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00:03:08,100 --> 00:03:13,110
times the charge creating the
field divided by the distance

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00:03:13,110 --> 00:03:16,210
squared, the distance we are
away from the charge.

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00:03:16,210 --> 00:03:18,890
So essentially, we've defined--
if you give me a

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force and a point around this
charge anywhere, I can now

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00:03:25,440 --> 00:03:26,610
tell you the exact force.

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00:03:26,610 --> 00:03:34,970
For example, if I told you that
I have a minus 1 coulomb

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00:03:34,970 --> 00:03:43,490
charge and the distance is equal
to-- oh, I don't know.

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00:03:43,490 --> 00:03:49,610
The distance is equal to let's
say-- let's make it easy.

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00:03:49,610 --> 00:03:51,710
Let's say 2 meters.

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00:03:51,710 --> 00:03:55,590
So first of all, we can say,
in general, what is the

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00:03:55,590 --> 00:03:58,370
electric field 2 meters
away from?

74
00:03:58,370 --> 00:04:01,310
So what is the electric
field out here?

75
00:04:01,310 --> 00:04:03,090
This is 2, right?

76
00:04:03,090 --> 00:04:04,320
And it's going to be
2 meters away.

77
00:04:04,320 --> 00:04:06,160
It's radial so it's actually
along this whole circle.

78
00:04:06,160 --> 00:04:07,180
What is the electric
field there?

79
00:04:07,180 --> 00:04:10,160
Well, the electric field at
that point is going to be

80
00:04:10,160 --> 00:04:11,430
equal to what?

81
00:04:11,430 --> 00:04:13,580
And it's also a vector
quantity, right?

82
00:04:13,580 --> 00:04:17,529
Because we're dividing a vector
quantity by a scalar

83
00:04:17,529 --> 00:04:18,519
quantity charge.

84
00:04:18,519 --> 00:04:22,300
So the electric field at that
point is going to be k times

85
00:04:22,300 --> 00:04:26,360
whatever charge it is divided
by 2 meters, so divided by 2

86
00:04:26,360 --> 00:04:29,180
meters squared, so that's 4,
right, distance squared.

87
00:04:29,180 --> 00:04:32,360
And so if I know the electric
field at any given point and

88
00:04:32,360 --> 00:04:35,000
then I say, well, what happens
if I put a negative 1 coulomb

89
00:04:35,000 --> 00:04:37,780
charge there, all I have to do
is say, well, the force is

90
00:04:37,780 --> 00:04:41,600
going to be equal to the charge
that I place there

91
00:04:41,600 --> 00:04:45,910
times the electric field
at that point, right?

92
00:04:45,910 --> 00:04:49,300
So in this case, we said the
electric field at this point

93
00:04:49,300 --> 00:04:54,950
is equal to-- and the units for
electric field are newtons

94
00:04:54,950 --> 00:04:56,790
per coulomb, and that
makes sense, right?

95
00:04:56,790 --> 00:04:58,890
Because it's force divided
by charge,

96
00:04:58,890 --> 00:05:00,650
so newtons per coulomb.

97
00:05:00,650 --> 00:05:02,770
So if we know that the electric
charge-- well, let me

98
00:05:02,770 --> 00:05:03,880
put some real numbers here.

99
00:05:03,880 --> 00:05:06,840
Let's say that this
is-- I don't know.

100
00:05:06,840 --> 00:05:08,782
It's going to be a really large
number, but let's say

101
00:05:08,782 --> 00:05:10,600
this-- let me pick
a smaller number.

102
00:05:10,600 --> 00:05:13,670
Let's say this is 1
times 10 to the

103
00:05:13,670 --> 00:05:16,536
minus 6 coulombs, right?

104
00:05:16,536 --> 00:05:20,010
If that's 1 times 10 to the
minus 6 coulombs, what is the

105
00:05:20,010 --> 00:05:21,940
electric field at that point?

106
00:05:21,940 --> 00:05:23,890
Let me switch colors again.

107
00:05:23,890 --> 00:05:25,960
What's the electric field
at that point?

108
00:05:25,960 --> 00:05:28,620
Well, the electric field at
that point is going to be

109
00:05:28,620 --> 00:05:33,170
equal to Coulomb's constant,
which is 9 times 10 to the

110
00:05:33,170 --> 00:05:37,910
ninth-- times the charge
generating the field-- times 1

111
00:05:37,910 --> 00:05:42,190
times 10 to the minus
6 coulombs.

