- [Instructor] Okay, so we know that electrical charges
create electric fields in the region around them
but people get confused by electric field problems
so you got to get good at at least two things here
if you wanna proficient at dealing with electrical field.
You should get good at determining the direction
of the electric field that's created by a charge.
If you've got some charge
and you wanna know which way does that charge
create an electric field,
you should get really good at that.
And if you know the direction of the field,
you should get good at finding the direction
of the electric force exerted on a charge.
If there's some charge floating around
in an electric field,
you should be able to say,
oh, okay, I can determine the electric force.
Not too bad.
If you get good at these two things,
these problems are gonna be way easier
and the whole process is gonna make a lot more sense.
Let's figure out how to do this.
How do you do these things?
We'll do the first one first.
Let's try to tackle this one.
Let's try to figure out how do you determine
the direction of the electric field
that's created by a charge.
Let's say we didn't know, this is what the electric field
look like around a positive charge.
I just gave this to you
but how do we know that this is what the electric field's
supposed to look like?
What we can do is this.
We can say that we know the definition of electric field
is that it's the amount of electrical force
exerted per charge.
In other words, if you took some test charge,
think of this Q as the test charge
and we usually just make this a positive test charge
so this is easier to think about.
If you took some positive test charge into some region
let's do that, let's put some positive test charge in here.
We take this test charge, we move it around.
All we have to do to figure out
the direction of the electric field,
since this Q would be positive,
we can just figure out what direction
is the electric force on that positive test charge.
In other words, the direction of the electric field E
is gonna be the same direction as the electric force
on a positive test charge.
Because if you know about vector equations,
look at this electric fields vector,
this electric forces vector.
This electric field is just gonna adopt
the same direction as the electric force
as long as this Q is positive.
If this Q were negative it would flip the sign
of this electric force
and then the E would point the opposite direction.
But if we keep our test charge positive
then we know, okay, the electric field's
just gonna point the same direction
as the electrical force on that positive test charge.
Here's what I mean.
We take our positive test charge.
We move it around.
If I wanna know the electric field at this spot right here,
I just ask myself,
which way does the electrical force
point on that test charge?
The electric force would point to the right
since it's being repelled
by this other positive charge over here.
I know that the electric force points to the right,
these charges repel each other.
And since the electric force points to the right,
that means the electric field in this region
also points to the right.
It might not have the same magnitude.
The electric force might be 20 newtons
and the electric field might be 10 newtons per coulomb
but they have the same direction.
And I can move this charge somewhere else,
let's say I move it over here.
Which way would the electric force point?
Well, these positive charges are still repelling.
I'd still have an electric force to the right.
That electric force would be smaller
but it would still point to the right
and that means the electric field
also still points to the right,
it would be smaller as well
but it would still point to the right.
And if we wanna determine the electric field elsewhere,
we can move our positive test charge,
I'll move it over to here.
I'll ask which way is the electric force
on this positive test charge?
That would be in this direction
since these positive charges are repelling each other,
they're pushing each other away
so this positive always gets pushed away
from this other positive charge.
And so, that also means that the electric field
is pointing in that direction as well.
We keep doing this.
I can move this somewhere else.
I can move this positive charge down here.
The charges repel so the electric force
would point downward.
And that means the electric field would also point down.
If you keep doing this,
if you keep mapping what's the direction
of the electric force on a positive test charge?
Eventually, you realize oh, it's always just gonna point
radially out away from this other positive charge.
And so we know the electric field
from a positive charge is just gonna point
radially outward, that's why we drew it like this.
Because this positive charge would push
some positive test charge radially away from it
since it would be repelling it.
Positive charges create electric fields
that point radially away from them.
Now what if the charge creating the field
were a negative charge?
So, let's try to figure that one out,
let me get rid of this.
Let's say the charge creating the electric field
were negative, a big negative charge,
how do we determine the electric field
direction around this negative charge?
We're gonna do the same thing,
we're gonna take our positive test charge
and we're gonna keep our test charge positive,
that way we know that the direction
of the electric force on this positive test charge
is gonna be the same direction
as the electric field in that region.
In other words, the positivity of this test charge
will just make it so that the electric field
and electric force point in the same direction.
And if we do that, I'll move this around.
We'll just put it at this point here,
we'll move this test charge here.
Which way is the force on that test charge?
This time it's getting attracted to this negative charge.
Opposite charges attract
so the electric force would point this way
and since it's a positive test charge
and it preserve the direction in this equation,
that means the electric field
also points in that leftward direction.
And we can keep mapping the field
we'll move the test charge over to here.
The electric force this time is gonna point up
because this positive test charges
is attracted to this negative charge.
And if the electric force points up,
that means the electric field also points up in that region.
And you'd realize the electric force
is always gonna pull a positive test charge
toward this negative creating the field around it.
And because of that, the electric field
created by a negative charge points radially inward
toward that negative charge.
This is different.
Positive charge created a field that pointed
radially away from
because it always repelled the positive test charge.
But a negative charge creates an electric field
that points radially into
because it's always attracting a positive test charge.
Basically what I'm saying is
that if we got rid of all these,
clean this up,
the electric field from a positive charge
points radially outward
but if it were a negative charge,
you'd have to erase all these arrowheads
and put them on the other end.
Because the electric field from a negative charge
points radially inward toward that negative charge.
In other words, the electric field created by
a negative charge at some point in space around it
is gonna point toward that negative charge
creating that electric field.
And so, that's how you could determine
the direction of the electric field created by a charge.
