# Electric Field of Parallel Plates

Hi. It’s Mr. Andersen and this AP Physics
essentials video 30. It is on the electric field of parallel plates. And we have already
learned so far that the electric field will look like this. It will go from the positive
to the negative. But we have not gotten into the details of that. Before we get there let
me give you a quick application of this. In biology we use gel electrophoresis. And what
you do is create an electric field across this gel. And then you can add DNA fragments
to it. So we are going to put DNA fragments in right here. And what happens is they will
respond to that electric field. And DNA has a negative charge and so what they are going
to do is they are going to migrate across that electric field. Now what is interesting
is the DNA is each going to have a different size. And so the small fragments will be able
to move really, really far. And the larger fragments will not move this far. And so we
can create a DNA fingerprint. And so if we have two parallel plates and we make sure
they are oppositely charged and we also make sure that charge is uniformly distributed
and we also make sure that we are really far from the edge, as long as those three things
are true, then we can represent the electric field like this. And if that is our electric
field, we know that the electric field strength is going to act perpendicular to those plates.
And it is also going to be constant or uniform throughout. In other words no matter where
you test the electric field inside here, it is going to give you the same value. It is
going to be the same direction and it is always going to be the same size. Now how do you
figure out the electric field strength here? There are a couple of ways we could do it.
We could look at the voltage across that gap. And then the displacement or r across the
gap. And that would tell us the electric field strength. Or we could just use the charge
of the plates and the area of those individual plates. And that is going to give use the
electric field strength as well. The last thing you should pick up from this video is
what happens if we add a charged particle to this electric field? What happens if I
take a proton, for example, and I give it a velocity in the horizontal right here? Can
you predict what is going to happen as it enters into the electric field? Remember positive
charges are going to follow the electric field. And so watch what happens as we let it go.
So it bends like that. But you can see that it continues to have the same velocity in
the horizontal. But what we are really doing is changing it the vertical. And so this works
exactly like projectile motion. However, projectile motion, that electric field is going to be
the gravitational field. So can you predict what will happen if I take a negative charge
and add it in that direction? Which way do you think it is going to go? Like that. It
looks just like throwing a baseball, that parabolic curve because it is the same thing.
It is moving horizontally and that is not affected by that change in the force in the
vertical. So in order to look at the electric field of parallel plates it is sometimes easier
to look at them individually. So if we look at the positive plate and we draw the electric
field lines it is going to look like that. It is all moving out from the plate. And now
if we draw the negative it is going to be moving towards the plate. And so if I know
simply just combine those two, it is going to look like this. Now you can see on the
edge, in order to figure out which way they are going we would have to do some vector
addition. And so we are just going to say that we are really far from the edge. And
then you can also see up here and down here that that net electric field, since it is
so close together in relation to the overall length of this plate, that it is also a net
of zero. The only place where they are going in the same direction is going to be in the
middle. And so we can treat that as our net electric field. That uniform electric field
on the inside. And if we want to figure out what the electric field strength is, we could
use the charge and the area of those plates. And so if we use this equation, what we have
here is the electric field strength is equal to Q, which is going to be the charge divided
by the permittivity of free space. Remember that is a constant. And so that is going to
offer resistance to an electric field. And then we are going to multiply that times area.
And so if we increase the charge on the top then we are going to increase the electric
field strength. And if we decrease the area then we are going to increase electric field
strength. So let me kind of walk you through that in a PHET simulation. We have here our
two plates. And we can add charge to that. And the charge will show up right here. And
then we can measure the electric field down below. So what we are looking at is what happens
when we increase Q. And then what happens when we increase or change A. And so what
we are going to do is put our electric field sensor right in the middle, so you can see
there is no electric field strength. And as we add charge to it, watch what happens to
our electric field. It is getting greater. And so what we could do is at this point we
solve for E. If I add more charge or I add more of the negative charge, you can see I
am increasing that electric field strength. Now what happens if we change the plate area?
As we decrease the plate area you can see that we are increasing the electric field
strength. Because it is in the denominator we decrease, we increase the electric field
strength. If we increase the area what we are doing is decreasing the electric field
strength. And so it is a really nice relationship between charge and the area of the plates
and then the electric field strength. But we could also go at it in a different direction.
We could look at the voltage or the potential across that gap. And then the distance or
the displacement between the two. Now voltage remember is the amount of work that we would
have to do to move a positive charge against that electric field. So that is going to be
the voltage. And then r is going to represent the displacement or the distance between those
two plates. And so here is our equation. Again if we increase the voltage we are going to
increase the electric field. And if we decrease that displacement we are going to increase
the electric field as well. And so we have another little simulation right here. So what
I have done is I have the electric field sensor in the middle. And now we have a voltmeter.
And so now as I add voltage I am increasing the volts, watch what happens to my electric
field. So an increase in the voltage, as we move it up to 1.5 volts is going to increase
that electric field. And we could move it in the opposite direction and we are going
to have the same thing. The more voltage you have, the more potential difference you have,
then the greater that electric field strength is. But watch what happens when we decrease
the distance between the two. So as we make it closer and closer together we are increasing
the electric field. Since r is in the denominator, by decreasing it we are actually increasing
the electric field strength. Last thing you really have to understand is how motion of
particles inside an electric field is similar to motion of objects on our planet. So imagine
I were to roll a ball across a table. And at the moment it goes off the edge of the
table, we take a similar ball and we drop it from a similar height. You maybe have done
this before. Which one is going to hit the ground first? Well the right answer is they
are both going to hit the ground at the same time. And the reason why is that they are
both is a gravitational field. And so even though this one is moving horizontally, that
does not affect the force and therefore the acceleration in the vertical. They both are
going to fall at the same rate. Now charged particles work the same way inside an electric
field. And so if this is our electric field what happens if we add a positive charge to
it? It is going to follow those electric field lines. But what happens if we shoot a positive,
let’s say a proton, horizontally into the electric field? It is just like that ball
rolling off of the table. It is going to accelerate down at the same rate as that one charge did
to begin with. Or if we add a negative charge, and that negative charge we shoot into that
electric field like this. It is going to do not what balls do on our planet. It is going
to actually go against the field. That is what is cool about electromagnetism. It is
going to go in that direction. But it is still following the similar as projectile motion
because we have this set electric field. And so did you learn to create representations
of the electric field between parallel plates? Again we have to be far enough from the edge,
and the plates have to be close enough together. Did you learn to calculate the magnitude and
determine the direction of the field? Again we could use voltage and displacement or separation.
Or we can use charge and area. And then finally did you learn to represent the motion of electrically
charged particles inside an electric field? It is similar to that of projectile motion.
I hope so. And I hope that was helpful.

