1
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2
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We've now learned that a current
or a stream of moving

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charges can be affected
by a magnetic field.

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00:00:08,330 --> 00:00:12,280
And we've also learned that it
can induce a magnetic field.

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So that begs the question,
what is the effect of one

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current carrying wire on another
current carrying wire?

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00:00:19,980 --> 00:00:20,760
Let's do that.

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Let's draw my first current
carrying wire in green.

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That's the first current
carrying wire.

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00:00:30,600 --> 00:00:35,030
And let's say that the current
is-- it's in magenta-- and

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we'll call this current 1.

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And then I have another
current carrying

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wire not too far away.

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And I will call that
current I2.

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Now what else do we need
to figure out?

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Oh, well, let me
just tell you.

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Let's say that they are
a radius of r apart.

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And I say radius because we
learned in the last video that

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the magnetic field created by
a current carrying wire is

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kind of a, you know, they're
kind of these circular

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cylinders around the wire.

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So let's say the distance from
this wire to that wire is r.

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That distance is r.

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00:01:23,220 --> 00:01:26,760
And so my question to you is--
well, first, just before we

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break into the math-- what's
going to happen?

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Well, we don't know the
magnitudes of the currents or

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anything just yet.

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But what's going to happen?

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What will be the net effect
on, let's say, this wire?

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00:01:37,690 --> 00:01:40,836
Let's say for some reason this
wire is fixed or we could say

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they're floating in space.

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Let's just focus on
wire 2 for now.

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This is wire 2, this
is wire 1.

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What's going to happen
to wire 2?

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Well, let's think about it.

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Wire 1-- the current
in it is going to

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generate a magnetic field.

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Now what's the shape of
that magnetic field

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going to look like?

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Well, we could take our right
hand, do that right hand wrap

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00:02:02,450 --> 00:02:03,060
around rule.

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00:02:03,060 --> 00:02:04,870
It's a little different than
the cross product rule,

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00:02:04,870 --> 00:02:06,520
although it's kind
of a byproduct.

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00:02:06,520 --> 00:02:13,800
So that's my right hand and
I'm wrapping it around.

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00:02:13,800 --> 00:02:17,380
So if I point my thumb in the
direction of the current-- so

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00:02:17,380 --> 00:02:19,480
that's the direction of the
current, just like I did--

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00:02:19,480 --> 00:02:21,430
then the magnetic field
goes in the

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00:02:21,430 --> 00:02:23,360
direction of my fingers.

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00:02:23,360 --> 00:02:28,900
So they're going to go
around this wire.

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00:02:28,900 --> 00:02:32,323
And so if I were to just draw
the magnetic field where it

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00:02:32,323 --> 00:02:36,010
intersects with this screen, on
the right hand side it will

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00:02:36,010 --> 00:02:37,120
go into the screen.

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00:02:37,120 --> 00:02:39,700
So we'll just see the
rear ends of the

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00:02:39,700 --> 00:02:41,560
magnetic field line.

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00:02:41,560 --> 00:02:43,190
And I'll draw it in the same
color as the current, so you

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00:02:43,190 --> 00:02:44,580
know it's being created by I1.

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00:02:44,580 --> 00:02:47,650


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00:02:47,650 --> 00:02:53,700
So I1-- its effect keeps going
out to infinity, although it

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gets much weaker
as we learned.

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00:02:55,770 --> 00:02:58,480
It's inversely proportional
with r.

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00:02:58,480 --> 00:02:59,720
But this is the field of I1.

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I can draw these-- I
don't want to crowd

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my page up too much.

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00:03:03,200 --> 00:03:05,110
And then on this side
of I1, what happens?

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00:03:05,110 --> 00:03:06,710
Well, on this side,
you can see the

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00:03:06,710 --> 00:03:07,980
fingers come back around.

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00:03:07,980 --> 00:03:09,860
So it pops out when
it intersects

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00:03:09,860 --> 00:03:12,660
with your video monitor.

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00:03:12,660 --> 00:03:16,720
So on this side, the vectors--
this is the top of an arrow,

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00:03:16,720 --> 00:03:19,960
coming out at you.

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00:03:19,960 --> 00:03:21,050
Fair enough.

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00:03:21,050 --> 00:03:24,410
So I1, by going in this
direction, is generating a

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00:03:24,410 --> 00:03:27,870
magnetic field that, at least
where I2 is concerned, that

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00:03:27,870 --> 00:03:33,590
magnetic field is going
into the page.

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00:03:33,590 --> 00:03:36,070
So what was our formula?