112
00:05:42,190 --> 00:05:45,980
And then we are 2 meters
away, so 2 squared.

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00:05:45,980 --> 00:05:51,455
So that equals 9 times 10 to
the third divided by 4.

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00:05:51,455 --> 00:05:52,540
So I don't know, what is that?

115
00:05:52,540 --> 00:06:00,970
2.5 times 10 to the third or
2,500 newtons per coulomb.

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00:06:00,970 --> 00:06:03,660
So we know that this is
generating a field that when

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00:06:03,660 --> 00:06:07,430
we're 2 meters away, at a radius
of 2 meters, so roughly

118
00:06:07,430 --> 00:06:11,800
that circle around it, this is
generating a field that if I

119
00:06:11,800 --> 00:06:15,300
were to put-- let's say I were
to place a 1 coulomb charge

120
00:06:15,300 --> 00:06:20,860
here, the force exerted on that
1 coulomb charge is going

121
00:06:20,860 --> 00:06:25,880
to be equal to 1 coulomb times
the electric fields, times

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00:06:25,880 --> 00:06:29,620
2,500 newtons per coulomb.

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00:06:29,620 --> 00:06:32,210
So the coulombs cancel out, and
you'll have 2,500 newtons,

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00:06:32,210 --> 00:06:35,090
which is a lot, and that's
because 1 coulomb is a very,

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00:06:35,090 --> 00:06:37,020
very large charge.

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00:06:37,020 --> 00:06:40,980
And then a question you should
ask yourself: If this is 1

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00:06:40,980 --> 00:06:42,830
times 10 to the negative 6
coulombs and this is 1

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00:06:42,830 --> 00:06:47,120
coulomb, in which direction
will the force be?

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00:06:47,120 --> 00:06:49,150
Well, they're both positive,
so the force is going to be

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00:06:49,150 --> 00:06:51,870
outwards, right?

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00:06:51,870 --> 00:06:56,040
So let's take this notion and
see if we can somehow draw an

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00:06:56,040 --> 00:06:58,490
electric field around a
particle, just to get an

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00:06:58,490 --> 00:07:01,870
intuition of what happens when
we later put a charge anywhere

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00:07:01,870 --> 00:07:03,120
near the particle.

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00:07:03,120 --> 00:07:06,720


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00:07:06,720 --> 00:07:10,440
So there's a couple of ways to
visualize an electric field.

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00:07:10,440 --> 00:07:13,330
One way to visualize it is if I
have a-- let's say I have a

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00:07:13,330 --> 00:07:15,640
point charge here Q.

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00:07:15,640 --> 00:07:20,820
What would be the path of a
positive charge if I placed it

140
00:07:20,820 --> 00:07:23,060
someplace on this Q?

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00:07:23,060 --> 00:07:28,000
Well, if I put a positive charge
here and this Q is

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00:07:28,000 --> 00:07:30,600
positive, that positive charge
is just going to accelerate

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00:07:30,600 --> 00:07:31,370
outward, right?

144
00:07:31,370 --> 00:07:34,890
It's just going to go straight
out, but it's going to

145
00:07:34,890 --> 00:07:36,810
accelerate at an ever-slowing
rate, right?

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00:07:36,810 --> 00:07:39,150
Because here, when you're really
close, the outward

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00:07:39,150 --> 00:07:42,030
force is very strong, and then
as you get further and further

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00:07:42,030 --> 00:07:46,290
away, the electrostatic force
from this charge becomes

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00:07:46,290 --> 00:07:49,170
weaker and weaker, or you could
say the field becomes

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00:07:49,170 --> 00:07:50,000
weaker and weaker.

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00:07:50,000 --> 00:07:53,660
But that's the path of a--
it'll just be radially

152
00:07:53,660 --> 00:07:56,410
outward-- of a positive
test charge.

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00:07:56,410 --> 00:07:58,140
And then if I put it here, well,
it would be radially

154
00:07:58,140 --> 00:07:59,580
outward that way.

155
00:07:59,580 --> 00:08:00,660
It wouldn't curve the
way I drew it.

156
00:08:00,660 --> 00:08:01,620
It would be a straight line.

157
00:08:01,620 --> 00:08:03,160
I should actually use
the line tool.

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00:08:03,160 --> 00:08:06,190
If I did it here, it would be
like that, but then I can't

159
00:08:06,190 --> 00:08:08,030
draw the arrows.

