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.