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- [Instructor] Okay, so we
know that electrical charges

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create electric fields
in the region around them

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but people get confused
by electric field problems

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so you got to get good at
at least two things here

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if you wanna proficient at
dealing with electrical field.

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You should get good at
determining the direction

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of the electric field
that's created by a charge.

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If you've got some charge

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and you wanna know which
way does that charge

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create an electric field,

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you should get really good at that.

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And if you know the
direction of the field,

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you should get good at
finding the direction

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of the electric force exerted on a charge.

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If there's some charge floating around

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in an electric field,

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you should be able to say,

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oh, okay, I can determine
the electric force.

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Not too bad.

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If you get good at these two things,

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these problems are gonna be way easier

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and the whole process is
gonna make a lot more sense.

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Let's figure out how to do this.

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How do you do these things?

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We'll do the first one first.

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Let's try to tackle this one.

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Let's try to figure out
how do you determine

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the direction of the electric field

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that's created by a charge.

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Let's say we didn't know, this
is what the electric field

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look like around a positive charge.

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I just gave this to you

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but how do we know that this
is what the electric field's

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supposed to look like?

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What we can do is this.

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We can say that we know the
definition of electric field

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is that it's the amount
of electrical force

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exerted per charge.

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In other words, if you
took some test charge,

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think of this Q as the test charge

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and we usually just make
this a positive test charge

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so this is easier to think about.

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If you took some positive
test charge into some region

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let's do that, let's put some
positive test charge in here.

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We take this test charge,
we move it around.

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All we have to do to figure out

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the direction of the electric field,

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since this Q would be positive,

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we can just figure out what direction

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is the electric force on
that positive test charge.

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In other words, the direction
of the electric field E

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is gonna be the same direction
as the electric force

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on a positive test charge.

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Because if you know
about vector equations,

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look at this electric fields vector,

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this electric forces vector.

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This electric field is just gonna adopt

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the same direction as the electric force

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as long as this Q is positive.

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If this Q were negative
it would flip the sign

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of this electric force

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and then the E would point
the opposite direction.

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But if we keep our test charge positive

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then we know, okay, the electric field's

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just gonna point the same direction

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as the electrical force on
that positive test charge.

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Here's what I mean.

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We take our positive test charge.

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We move it around.

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If I wanna know the electric
field at this spot right here,

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I just ask myself,

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which way does the electrical force

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point on that test charge?

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The electric force
would point to the right

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since it's being repelled

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by this other positive charge over here.

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I know that the electric
force points to the right,

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these charges repel each other.

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And since the electric
force points to the right,

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that means the electric
field in this region

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also points to the right.

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It might not have the same magnitude.

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The electric force might be 20 newtons

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and the electric field might
be 10 newtons per coulomb

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but they have the same direction.

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And I can move this charge somewhere else,

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let's say I move it over here.

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Which way would the electric force point?

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Well, these positive
charges are still repelling.

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I'd still have an electric
force to the right.

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That electric force would be smaller

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but it would still point to the right

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and that means the electric field

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also still points to the right,

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it would be smaller as well

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but it would still point to the right.

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And if we wanna determine
the electric field elsewhere,

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we can move our positive test charge,

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I'll move it over to here.

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I'll ask which way is the electric force

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on this positive test charge?

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That would be in this direction

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since these positive charges
are repelling each other,

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they're pushing each other away

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so this positive always gets pushed away

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from this other positive charge.

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And so, that also means
that the electric field

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is pointing in that direction as well.

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We keep doing this.

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I can move this somewhere else.

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I can move this positive charge down here.

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The charges repel so the electric force

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would point downward.

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And that means the electric
field would also point down.

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If you keep doing this,

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if you keep mapping what's the direction

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of the electric force on
a positive test charge?

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Eventually, you realize oh,
it's always just gonna point

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radially out away from
this other positive charge.

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And so we know the electric field

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from a positive charge is just gonna point

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radially outward, that's
why we drew it like this.

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Because this positive charge would push

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some positive test charge
radially away from it

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since it would be repelling it.

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Positive charges create electric fields

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that point radially away from them.

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Now what if the charge creating the field

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were a negative charge?

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So, let's try to figure that one out,

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let me get rid of this.

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Let's say the charge
creating the electric field

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were negative, a big negative charge,

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how do we determine the electric field

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direction around this negative charge?

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We're gonna do the same thing,

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we're gonna take our positive test charge

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and we're gonna keep our
test charge positive,

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that way we know that the direction

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of the electric force on
this positive test charge

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is gonna be the same direction

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as the electric field in that region.