160
00:08:08,030 --> 00:08:11,200
If I was here, it would
out like that.

161
00:08:11,200 --> 00:08:13,700
I think you get the picture.

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00:08:13,700 --> 00:08:17,890
At any point, a positive test
charge would just go straight

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00:08:17,890 --> 00:08:21,140
out away from our charge Q.

164
00:08:21,140 --> 00:08:23,550
And to some degree, one measure
of-- and these are

165
00:08:23,550 --> 00:08:25,240
called electric field lines.

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00:08:25,240 --> 00:08:29,700
And one measure of how strong
the field is, is if you

167
00:08:29,700 --> 00:08:37,120
actually took a unit area
and you saw how dense

168
00:08:37,120 --> 00:08:37,960
the field lines are.

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00:08:37,960 --> 00:08:42,320
So here, they're relatively
sparse, while if I did that

170
00:08:42,320 --> 00:08:46,750
same area up here-- I know
it's not that obvious.

171
00:08:46,750 --> 00:08:48,910
I'm getting more
field lines in.

172
00:08:48,910 --> 00:08:50,220
But actually, that's not a good
way to view it because

173
00:08:50,220 --> 00:08:51,620
I'm covering so much area.

174
00:08:51,620 --> 00:08:54,820
Let me undo both of them.

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00:08:54,820 --> 00:08:57,470
You can imagine if I had a lot
more lines, if I did this

176
00:08:57,470 --> 00:08:59,880
area, for example, in that area,
I'm capturing two of

177
00:08:59,880 --> 00:09:00,800
these field lines.

178
00:09:00,800 --> 00:09:04,410
Well, if I did that exact same
area out here, I'm only

179
00:09:04,410 --> 00:09:07,070
capturing one of the field
lines, although you could have

180
00:09:07,070 --> 00:09:08,460
a bunch more in between here.

181
00:09:08,460 --> 00:09:09,800
And that makes sense, right?

182
00:09:09,800 --> 00:09:15,470
Because as you get closer and
closer to the source of the

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00:09:15,470 --> 00:09:17,380
electric field, the charge
gets stronger.

184
00:09:17,380 --> 00:09:18,905
Another way that you could have
done this, and this would

185
00:09:18,905 --> 00:09:23,320
have actually more clearly shown
the magnitude of the

186
00:09:23,320 --> 00:09:27,046
field at any point, is you could
have-- you could say,

187
00:09:27,046 --> 00:09:30,470
OK, if that's my charge Q, you
could say, well, really close,

188
00:09:30,470 --> 00:09:31,300
the field is strong.

189
00:09:31,300 --> 00:09:35,440
So at this point, the vector,
the newtons per coulomb, is

190
00:09:35,440 --> 00:09:41,430
that strong, that strong, that
strong, that strong.

191
00:09:41,430 --> 00:09:42,630
We're just taking
sample points.

192
00:09:42,630 --> 00:09:46,360
You can't possibly draw them
at every single point.

193
00:09:46,360 --> 00:09:48,680
So at that point, that's
the vector.

194
00:09:48,680 --> 00:09:50,420
That's the electric
field vector.

195
00:09:50,420 --> 00:09:52,320
But then if we go a little bit
further out, the vector is

196
00:09:52,320 --> 00:09:56,090
going to be-- it falls off.

197
00:09:56,090 --> 00:09:57,770
This one should be shorter, then
this one should be even

198
00:09:57,770 --> 00:09:59,510
shorter, right?

199
00:09:59,510 --> 00:10:01,990
You could pick any point and you
could actually calculate

200
00:10:01,990 --> 00:10:04,370
the electric field vector, and
the further you go out, the

201
00:10:04,370 --> 00:10:08,130
shorter and shorter the electric
field vectors get.

202
00:10:08,130 --> 00:10:11,340
And so, in general, there's all
sorts of things you can

203
00:10:11,340 --> 00:10:14,240
draw the electric fields for.

204
00:10:14,240 --> 00:10:17,560
Let's say that this is a
positive charge and that this

205
00:10:17,560 --> 00:10:18,640
is a negative charge.

206
00:10:18,640 --> 00:10:21,010
Let me switch colors so I don't
have to erase things.

207
00:10:21,010 --> 00:10:24,740
If I have to draw the path of
a positive test charge, it

208
00:10:24,740 --> 00:10:29,490
would go out radially from
this charge, right?

