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Lecture Comments (9)

2 answers

Last reply by: Peter Ke
Wed Apr 27, 2016 3:48 PM

Post by Peter Ke on February 21 at 08:44:55 AM

For example 1, shouldn't r=.9 and you square it because the radius of the diameter of 1.8 is .9?

1 answer

Last reply by: Professor Selhorst-Jones
Sat Feb 15, 2014 12:07 AM

Post by Jon Zelis on February 14, 2014

Thank you for this lecture. You've really cleared up alot.

1 answer

Last reply by: Professor Selhorst-Jones
Sat Sep 14, 2013 10:11 AM

Post by Ikze Cho on September 14, 2013

about the conceptual example 3,
on the other side of the positive bar (side facing away from the negative bar) there would be "lines" moving straight away, perpendicular to the bar and in opposite direction of the drawn in "lines", right?


1 answer

Last reply by: Professor Selhorst-Jones
Mon Apr 22, 2013 12:54 PM

Post by varsha sharma on April 15, 2013

is center of earth negatively charged

Electric Fields & Potential

  • An electric field (E) is a location that exerts a force on a charge based on the amount of the charge. Given a point charge q1 and a distance r, we can figure out this value.

    = k q1



    The electric field always points in the direction a positive charge would move.
  • The strength of an electric field is measured in newtons per coulomb ([N/C]).
  • Electric field lines are a way to visualize electric fields at many points. They always point in the direction a positive charge would move.
  • A Faraday cage is a fully enclosing conductor. Electric fields outside the cage will have no effect inside of it, and vice-versa.
  • Electric potential (V) is connected to the amount of work involved in moving a charge and how much charge we are moving. Each location has a potential V tied to it. To figure out how much work is involved in moving from one location to another, we need to look at the potential difference:
    ∆V = W

  • Electric potential is measured in volts (V): joules per coulomb ([J/C]). A difference in electric potentials is called a voltage.
  • Like setting a base height when we worked with gravitational potential energy, we need to set an arbitrary base electric potential. We often use the ground (the literal body of the Earth) for this, setting it as 0V.
  • An electron-volt is a very small unit of energy. It is how much energy is involved in moving a single elementary charge (e) across a voltage of 1V:
    1 eV = 1.602 ·10−19J.
  • An equipotential surface is something where it takes no work to move charge around (equal electric potential means no voltage means no work).

Electric Fields & Potential

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Electric Fields 0:53
    • Electric Fields Overview
    • Size of q2 (Second Charge)
    • Size of q1 (First Charge)
    • Electric Field Strength: Newtons Per Coulomb
  • Electric Field Lines 4:19
    • Electric Field Lines
    • Conceptual Example 1
    • Conceptual Example 2
    • Conceptual Example 3
    • Conceptual Example 4
  • Faraday Cage 8:47
    • Introduction to Faraday Cage
    • Why Does It Work?
  • Electric Potential Energy 11:40
    • Electric Potential Energy
  • Electric Potential 13:44
    • Electric Potential
    • Difference Between Two States
    • Electric Potential is Measured in Volts
  • Ground Voltage 16:09
    • Potential Differences and Reference Voltage
    • Ground Voltage
  • Electron-volt 19:17
    • Electron-volt
  • Equipotential Surfaces 20:29
    • Equipotential Surfaces
  • Equipotential Lines 21:21
    • Equipotential Lines
  • Example 1: Electric Field 22:40
  • Example 2: Change in Energy 24:25
  • Example 3: Constant Electrical Field 27:06
  • Example 4: Electrical Field and Change in Voltage 29:06
  • Example 5: Voltage and Energy 32:14

Transcription: Electric Fields & Potential

Hi! Welcome back to Today we’re going to talk about electric fields and potential.0000

When we first learned about gravity, we learned about it as a constant. Later we discovered that gravity varies based on distance and the mass involved but none the less it’s still really useful to be able to treat the force of gravity as simply mg.0007

We can treat this gravity field that affects any object with any mass with the same acceleration. We’re going to have this constant mg.0019

Whatever the mass of the object is in the field times the gravity. Finding the gravity field for any object, g. For finding the gravity field for any object, getting that g can be really, really great to simplify things.0028

We do the exact same thing with electricity. We’re going to try find the electric field. We also want to see what kind of potential there is to move charges around.0042

We’ll also look for electric potential. First the idea of electric fields. If we’ve got a charge q1 fixed in space and then we place a second charge q2 near it there will be a force, fe, f electricity that will be exerted on the second charge.0050

