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00:00:00,900 --> 00:00:06,040
So not only can a magnetic field
exert some force on a

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00:00:06,040 --> 00:00:09,230
moving charge, we're now going
to learn that a moving charge

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or a current can actually
create a magnetic field.

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00:00:12,160 --> 00:00:15,010
So there is some type
of symmetry here.

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00:00:15,010 --> 00:00:18,600
And as we'll learn later when
we learn our calculus and we

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00:00:18,600 --> 00:00:25,810
do this in a slightly more
rigorous way, we'll see that

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00:00:25,810 --> 00:00:29,010
magnetic fields and electric
fields are actually two sides

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00:00:29,010 --> 00:00:32,430
of the same coin, of
electromagnetic fields.

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00:00:32,430 --> 00:00:33,880
But anyway, we won't worry
about that now.

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00:00:33,880 --> 00:00:36,260
And I think it's enough to
ponder right now that a

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current can actually induce
a magnetic field.

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00:00:39,220 --> 00:00:40,570
And actually, just
a moving electron

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00:00:40,570 --> 00:00:42,320
creates a magnetic field.

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And it does it in a surface of a
sphere-- I won't go into all

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that right now.

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Because the math gets a little
bit fancy there.

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But what you might encounter in
your standard high school

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00:00:50,600 --> 00:00:52,950
physics class-- that's not
getting deeply into vector

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00:00:52,950 --> 00:00:57,180
calculus-- is that if you
just have a wire--

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00:00:57,180 --> 00:00:58,820
let me draw a wire.

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00:00:58,820 --> 00:01:00,780
That's my wire.

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00:01:00,780 --> 00:01:10,030
And it's carrying some current
I, it turns out that this wire

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will generate a magnetic
field.

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And the shape of that magnetic
field is going to be

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00:01:14,840 --> 00:01:19,960
co-centric circles
around this wire.

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00:01:19,960 --> 00:01:22,730
Let me see if I can draw that.

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So here I'll draw it just like
how I do when I try to do

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00:01:25,730 --> 00:01:29,510
rotations of solids in
the calculus video.

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So the magnetic field would go
behind and in front and it

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goes like that.

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Or another way you can think
about it is if-- let's go down

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00:01:40,130 --> 00:01:42,930
here-- is on the left
side of this wire.

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00:01:42,930 --> 00:01:45,840
If you say that the wire's in
the plane of this video, the

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00:01:45,840 --> 00:01:49,110
magnetic field is popping
out of your screen.

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00:01:49,110 --> 00:01:52,650


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00:01:52,650 --> 00:01:55,500
And on this side, on the right
side, the magnetic field is

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popping into the screen.

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00:01:57,980 --> 00:02:00,000
It's going into the screen.

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And you could imagine
that, right?

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00:02:01,400 --> 00:02:04,840
You could imagine if, on this
drawing up here, you could say

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00:02:04,840 --> 00:02:06,370
this is where it intersects
the screen.

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00:02:06,370 --> 00:02:09,240
All of this is kind of
behind the screen.

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And all of this is in
front of the screen.

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00:02:11,440 --> 00:02:13,460
And this is where it's
popping out.

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00:02:13,460 --> 00:02:15,430
And this is where it's popping
into the screen.

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00:02:15,430 --> 00:02:16,770
Hopefully that makes a
little bit of sense.

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00:02:16,770 --> 00:02:20,180
And how did I know that it's
rotating this way?

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00:02:20,180 --> 00:02:22,370
Well, it actually does come out
of the cross product when

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00:02:22,370 --> 00:02:24,950
you do it with a regular
charge and all of that.

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00:02:24,950 --> 00:02:26,740
But we're not going to go
into that right now.

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00:02:26,740 --> 00:02:28,670
And so there's a different
right hand rule

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00:02:28,670 --> 00:02:29,640
that you can use.

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00:02:29,640 --> 00:02:34,130
And it's literally you hold
this wire, or you imagine

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00:02:34,130 --> 00:02:37,810
holding this wire, with your
right hand with your thumb

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00:02:37,810 --> 00:02:39,570
going in the direction
of the current.

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00:02:39,570 --> 00:02:42,010
And if you hold this wire with
your thumb going in the

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00:02:42,010 --> 00:02:44,790
direction of the current, your
fingers are going to go in the

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00:02:44,790 --> 00:02:47,890
direction of the
magnetic field.

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00:02:47,890 --> 00:02:51,030
So let me see if I
can draw that.

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00:02:51,030 --> 00:02:52,830
I will draw it in blue.

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So if this is my thumb, my thumb
is going along the top

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of the wire.