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00:03:36,070 --> 00:03:38,530
And this all came from the
first formula we learned

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00:03:38,530 --> 00:03:39,960
about, the effect of a magnetic
field soon. on a

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00:03:39,960 --> 00:03:40,510
moving charge.

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00:03:40,510 --> 00:03:44,470
But what was the formula of the
net magnetic force on a

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00:03:44,470 --> 00:03:46,500
current carrying wire?

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00:03:46,500 --> 00:03:56,050
It was the force-- I'll do it in
blue-- it's a vector, has a

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00:03:56,050 --> 00:03:59,420
magnitude and direction--
is equal to the current.

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00:03:59,420 --> 00:04:02,820
Well, in this case, we want
to know the force on this

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00:04:02,820 --> 00:04:04,940
current, on current 2, right?

86
00:04:04,940 --> 00:04:09,160
Caused by this magnetic field,
by magnetic field 1.

87
00:04:09,160 --> 00:04:16,220
So it will be equal to I2, the
magnitude of this current,

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00:04:16,220 --> 00:04:20,250
times L-- where L is-- because
you can't just say, oh well,

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00:04:20,250 --> 00:04:21,370
what is the effect
on this wire?

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00:04:21,370 --> 00:04:24,160
You have to know how much wire
is under consideration.

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00:04:24,160 --> 00:04:26,520
So let's say we have
a length of wire.

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00:04:26,520 --> 00:04:28,240
And then of course, if you know
the length of wire and we

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00:04:28,240 --> 00:04:30,110
knew its mass and we knew the
force on it, we could figure

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00:04:30,110 --> 00:04:31,570
out its acceleration
in some directions.

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00:04:31,570 --> 00:04:34,120
So let's say that
this distance is

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L, and it's a vector.

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00:04:35,800 --> 00:04:38,540
L goes in the same direction
as the current.

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00:04:38,540 --> 00:04:39,790
That's just the convention
we're using.

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00:04:39,790 --> 00:04:41,420
It makes things simple.

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00:04:41,420 --> 00:04:44,010
So that's L.

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00:04:44,010 --> 00:04:50,680
So the force on this wire, or at
least the length L of this

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00:04:50,680 --> 00:04:55,720
wire, is going to be equal
to current 2 times L.

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00:04:55,720 --> 00:04:58,840
We could call that even L2, just
so that you know that it

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00:04:58,840 --> 00:04:59,980
deals with wire 2.

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00:04:59,980 --> 00:05:02,400
That's a vector quantity.

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00:05:02,400 --> 00:05:03,420
I could make it a full arrow.

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00:05:03,420 --> 00:05:03,940
Doesn't matter.

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00:05:03,940 --> 00:05:04,670
It's just a notation.

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00:05:04,670 --> 00:05:06,870
I've seen professors do it
either way, I've seen it

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00:05:06,870 --> 00:05:08,780
written either way, as well.

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00:05:08,780 --> 00:05:12,180
Cross the magnetic field
that it's in.

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00:05:12,180 --> 00:05:14,150
What's the magnetic field
that it's in?

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00:05:14,150 --> 00:05:16,080
The magnetic field-- I'll do
it in magenta, because it's

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00:05:16,080 --> 00:05:18,770
the magnetic field created
by current 1.

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00:05:18,770 --> 00:05:26,670
So it's magnetic field 1, which
is this magnetic field.

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00:05:26,670 --> 00:05:30,960
So before going into the math,
let's just figure out what

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00:05:30,960 --> 00:05:33,380
direction is this net force
going to be in?

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00:05:33,380 --> 00:05:37,000
So here we say, well, the
current is a scalar, so that's

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00:05:37,000 --> 00:05:38,470
not going to affect
the direction.

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00:05:38,470 --> 00:05:40,850
What's the direction of L2?

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00:05:40,850 --> 00:05:42,290
This is L2.

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00:05:42,290 --> 00:05:44,640
I didn't label it L2
on the diagram.

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00:05:44,640 --> 00:05:46,190
What's the direction of L2?

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00:05:46,190 --> 00:05:47,180
Well, it's up.

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00:05:47,180 --> 00:05:50,650
And then the direction of B1,
the magnetic field created by

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00:05:50,650 --> 00:05:53,400
current 1, is going into
the page here.

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00:05:53,400 --> 00:05:57,520
So here we just do the standard
cross product.

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00:05:57,520 --> 00:05:59,380
Let me see if I can
pull this off.

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00:05:59,380 --> 00:06:01,400
This is actually an
easy one to draw.

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00:06:01,400 --> 00:06:08,660
So I put my index finger
in the direction of L2.