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## 38 thoughts on “Electric Field of Parallel Plates”

1. Th3z0mbi3surviv0r says:

Second

2. New J says:

Mr. Anderson, these videos are amazing and truly helpful for someone self studying for AP Physics. When is the next set going to be released?

3. Tschoo says:

Thank you Mr. Anderson. I am personally a philsophy student and you help me with those videos to stay clear from metaphysical nonsense!

4. TouchablePhysics says:

That's awesome!! Thanks.

5. Matt Perkins says:

Excellent video. I am using this for my Physics Class. We cover most of this material and it is presented very clearly.

6. David Michael says:

Hi Thanks Mr Anderson for this. As a beginner could you explain please if this field is what is called an electrostatic field? And does it produce negative and or positive ions between plates? If yes how could one alter the experiment to produce mostly a stream of negative ions? Thanks for your help.

7. suman manna says:

its osham
its superb

which software u used to create such presentation?

thank you so much for software

10. Dinesh Raja says:

It was really good…liked the way the video was created with all the simulation software and animation!
GREAT WORK DUDE!!!

11. greatsea says:

shouldn't the field lines at the edges of the negatively charged plate be pointing inward?

12. GabeThinks says:

Omg your videos are amazing. I like when people teach like this because you can tell that they genuinely understand the information because they're able to teach it at any level, which is super important!

13. KPOP ENGLISH AND HINDI music world says:

a very good video

14. Niraj Shah says:

sir, as we know that electric field increases with the decrease in cross-sectional area of the electrodes and vice-versa. but what happen to electric potential if we decrease or increase the cross-sectional area of the electrodes.

15. Lan Nguyen says:

thank you so much! you are a blessing to students

16. sri mohanty says:

Very nice concept clearing video

17. gautham krishnan says:

what is that motion called

18. Ashwyn sam mathew says:

Why doesn't the first equation E= sigma/(epsilon * Area) not account for the distance between the plates?

19. Jin Shikami says:

Hey could you try this app? Any feedback is appreciated! https://play.google.com/store/apps/details?id=summersedge23.com.circuitbreaker.lite&hl=en

Is there a difference in the electric field ..if the plates made from conducting material or non conduction material ? ..and what is the electric field caused by one conducting plate ?

21. ibtizam Choudhury says:

👌👌👌👌👌

22. Daniel Webb says:

YOU ARE AWESOMEE

23. Yuqian Zhang says:

thank you so much

24. Emily Mesa says:

Thank you sooo much!!

25. WasIm Niazi says:

thanks

26. Antlether Filigenzi says:

Cool video, can you make one about a homogeneous electric field, where the plates are parallel but not the same area?

27. Burhanuddin Telwala says:

this solved a daunting doubt in my mind for 3 months

28. Shreyas Bangera says:

What if both the plates are positively charged? How would the electric field lines be? (at the edges and inside).
How can I prevent fringing of electric field lines?

29. Mikalele says:

Thank you!

30. stivep1 says:

Can you share with us – What program do you use for your video graphics?

31. Alosh lover says:

how does the error in the distance between plates influence results????

32. 1st proton of the Hydrogen atom says:

omg youre like Lewis in chemistry. So useful yet underrated

33. Fifi Ding says:

thank you so much :"D this is going to save my extra credits

34. Homie McCool says:

Dis shit some good good

35. Shashi Kumar says:

I am speaking from India. your explanation is much better than all.

36. umara khalid says:

Why fringes formed at the edges

37. apiwat magkeethum says:

could you explain a role of e_0 in the equation?

38. Vicheka Phan says:

Ort jes teh very