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00:03:00,690 --> 00:03:03,045
And then my hand is curling
around the wire.

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00:03:03,045 --> 00:03:06,000


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00:03:06,000 --> 00:03:06,700
Those are my knuckles.

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Those are the veins
on my hand.

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This is my nail.

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So as you can see, if I was
holding that same wire-- let

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00:03:16,490 --> 00:03:17,760
me draw the wire.

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00:03:17,760 --> 00:03:21,490
So if I was holding that same
wire, we see that my thumb is

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00:03:21,490 --> 00:03:22,970
going in the direction
of the current.

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00:03:22,970 --> 00:03:25,910
So this is a slightly new
thing to memorize.

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00:03:25,910 --> 00:03:27,730
And what is the magnetic
field doing?

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00:03:27,730 --> 00:03:30,840
Well, it's going in the
direction of my fingers.

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00:03:30,840 --> 00:03:33,930
My fingers are popping out
on this side of the wire.

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00:03:33,930 --> 00:03:35,760
They're coming out on this
side of the wire.

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00:03:35,760 --> 00:03:37,560
And they're going in, or
at least my hand is

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00:03:37,560 --> 00:03:39,460
going in, on that side.

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00:03:39,460 --> 00:03:42,490
It's going into the screen.

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00:03:42,490 --> 00:03:44,570
Hopefully that makes sense.

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00:03:44,570 --> 00:03:46,070
Now, how can we quantify?

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00:03:46,070 --> 00:03:48,280
Well, before we quantify, let's
get a little bit more of

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00:03:48,280 --> 00:03:49,890
the intuition of what's
happening.

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00:03:49,890 --> 00:03:52,730
It turns out that the closer
you get to the wire, the

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00:03:52,730 --> 00:03:56,290
stronger the magnetic field, and
the further you get out,

87
00:03:56,290 --> 00:03:57,800
the weaker the magnetic field.

88
00:03:57,800 --> 00:04:00,510
And that kind of makes sense
if you imagine the magnetic

89
00:04:00,510 --> 00:04:01,760
field spreading out.

90
00:04:01,760 --> 00:04:04,380


91
00:04:04,380 --> 00:04:06,460
I don't want to go into too
sophisticated analogies.

92
00:04:06,460 --> 00:04:08,830
But if you imagine the magnetic
field spreading out,

93
00:04:08,830 --> 00:04:10,580
and as it goes further and
further out it kind of gets

94
00:04:10,580 --> 00:04:12,705
distributed over a wider and
wider circumference.

95
00:04:12,705 --> 00:04:15,270
And actually the formula I'm
going to give you kind of has

96
00:04:15,270 --> 00:04:16,870
a taste for that.

97
00:04:16,870 --> 00:04:20,450
So the formula for the magnetic
field-- and it really

98
00:04:20,450 --> 00:04:23,110
is defined with a cross product
and things like that,

99
00:04:23,110 --> 00:04:25,920
but for our purposes we won't
worry about that.

100
00:04:25,920 --> 00:04:29,350
You'll just have to know that
this is the shape if the

101
00:04:29,350 --> 00:04:30,950
current is going in
that direction.

102
00:04:30,950 --> 00:04:33,880
And, of course, if the current
was going downwards then the

103
00:04:33,880 --> 00:04:35,550
magnetic field would just
reverse directions.

104
00:04:35,550 --> 00:04:36,640
But it would still
be in co-centric

105
00:04:36,640 --> 00:04:38,220
circles around the wire.

106
00:04:38,220 --> 00:04:42,870
But anyway, what is the
magnitude of that field?

107
00:04:42,870 --> 00:04:49,630
The magnitude of that magnetic
field is equal to mu-- which

108
00:04:49,630 --> 00:04:52,240
is a Greek letter, which I will
explain in a second--

109
00:04:52,240 --> 00:04:58,120
times the current divided
by 2 pi r.

110
00:04:58,120 --> 00:05:00,590
So this has a little bit
of a feel for what

111
00:05:00,590 --> 00:05:01,280
I was saying before.

112
00:05:01,280 --> 00:05:04,430
That the further you go out--
where r is how far you are

113
00:05:04,430 --> 00:05:09,410
from the wire-- the further you
go out, if r gets bigger,

114
00:05:09,410 --> 00:05:12,750
the magnitude of the magnetic
field is going to get weaker.

115
00:05:12,750 --> 00:05:14,650
And this 2 pi r, that
looks a lot like the

116
00:05:14,650 --> 00:05:16,140
circumference of a circle.

117
00:05:16,140 --> 00:05:17,225
So that gives you
a taste for it.