If it's a positive charge you know
the electric field points radially out from that positive.
And if it's a negative charge,
you know the field points radially inward
toward that negative charge.
Okay, so that was number one here.
We found the direction
of the electric field created by a charge.
Check, we've done this.
Now we should get good at finding
the direction of the electric force
exerted on a charge in a field.
What does that mean?
Let's say you had a region of space
with electric field pointing to the right.
What's creating this electric field?
I don't know.
It doesn't even really matter.
This is why the electric field is a cool idea.
I don't really need to know
what created this electric field.
I mean, it could be positive charges over here
creating fields that point radially away from them.
But it could also be negative charges over here
creating fields that point radially toward them
or both, we don't really know.
It doesn't really matter.
As long as I now have an electric field
that points to the right,
I can figure out the direction of the electric force
on a charge in that field.
Let's put a charge in this field.
We'll just start with a positive charge.
We'll put this charge in here.
Since the electric field is equal to
the electric force on a charge
divided by that charge,
if this is a positive charge
and this charge we put down here is positive,
then the electric force points in the same direction
as the electric field and vice versa.
The electric field and electric force
would point the same direction
if the charge feeling that force is a positive charge.
This is just a long way of saying
that the electric force on a positive charge
is gonna point in the same direction
as the electric field in that region.
If there's an electric field that points to the right
like we have in here
then the electric force on a positive charge in that region
is also gonna point to the right.
And you might be thinking well,
duh, isn't that kind of obvious?
Doesn't this equation say
that the electric force has to be
the same direction as the electric field.
Almost, not quite.
There's one exception.
If this charge in here were negative,
if you put a negative charge in here,
now this force vector gets multiplied by a negative,
well, divided by a negative but the same thing.
Dividing by negative ones like multiplying by negative one.
You would swap the direction of this force vector
and this electric field would point
the opposite direction as the force
on a negative charge in that region,
and that's confusing.
In other words, check this out.
Say we took a negative charge in this region
and we wanted to know which way
would the electric force be on this negative charge
due to this electric field that points to the right.
Well, if the electric field points to the right
and this charge is negative,
then the electric force has to point to the left.
And the reason is if this force vector is leftward
and we divide it by a negative sign,
that's gonna take this force vector
and turn it from left to right.
That means the electric field
would be pointing to the right.
If the charge experiencing the electric force is negative
because multiplying a vector by negative one
changes its direction,
the electric force and the electric field
are gonna have opposite directions.
A negative charge feels a force
in the opposite direction as the electric field
but a positive charge feels a force
in the same direction as the electric field.
And I'll repeat that because it's important.
Positive charges experience an electric force
in the same direction as the electric field.
And negative charges experience an electric force
in the opposite direction as the electric field.
People mess this up all the time.
This confuses people a lot
so here's a way that might make it seem a little simpler.
Notice that neither of these charges
are creating this electric field
that's exerting the force on them
but let's draw some possibilities
for charges that might be creating this electric field.
One way to create an electric field to the right
is by having a bunch of positive charges over here,
creating electric fields that point radially away from them.
That would create an electric field to the right.
And what would be the force on these charges then?
Well, we know positive charges repel other positive charges
so the electric forces to the right.
And positive charges attract negative charges
so the electric force would point to the left.
This convention of electric forces pointing
in the same direction as the electric field
for a positive charge
and electric forces pointing in the opposite direction
of the electric field for a negative charge
agrees with what we already know
about opposites attracting and likes repelling.
It's just that people get confused
when we don't draw these charges
that are creating the electric field,
sometimes people forget how to find
the direction of the force.
If you want to, you can always draw them in there.
The other possibility is that
to create fields to the right,
we can put negative charges over here.
These might be creating that electric field
because they'd create fields
that point radially into them
because that's what negative charges do.
And which way will the forces be?
These negatives would be attracting
this positive to the right just like we said
in the same direction as the electric field.
Whether that electric field created by
positives or negatives, it doesn't matter.
If the electric field points to the right,
positive charges feel the force to the right.
And then a negative charge in this region
would be repelled by these negatives
or attracted by these positives
and it would feel a force to the left.
It doesn't matter whether it was positives
or negatives creating the field.
If the field points right,
positive charges are gonna feel a force
in that region to the right.
Negative charges are gonna feel a force
in that region to the left.
Let's do one more for practice.
Let's say you had this example.
Let's say you had a negative charge
and it was experiencing an electric force downward.
Now we wanna know what direction
is the electric field in this region?
Well, if the electric force
on a negative charge is downward,
the only way that happens is
for there to be an electric field
in this region that points upward.
Because negative charges are gonna feel
an electric force in the opposite direction
as the electric field.
The direction of the E would be the opposite direction
as the direction of F
or it could just ask what charge would cause
an electric force downward on this negative charge?
A big positive charge down here would do it.
Well, positive charges create fields
that point radially away from them.
So in this region up here
it would have to point radially upward
since that's a away from the positive charge.
Or you could say something else
that would cause an electric force
downward on this negative charge
would be a big negative charge up here.
And negative charges always create fields
that point radially into them.
What would the field be in this region down here,
it would still point upward
because upward would be radially in
toward the negative charge creating that field.
Recapping, you can find the direction
of the electric field created by a charge
since positive charges create fields
that point radially away from them.
And negative charges create fields
that point radially toward them.
And you can find the direction of
the electric force on a charge
since positive charges are gonna feel an electric force
in the same direction as the electric field in that region.
And negative charges are gonna feel an electric force
in the opposite direction
to the electric field in that region.