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  • - [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.

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

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A2 US electric electric field charge field positive direction

Electric field direction | Electric charge, field, and potential | Physics | Khan Academy

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    yukang920108 posted on 2022/07/19
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UK /ɪˈventʃuəli/

  • adverb
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process

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UK /prə'ses/

  • verb
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UK /bʌntʃ/

  • other
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practice

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  • other
  • To carry out or perform (a particular activity, method, or custom) habitually or regularly.
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