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00:05:17,225 --> 00:05:20,730
I know I haven't proved
anything rigorously.

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00:05:20,730 --> 00:05:22,730
But it at least gives you a
sense of, look there's a

120
00:05:22,730 --> 00:05:23,450
little formula for

121
00:05:23,450 --> 00:05:24,350
circumference of a circle here.

122
00:05:24,350 --> 00:05:25,400
And that kind of makes
sense, right?

123
00:05:25,400 --> 00:05:27,280
Because the magnetic
field at that point

124
00:05:27,280 --> 00:05:29,770
is kind of a circle.

125
00:05:29,770 --> 00:05:33,940
The magnitude is equal at an
equal radius around that wire.

126
00:05:33,940 --> 00:05:36,770
Now what is this mu, this thing
that looks like a u?

127
00:05:36,770 --> 00:05:39,380
Well, that's the permeability
of the material

128
00:05:39,380 --> 00:05:40,330
that the wire's in.

129
00:05:40,330 --> 00:05:41,990
So the magnetic field is
actually going to have a

130
00:05:41,990 --> 00:05:44,820
different strength depending on
whether this wire is going

131
00:05:44,820 --> 00:05:48,420
through rubber, whether it's
going through a vacuum, or

132
00:05:48,420 --> 00:05:50,840
air, or metal, or water.

133
00:05:50,840 --> 00:05:54,400
And for the purposes of your
high school physics class, we

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00:05:54,400 --> 00:05:56,990
assume that it's going
through air normally.

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00:05:56,990 --> 00:06:01,930
And the value for air
is pretty close to

136
00:06:01,930 --> 00:06:03,310
the value for a vacuum.

137
00:06:03,310 --> 00:06:05,600
And it's called the permeability
of a vacuum.

138
00:06:05,600 --> 00:06:07,410
And I forget what
that value is.

139
00:06:07,410 --> 00:06:08,200
I could look it up.

140
00:06:08,200 --> 00:06:09,820
But it actually turns
out that your

141
00:06:09,820 --> 00:06:11,010
calculator has that value.

142
00:06:11,010 --> 00:06:12,710
So let's do a problem,
just to put some

143
00:06:12,710 --> 00:06:14,580
numbers to the formula.

144
00:06:14,580 --> 00:06:19,460
So let's say I had this current
and it is-- I don't

145
00:06:19,460 --> 00:06:22,032
know, the current is equal
to-- I'm going

146
00:06:22,032 --> 00:06:22,780
to make up a number.

147
00:06:22,780 --> 00:06:25,740
2 amperes.

148
00:06:25,740 --> 00:06:33,320
And let's say that I just pick
a point right here that is--

149
00:06:33,320 --> 00:06:36,670
let's say that that's
3 meters away

150
00:06:36,670 --> 00:06:37,950
from the wire in question.

151
00:06:37,950 --> 00:06:39,980
So my question to you is what
is the magnitude in the

152
00:06:39,980 --> 00:06:43,760
direction of the magnetic
field right there?

153
00:06:43,760 --> 00:06:45,140
Well, the magnitude is easy.

154
00:06:45,140 --> 00:06:46,650
We just substitute
in this equation.

155
00:06:46,650 --> 00:06:50,540
So the magnitude of the magnetic
field at this point

156
00:06:50,540 --> 00:06:53,410
is equal to-- and we assume that
the wire's going through

157
00:06:53,410 --> 00:06:57,270
air or a vacuum-- the
permeability of free space--

158
00:06:57,270 --> 00:06:59,770
that's just a constant, though
it looks fancy-- times the

159
00:06:59,770 --> 00:07:04,910
current times 2 amperes
divided by 2 pi r.

160
00:07:04,910 --> 00:07:05,345
What's r?

161
00:07:05,345 --> 00:07:07,350
It's 3 meters.

162
00:07:07,350 --> 00:07:09,020
So 2 pi times 3.

163
00:07:09,020 --> 00:07:13,260
So it equals the permeability
of free space.

164
00:07:13,260 --> 00:07:13,510
So let's see.

165
00:07:13,510 --> 00:07:16,630
The 2 and the 2 cancel
out over 3 pi.

166
00:07:16,630 --> 00:07:18,350
So how do we calculate that?

167
00:07:18,350 --> 00:07:24,040
Well, we get out our trusty
TI-85 calculator.

168
00:07:24,040 --> 00:07:28,510
And I think you'll be maybe
pleasantly surprised or

169
00:07:28,510 --> 00:07:31,330
shocked to realize that-- I
deleted everything just so you

170
00:07:31,330 --> 00:07:34,280
can see how I get there--
that it actually has the

171
00:07:34,280 --> 00:07:36,640
permeability of free
space stored in it.