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00:06:08,660 --> 00:06:10,560
And then I put my middle
finger in the

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00:06:10,560 --> 00:06:11,760
direction of the field.

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00:06:11,760 --> 00:06:13,500
So my middle finger's going
to point straight

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down into this page.

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00:06:15,560 --> 00:06:17,880
My other fingers just do what
they would naturally do.

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And then my thumb
would go in the

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00:06:19,290 --> 00:06:20,220
direction of the net force.

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00:06:20,220 --> 00:06:23,190
This is just the
cross product.

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00:06:23,190 --> 00:06:25,700
You'll see teachers teach the
cross product other ways,

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where they tell you to put your
thumb in the direction of

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00:06:27,720 --> 00:06:29,780
the field, and this and
that, your palm--

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00:06:29,780 --> 00:06:30,590
those are all valid.

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00:06:30,590 --> 00:06:32,030
They're just different
variations of the same thing.

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00:06:32,030 --> 00:06:33,580
I find this one easier
to remember.

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00:06:33,580 --> 00:06:35,910
Because when I take the cross
product, index finger is the

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00:06:35,910 --> 00:06:36,900
first term of the
cross product.

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00:06:36,900 --> 00:06:39,040
Middle finger is the second
term of the cross product.

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00:06:39,040 --> 00:06:42,980
Thumb is the direction
of the cross product.

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00:06:42,980 --> 00:06:46,830
So anyway, this is the
direction of L2.

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00:06:46,830 --> 00:06:49,300
The magnetic field, we already
know, goes into the page.

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00:06:49,300 --> 00:06:53,350
So my middle finger is
going into the page.

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00:06:53,350 --> 00:06:56,510
And my thumb is in the direction
of the force on the

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00:06:56,510 --> 00:06:57,620
magnetic field.

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00:06:57,620 --> 00:07:00,560
So that's the direction
of the force.

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00:07:00,560 --> 00:07:02,180
So there you have it.

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00:07:02,180 --> 00:07:05,420
If this current is moving in
this direction and its field

157
00:07:05,420 --> 00:07:08,580
is-- we know from this wrap
around rule that pops out here

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00:07:08,580 --> 00:07:10,950
and it goes in here-- the effect
that it has on this

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00:07:10,950 --> 00:07:15,260
other wire is that where the
current is going in the same

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00:07:15,260 --> 00:07:17,430
direction, is that it
will be attracted.

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00:07:17,430 --> 00:07:22,130
So the net force you is going
in that direction.

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00:07:22,130 --> 00:07:26,870
We could say the force
from 1 on 2.

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00:07:26,870 --> 00:07:27,900
That's just my convention.

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00:07:27,900 --> 00:07:30,300
Maybe other people would have
written it the force

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00:07:30,300 --> 00:07:33,780
given to 2 by 1.

166
00:07:33,780 --> 00:07:36,170
That's the force given
by 1 to 2.

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00:07:36,170 --> 00:07:37,750
That's how I'm writing it.

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00:07:37,750 --> 00:07:42,540
Now what's going to be the force
on current 1 from I2?

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00:07:42,540 --> 00:07:44,040
Well, it's going to be the
current-- well, it's going to

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00:07:44,040 --> 00:07:45,350
be the force there.

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00:07:45,350 --> 00:07:47,460
Well it's going to be
the same thing.

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00:07:47,460 --> 00:07:50,190
Let me draw I2's
magnetic field.

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00:07:50,190 --> 00:07:52,600
You do the wrap around rule,
it's going to look the same.

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00:07:52,600 --> 00:07:56,200
So I2, sure, on this side its
field is going to be going

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00:07:56,200 --> 00:07:59,240
into the page.

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00:07:59,240 --> 00:08:01,280
But what's I2's field going
to be doing here?

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00:08:01,280 --> 00:08:02,600
It's going to be popping out.

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00:08:02,600 --> 00:08:05,960


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00:08:05,960 --> 00:08:07,800
I just did the wrap around--
take this wrap around, wrap it

180
00:08:07,800 --> 00:08:09,280
around that wire.

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00:08:09,280 --> 00:08:11,880
So that's the field of I2.

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00:08:11,880 --> 00:08:19,250
So then we can write down that
the force-- and let's take, I

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00:08:19,250 --> 00:08:22,660
don't know, this is
some distance.

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00:08:22,660 --> 00:08:25,300
Let's call that L1.

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00:08:25,300 --> 00:08:33,860
So the force from current 2 on
wire 1 of length L1, from here

186
00:08:33,860 --> 00:08:44,940
to here, is equal to current 1
times L1-- which is a vector--

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00:08:44,940 --> 00:08:48,950
cross the magnetic field
created by current 2.