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In other words, the
positivity of this test charge

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will just make it so
that the electric field

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and electric force point
in the same direction.

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And if we do that, I'll move this around.

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We'll just put it at this point here,

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we'll move this test charge here.

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Which way is the force
on that test charge?

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This time it's getting attracted
to this negative charge.

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Opposite charges attract

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so the electric force would point this way

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and since it's a positive test charge

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and it preserve the
direction in this equation,

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that means the electric field

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also points in that leftward direction.

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And we can keep mapping the field

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we'll move the test charge over to here.

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The electric force this
time is gonna point up

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because this positive test charges

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is attracted to this negative charge.

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And if the electric force points up,

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that means the electric field
also points up in that region.

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And you'd realize the electric force

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is always gonna pull
a positive test charge

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toward this negative
creating the field around it.

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And because of that, the electric field

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created by a negative charge
points radially inward

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toward that negative charge.

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This is different.

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Positive charge created
a field that pointed

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radially away from

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because it always repelled
the positive test charge.

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But a negative charge
creates an electric field

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that points radially into

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because it's always attracting
a positive test charge.

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Basically what I'm saying is

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that if we got rid of all these,

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clean this up,

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the electric field from a positive charge

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points radially outward

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but if it were a negative charge,

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you'd have to erase all these arrowheads

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and put them on the other end.

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Because the electric field
from a negative charge

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points radially inward
toward that negative charge.

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In other words, the
electric field created by

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a negative charge at some
point in space around it

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is gonna point toward that negative charge

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creating that electric field.

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And so, that's how you could determine

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the direction of the electric
field created by a charge.

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If it's a positive charge you know

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the electric field points
radially out from that positive.

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And if it's a negative charge,

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you know the field points radially inward

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toward that negative charge.

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Okay, so that was number one here.

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We found the direction

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of the electric field created by a charge.

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Check, we've done this.

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Now we should get good at finding

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the direction of the electric force

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exerted on a charge in a field.

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What does that mean?

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Let's say you had a region of space

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with electric field pointing to the right.

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What's creating this electric field?

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I don't know.

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It doesn't even really matter.

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This is why the electric
field is a cool idea.

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I don't really need to know

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what created this electric field.

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I mean, it could be
positive charges over here

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creating fields that point
radially away from them.

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But it could also be
negative charges over here

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creating fields that
point radially toward them

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or both, we don't really know.

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It doesn't really matter.

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As long as I now have an electric field

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that points to the right,

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I can figure out the direction
of the electric force

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on a charge in that field.

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Let's put a charge in this field.

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We'll just start with a positive charge.

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We'll put this charge in here.

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Since the electric field is equal to

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the electric force on a charge

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divided by that charge,

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if this is a positive charge

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and this charge we put
down here is positive,

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then the electric force
points in the same direction

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as the electric field and vice versa.

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The electric field and electric force

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would point the same direction

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if the charge feeling that
force is a positive charge.

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This is just a long way of saying

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that the electric force
on a positive charge

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is gonna point in the same direction

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as the electric field in that region.

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If there's an electric field
that points to the right

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like we have in here

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then the electric force on a
positive charge in that region

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is also gonna point to the right.

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And you might be thinking well,

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duh, isn't that kind of obvious?

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Doesn't this equation say

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that the electric force has to be

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the same direction as the electric field.

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Almost, not quite.

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There's one exception.

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If this charge in here were negative,

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if you put a negative charge in here,

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now this force vector gets
multiplied by a negative,

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well, divided by a negative
but the same thing.

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Dividing by negative ones like
multiplying by negative one.

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You would swap the direction
of this force vector

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and this electric field would point

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the opposite direction as the force

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on a negative charge in that region,

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and that's confusing.

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In other words, check this out.

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Say we took a negative
charge in this region

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and we wanted to know which way

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00:08:22,930 --> 00:08:25,225
would the electric force
be on this negative charge

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00:08:25,225 --> 00:08:27,544
due to this electric field
that points to the right.

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00:08:27,544 --> 00:08:29,696
Well, if the electric
field points to the right

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00:08:29,696 --> 00:08:31,173
and this charge is negative,

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then the electric force
has to point to the left.

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00:08:33,961 --> 00:08:36,960
And the reason is if this
force vector is leftward

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00:08:36,960 --> 00:08:38,910
and we divide it by a negative sign,

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that's gonna take this force vector

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and turn it from left to right.

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That means the electric field

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would be pointing to the right.