172
00:07:36,640 --> 00:07:39,220
So what you do is you go to
second and you press constant,

173
00:07:39,220 --> 00:07:41,330
which is the 4 button.

174
00:07:41,330 --> 00:07:43,560
It's in the built-in
constants.

175
00:07:43,560 --> 00:07:44,790
Let's see, it's not
one of those.

176
00:07:44,790 --> 00:07:46,430
You press more.

177
00:07:46,430 --> 00:07:48,040
It's not one of those,
press more.

178
00:07:48,040 --> 00:07:49,170
Oh look at that.

179
00:07:49,170 --> 00:07:50,700
Mu not.

180
00:07:50,700 --> 00:07:52,270
The permeability
of free space.

181
00:07:52,270 --> 00:07:54,120
That's what I need.

182
00:07:54,120 --> 00:07:57,190
And I have to divide
it by 3 pi.

183
00:07:57,190 --> 00:08:00,570
Divide it by 3-- and
then where is pi?

184
00:08:00,570 --> 00:08:01,210
There it is.

185
00:08:01,210 --> 00:08:03,000
It's over the power sign.

186
00:08:03,000 --> 00:08:05,880
Divided by 3 pi.

187
00:08:05,880 --> 00:08:10,480
It equals 1.3 times 10 to
the negative seventh.

188
00:08:10,480 --> 00:08:11,940
It's going to be teslas.

189
00:08:11,940 --> 00:08:17,820
The magnetic field is going to
be equal to 1.3 times 10 to

190
00:08:17,820 --> 00:08:20,270
the minus seventh teslas.

191
00:08:20,270 --> 00:08:23,290
So it's a fairly weak
magnetic field.

192
00:08:23,290 --> 00:08:27,220
And that's why you don't have
metal objects being thrown

193
00:08:27,220 --> 00:08:31,520
around by the wires behind
your television set.

194
00:08:31,520 --> 00:08:33,650
But anyway, hopefully that gives
you a little bit-- and

195
00:08:33,650 --> 00:08:36,289
just so you know how it
all fits together.

196
00:08:36,289 --> 00:08:40,700
We're saying that these moving
charges, not only can they be

197
00:08:40,700 --> 00:08:42,909
affected by a magnetic field,
not only can a current be

198
00:08:42,909 --> 00:08:45,870
affected by a magnetic field
or just a moving charge, it

199
00:08:45,870 --> 00:08:47,270
actually creates them.

200
00:08:47,270 --> 00:08:49,840
And that kind of creates a
little bit of symmetry in your

201
00:08:49,840 --> 00:08:50,270
head, hopefully.

202
00:08:50,270 --> 00:08:52,770
Because that was also true
of electric field.

203
00:08:52,770 --> 00:08:57,170
A charge, a stationary charge,
is obviously pulled or pushed

204
00:08:57,170 --> 00:08:58,760
by a static electric field.

205
00:08:58,760 --> 00:09:01,910
And it also creates its own
static electric field.

206
00:09:01,910 --> 00:09:03,640
So it's always in the
back of your mind.

207
00:09:03,640 --> 00:09:05,180
Because if you keep studying
physics, you're going to

208
00:09:05,180 --> 00:09:09,000
actually prove to yourself that
electric and magnetic

209
00:09:09,000 --> 00:09:11,790
fields are two sides
of the same coin.

210
00:09:11,790 --> 00:09:14,150
And it just looks like a
magnetic field when you're in

211
00:09:14,150 --> 00:09:15,930
a different frame of reference,
When something is

212
00:09:15,930 --> 00:09:17,020
whizzing past you.

213
00:09:17,020 --> 00:09:19,650
While if you were whizzing along
with it, then that thing

214
00:09:19,650 --> 00:09:20,350
would look static.

215
00:09:20,350 --> 00:09:21,830
And then it might look a
little bit more like an

216
00:09:21,830 --> 00:09:22,820
electric field.

217
00:09:22,820 --> 00:09:25,230
But anyway, I'll leave
you there now.

218
00:09:25,230 --> 00:09:29,160
And in the next video I will
show you what happens when we

219
00:09:29,160 --> 00:09:33,440
have two wires carrying current

220
00:09:33,440 --> 00:09:34,660
parallel to each other.

221
00:09:34,660 --> 00:09:37,630
And you might guess that they
might actually attract or

222
00:09:37,630 --> 00:09:38,560
repel each other.

223
00:09:38,560 --> 00:00:00,000
Anyway, I'll see you
in the next video.