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00:08:48,950 --> 00:08:53,430


189
00:08:53,430 --> 00:08:55,460
And so we can do the same
cross product here.

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00:08:55,460 --> 00:09:01,510
Put our index finger in
the direction of L1.

191
00:09:01,510 --> 00:09:02,930
That's what you do with
the first element

192
00:09:02,930 --> 00:09:04,140
of the cross product.

193
00:09:04,140 --> 00:09:07,820
And then you put your middle
finger in the direction of B2.

194
00:09:07,820 --> 00:09:10,800
And then your thumb is going to
tell you what the net force

195
00:09:10,800 --> 00:09:11,260
is going to be.

196
00:09:11,260 --> 00:09:12,810
So let me draw that.

197
00:09:12,810 --> 00:09:16,360
So let me draw my hand.

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00:09:16,360 --> 00:09:18,390
And just so you know, before I
do any of these, I actually

199
00:09:18,390 --> 00:09:20,800
look at my hand, just
to make sure I'm

200
00:09:20,800 --> 00:09:21,450
drawing the right thing.

201
00:09:21,450 --> 00:09:26,020
So my index finger in the
direction of I1, my middle

202
00:09:26,020 --> 00:09:28,710
finger-- sorry, my index finger
in the direction of L1,

203
00:09:28,710 --> 00:09:31,750
which is the same as I1, and
then my middle finger is going

204
00:09:31,750 --> 00:09:33,160
to do what the magnetic
field is doing.

205
00:09:33,160 --> 00:09:34,560
So my middle finger is actually
going to point

206
00:09:34,560 --> 00:09:36,300
straight up.

207
00:09:36,300 --> 00:09:39,220
And then my other fingers are
just going to do what they do.

208
00:09:39,220 --> 00:09:41,790
And so now you're looking
at the palm of my hand.

209
00:09:41,790 --> 00:09:47,350
And my thumb-- let me make sure
I'm doing this correctly.

210
00:09:47,350 --> 00:09:48,600
Oh, no.

211
00:09:48,600 --> 00:09:50,990


212
00:09:50,990 --> 00:09:53,370
I was drawing my left hand.

213
00:09:53,370 --> 00:09:54,850
See, that's an error.

214
00:09:54,850 --> 00:09:56,400
You don't want to draw your left
hand when you're doing

215
00:09:56,400 --> 00:09:58,280
the right hand rule with
cross products.

216
00:09:58,280 --> 00:10:01,630
So let me draw it down here.

217
00:10:01,630 --> 00:10:04,470
My index finger going in
the direction of L1.

218
00:10:04,470 --> 00:10:07,280


219
00:10:07,280 --> 00:10:11,180
My middle finger's popping
straight up, because the

220
00:10:11,180 --> 00:10:14,040
magnetic field created by
I2 is popping straight

221
00:10:14,040 --> 00:10:15,080
out of the page here.

222
00:10:15,080 --> 00:10:17,460
So my middle finger goes
straight up and my other

223
00:10:17,460 --> 00:10:19,830
fingers do what they
need to do.

224
00:10:19,830 --> 00:10:21,860
Looking at the palm.

225
00:10:21,860 --> 00:10:24,460
And then my thumb will
go in that direction.

226
00:10:24,460 --> 00:10:30,290
So the cross product of L with
B2 popping out of this page,

227
00:10:30,290 --> 00:10:33,050
the net force is going to
be in this direction.

228
00:10:33,050 --> 00:10:35,110
So there's a little bit
of symmetry here.

229
00:10:35,110 --> 00:10:37,920
This wire's going to be
attracted towards that wire,

230
00:10:37,920 --> 00:10:40,420
and this wire's going to be
attracted to that wire.

231
00:10:40,420 --> 00:10:42,240
They're both going to--
eventually if they were

232
00:10:42,240 --> 00:10:45,220
floating in space, they would
slowly get closer and closer

233
00:10:45,220 --> 00:10:47,000
to each other and their radiuses
would get closer and

234
00:10:47,000 --> 00:10:50,370
closer and they would accelerate
to each other, at

235
00:10:50,370 --> 00:10:52,310
ever increasing rates
actually.

236
00:10:52,310 --> 00:10:53,540
Anyway, I'm out of time.

237
00:10:53,540 --> 00:10:56,480
In the next video I'll do this
same principle, but we'll do

238
00:10:56,480 --> 00:10:57,380
it with some numbers.

239
00:10:57,380 --> 00:10:58,630
See

240
00:10:58,630 --> 00:00:00,000