209
00:10:29,490 --> 00:10:32,350
But then as it goes out, it'll
start being attracted to this

210
00:10:32,350 --> 00:10:35,820
one the closer it gets to the
negative, and then it'll curve

211
00:10:35,820 --> 00:10:40,720
in to the negative charge and
these arrows go like this.

212
00:10:40,720 --> 00:10:43,580
And if I went from here, the
positive one will be repelled

213
00:10:43,580 --> 00:10:47,140
really strong, really strong,
it'll accelerate fast and it's

214
00:10:47,140 --> 00:10:49,230
rate of acceleration will slow
down, but then as it gets

215
00:10:49,230 --> 00:10:51,870
closer to the negative one,
it'll speed up again, and then

216
00:10:51,870 --> 00:10:52,860
that would be its path.

217
00:10:52,860 --> 00:10:55,260
Similarly, if there was a
positive test charge here, its

218
00:10:55,260 --> 00:10:59,430
path would be like
that, right?

219
00:10:59,430 --> 00:11:02,600
If it was here, its path
would be like that.

220
00:11:02,600 --> 00:11:05,704
If it was here, it's path
would be like that.

221
00:11:05,704 --> 00:11:09,800
If it was there, maybe its path
is like that, and at some

222
00:11:09,800 --> 00:11:14,980
point, its path might never get
to that-- this out here

223
00:11:14,980 --> 00:11:16,440
might just go straight
out that way.

224
00:11:16,440 --> 00:11:19,130


225
00:11:19,130 --> 00:11:21,130
That one would just go straight
out, and here, the

226
00:11:21,130 --> 00:11:22,550
field lines would just
come in, right?

227
00:11:22,550 --> 00:11:24,950
A positive test charge would
just be naturally attracted to

228
00:11:24,950 --> 00:11:26,470
that negative charge.

229
00:11:26,470 --> 00:11:29,490
So that's, in general, what
electric field lines show, and

230
00:11:29,490 --> 00:11:33,570
we could use our little area
method and see that over here,

231
00:11:33,570 --> 00:11:36,970
if we picked a given area, the
electric field is much weaker

232
00:11:36,970 --> 00:11:38,580
than if we picked that
same area right here.

233
00:11:38,580 --> 00:11:42,120
We're getting more field lines
in than we do right there.

234
00:11:42,120 --> 00:11:43,650
So that hopefully gives you
a little sense for what an

235
00:11:43,650 --> 00:11:44,820
electric field is.

236
00:11:44,820 --> 00:11:47,920
It's really just a way of
visualizing what the impact

237
00:11:47,920 --> 00:11:49,810
would be on a test charge
if you bring it

238
00:11:49,810 --> 00:11:51,010
close to another charge.

239
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And hopefully, you
know a little bit

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about Coulomb's constant.

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And let's just do a very
simple-- I'm getting this out

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of the AP Physics book, but they
say-- let's do a little

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simple problem: Calculate the
static electric force between

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a 6 times 10 to the negative
sixth coulomb charge.

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So 6 times-- oh, no, that's
not on an electric field.

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Oh, here it says: What is the
force acting on an electron

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placed in an external electric
field where the electric field

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is-- they're saying it is 100
newtons per coulomb at that

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point, wherever the
electron is.

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00:12:29,130 --> 00:12:32,250
So the force on that, the force
in general, is just

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going to be the charge times the
electric field, and they

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say it's an electron,
so what's the

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charge of an electron?

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Well, we know it's negative, and
then in the first video,

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we learned that its charge is
1.6 times 10 to the negative

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00:12:45,860 --> 00:12:54,660
nineteenth coulombs times
100 newtons per coulomb.

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The coulombs cancel out.

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00:12:56,200 --> 00:12:58,600
And this is 10 squared, right?

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This is 10 to the positive 2, so
it'll be 10 to the minus 19

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times 10 to the positive 2.

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00:13:05,160 --> 00:13:10,650
The force will be minus
1.6 times 10 to

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00:13:10,650 --> 00:13:12,840
the minus 17 newtons.

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00:13:12,840 --> 00:13:14,150
So the problems are
pretty simple.

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00:13:14,150 --> 00:13:15,952
I think the more important thing
with electric fields is

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to really understand intuitively
what's going on,

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and kind of how it's stronger
near the point charges, and

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00:13:23,530 --> 00:13:26,080
how it gets weaker as it goes
away, and what the field lines

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00:13:26,080 --> 00:13:28,710
depict, and how they can be used
to at least approximate

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the strength of the field.

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I will see you in
the next video.