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00:08:44,091 --> 00:08:47,229
If the charge experiencing
the electric force is negative

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00:08:47,229 --> 00:08:49,626
because multiplying a
vector by negative one

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changes its direction,

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the electric force and the electric field

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00:08:53,167 --> 00:08:54,950
are gonna have opposite directions.

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00:08:54,950 --> 00:08:56,708
A negative charge feels a force

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00:08:56,708 --> 00:08:59,590
in the opposite direction
as the electric field

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00:08:59,590 --> 00:09:01,310
but a positive charge feels a force

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00:09:01,310 --> 00:09:03,866
in the same direction
as the electric field.

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00:09:03,866 --> 00:09:05,569
And I'll repeat that
because it's important.

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00:09:05,569 --> 00:09:08,963
Positive charges experience
an electric force

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00:09:08,963 --> 00:09:11,627
in the same direction
as the electric field.

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00:09:11,627 --> 00:09:14,567
And negative charges
experience an electric force

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00:09:14,567 --> 00:09:17,622
in the opposite direction
as the electric field.

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00:09:17,622 --> 00:09:18,867
People mess this up all the time.

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00:09:18,867 --> 00:09:20,514
This confuses people a lot

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00:09:20,514 --> 00:09:23,067
so here's a way that might
make it seem a little simpler.

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00:09:23,067 --> 00:09:24,760
Notice that neither of these charges

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are creating this electric field

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00:09:26,757 --> 00:09:28,257
that's exerting the force on them

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00:09:28,257 --> 00:09:29,839
but let's draw some possibilities

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00:09:29,839 --> 00:09:32,830
for charges that might be
creating this electric field.

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00:09:32,830 --> 00:09:34,863
One way to create an
electric field to the right

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00:09:34,863 --> 00:09:37,646
is by having a bunch of
positive charges over here,

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00:09:37,646 --> 00:09:41,047
creating electric fields that
point radially away from them.

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00:09:41,047 --> 00:09:42,788
That would create an
electric field to the right.

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00:09:42,788 --> 00:09:45,156
And what would be the force
on these charges then?

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00:09:45,156 --> 00:09:48,506
Well, we know positive charges
repel other positive charges

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00:09:48,506 --> 00:09:50,063
so the electric forces to the right.

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00:09:50,063 --> 00:09:52,658
And positive charges
attract negative charges

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00:09:52,658 --> 00:09:54,530
so the electric force
would point to the left.

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00:09:54,530 --> 00:09:56,912
This convention of
electric forces pointing

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00:09:56,912 --> 00:09:59,051
in the same direction
as the electric field

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00:09:59,051 --> 00:10:00,338
for a positive charge

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00:10:00,338 --> 00:10:02,463
and electric forces pointing
in the opposite direction

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00:10:02,463 --> 00:10:04,268
of the electric field
for a negative charge

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00:10:04,268 --> 00:10:05,787
agrees with what we already know

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00:10:05,787 --> 00:10:08,185
about opposites attracting
and likes repelling.

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00:10:08,185 --> 00:10:09,374
It's just that people get confused

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00:10:09,374 --> 00:10:10,934
when we don't draw these charges

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00:10:10,934 --> 00:10:12,620
that are creating the electric field,

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00:10:12,620 --> 00:10:14,047
sometimes people forget how to find

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00:10:14,047 --> 00:10:15,532
the direction of the force.

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00:10:15,532 --> 00:10:17,244
If you want to, you can
always draw them in there.

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00:10:17,244 --> 00:10:18,901
The other possibility is that

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00:10:18,901 --> 00:10:20,610
to create fields to the right,

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00:10:20,610 --> 00:10:22,724
we can put negative charges over here.

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00:10:22,724 --> 00:10:24,542
These might be creating
that electric field

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00:10:24,542 --> 00:10:25,772
because they'd create fields

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00:10:25,772 --> 00:10:27,709
that point radially into them

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00:10:27,709 --> 00:10:29,338
because that's what negative charges do.

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00:10:29,338 --> 00:10:30,571
And which way will the forces be?

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00:10:30,571 --> 00:10:32,316
These negatives would be attracting

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00:10:32,316 --> 00:10:34,551
this positive to the
right just like we said

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00:10:34,551 --> 00:10:36,664
in the same direction
as the electric field.

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00:10:36,664 --> 00:10:38,513
Whether that electric field created by

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00:10:38,513 --> 00:10:40,533
positives or negatives, it doesn't matter.

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00:10:40,533 --> 00:10:42,238
If the electric field points to the right,

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00:10:42,238 --> 00:10:44,503
positive charges feel
the force to the right.

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00:10:44,503 --> 00:10:46,085
And then a negative charge in this region

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00:10:46,085 --> 00:10:47,897
would be repelled by these negatives

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00:10:47,897 --> 00:10:49,749
or attracted by these positives

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00:10:49,749 --> 00:10:51,536
and it would feel a force to the left.

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00:10:51,536 --> 00:10:53,909
It doesn't matter whether it was positives

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00:10:53,909 --> 00:10:55,904
or negatives creating the field.

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00:10:55,904 --> 00:10:57,494
If the field points right,

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00:10:57,494 --> 00:10:59,076
positive charges are gonna feel a force

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00:10:59,076 --> 00:11:00,350
in that region to the right.

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00:11:00,350 --> 00:11:01,777
Negative charges are gonna feel a force

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00:11:01,777 --> 00:11:03,557
in that region to the left.

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00:11:03,557 --> 00:11:04,765
Let's do one more for practice.

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00:11:04,765 --> 00:11:06,316
Let's say you had this example.

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00:11:06,316 --> 00:11:07,523
Let's say you had a negative charge

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00:11:07,523 --> 00:11:10,585
and it was experiencing an
electric force downward.

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00:11:10,585 --> 00:11:12,249
Now we wanna know what direction

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00:11:12,249 --> 00:11:14,429
is the electric field in this region?

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00:11:14,429 --> 00:11:15,589
Well, if the electric force

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00:11:15,589 --> 00:11:17,500
on a negative charge is downward,

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00:11:17,500 --> 00:11:18,733
the only way that happens is

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00:11:18,733 --> 00:11:20,277
for there to be an electric field

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00:11:20,277 --> 00:11:22,115
in this region that points upward.

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00:11:22,115 --> 00:11:23,724
Because negative charges are gonna feel

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00:11:23,724 --> 00:11:26,059
an electric force in
the opposite direction

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00:11:26,059 --> 00:11:27,469
as the electric field.

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00:11:27,469 --> 00:11:30,060
The direction of the E would
be the opposite direction

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00:11:30,060 --> 00:11:31,261
as the direction of F

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00:11:31,261 --> 00:11:33,277
or it could just ask
what charge would cause

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00:11:33,277 --> 00:11:35,842
an electric force downward
on this negative charge?

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00:11:35,842 --> 00:11:37,944
A big positive charge
down here would do it.

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00:11:37,944 --> 00:11:39,675
Well, positive charges create fields

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00:11:39,675 --> 00:11:41,652
that point radially away from them.

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00:11:41,652 --> 00:11:42,748
So in this region up here

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00:11:42,748 --> 00:11:44,891
it would have to point radially upward

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00:11:44,891 --> 00:11:47,137
since that's a away from
the positive charge.

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00:11:47,137 --> 00:11:48,601
Or you could say something else

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00:11:48,601 --> 00:11:49,762
that would cause an electric force

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00:11:49,762 --> 00:11:51,648
downward on this negative charge

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00:11:51,648 --> 00:11:53,789
would be a big negative charge up here.

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00:11:53,789 --> 00:11:55,551
And negative charges always create fields

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00:11:55,551 --> 00:11:57,413
that point radially into them.

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00:11:57,413 --> 00:11:59,408
What would the field be
in this region down here,

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00:11:59,408 --> 00:12:01,168
it would still point upward

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00:12:01,168 --> 00:12:03,880
because upward would be radially in

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00:12:03,880 --> 00:12:06,808
toward the negative charge
creating that field.

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00:12:06,808 --> 00:12:08,571
Recapping, you can find the direction

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00:12:08,571 --> 00:12:10,984
of the electric field created by a charge

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00:12:10,984 --> 00:12:12,829
since positive charges create fields

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00:12:12,829 --> 00:12:14,925
that point radially away from them.

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00:12:14,925 --> 00:12:16,404
And negative charges create fields

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00:12:16,404 --> 00:12:18,287
that point radially toward them.

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00:12:18,287 --> 00:12:19,438
And you can find the direction of

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00:12:19,438 --> 00:12:21,669
the electric force on a charge

388
00:12:21,669 --> 00:12:24,539
since positive charges are
gonna feel an electric force

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00:12:24,539 --> 00:12:27,632
in the same direction as the
electric field in that region.

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00:12:27,632 --> 00:12:29,829
And negative charges are
gonna feel an electric force

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00:12:29,829 --> 00:12:31,441
in the opposite direction

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00:12:31,441 --> 00:00:00,000
to the electric field in that region.