There’ll also be a force exerted on first charge but it’s fixed in space so we know it will stay still. So there will be some force exerted on that second charge.0066

We could also get some idea of what these forces would be like without actually having to place that second charge.0076

Instead of waiting for that second charge to be placed so we can describe the resulting force we can describe the space around the first charge.0082

Anything placed in the space around the first charge will be effected by its electric field, e. Of course the size of q2, the size of the second charge will affect the magnitude of the force.0089

So we have to correct by this, we have to normalize. We’re going to divide out q2. The size of the electric field is equal to that electric force divided by the charge, the second charge placed in it.0101

We can also do this from the point of view of the first charge, q1. Since the force of electricity is fe = k q1 q2 / r² we can find the electric field by the amount q1 that it contributes at a given distance.0114

All that would be left is just to multiply by q2 later to figure out the force. At a given distance we can know that we’re going to have some electric field and with an electric field in place we just put in some charge, we multiply that charge and boom we’ve got the force.0133

Really, really handy if we’re going to have a lot of charges cycling through a continuous electric field. If we’ve got some big stationary charge and we’re going to be putting in one little charge after another.0147

This is a really, really handy thing to have. Just on the Earth we’ve got this big stationary object and we’re going to be occasionally working with one seagull or one falling rock or one little thing at a time.0159

We’ll want to figure out what the gravitational forces similarly we’ll want to figure out what’s the electric force.0171

The electric field strength is given as Newtons per coulomb. This makes a lot of sense; you put in a larger charge you get more force out.0178

You put in one coulomb you get out one Newton if it’s a one Newton per coulomb field. You put in five coulombs in that one Newton per coulomb field you get five Newtons out.0185

The more coulombs you put, in the more charge you put in the more force you get out, the more Newtons you get out.0195

Note, this is really, really important thing to note. The electric field points in the direction of positive charge would move. If you’ve got an electric field pointing to the right where positive is to the right that means that a positive charge would be moved to the right.0199

A negative charge would be moved to the left. I’m going to point this out again. Positive charge, this really does need to be stressed because it’s easy to forget this.0214

If you forget this it’s going to completely screw things up. Remember electric fields point positive.0224

All of electricity is set up around the idea of positive charges moving around. We work in terms and ideas of the positive charge.0229

In reality it’s the electron that moves around but this sort of stuff got set in convention before we really realized that it was the electric charge being created by the electron moving around.0237

So we thought it was positive charges moving around. It was a 50/50 choice, we got unlucky as humanity.0247

Oh well it still works out fine and we’re just stuck with convention at this point.0254

Electric field lines, so just as we can visually describe the gravity field by the direction an object would be pulled we can visually describe an electric field by the direction of positive charge.0261

Once again positive charge would be moved. If we’ve got Earth sitting there, any object is going too pulled towards the center of Earth.0271

Similarly if we had a very large seeming electron, we had an electron or a negatively charged particle sitting here any positive charge would be pulled towards the center of that particle.0280

If on the other hand we had a negative thing it would wind up getting pushed away. The electric field line just gives us a way to visually describe what’s going on.0291

We can see where the positive charges or a positive test charge would get shuttled. We can see what path it wind up taking.0301

Similarly if we reserve the given path we’ll see what path a negative electric test charge would take.0309

Either way. If we’ve got more complicated thing we’re now able to see and analyze motion in electric fields that we wouldn’t immediately notice.0316

We can see what’s going to happen in an electric field that is unusual. If we have a positive charge and a negative charge we’re going to wind up not just getting sucked in if we’re on that horizontal line, but say like here, we’ll start off if we’re positive.0327

At first the positive is going to push us away because it will be stronger but over time it’s going to be continuing to push us up but now the negatives going to pulling us in.0342

Now it’s going to pulling us in and it’s going to be stronger and then positive isn’t going to really have much effect.0349

The negative overcomes and pulls us in. Similar sort of thing goes over here; positive starts to push away but now the negative has some effect, it turns us back around, we pull around and we’ll wind up getting a little bit of whiplash as we go a little too fast because we’ve been accelerated too much.0354

We’ll get yanked back in. However from the real extreme the positive force will manage to always block us out from being able to get sucked in by the negative force.0367

Similarly here we’ll just get pulled in directly. We’ll have a bunch more of these and we’ll just get the chance to see some things.0376

If we had two positive charges, if we were on either one of these…if we were on the horizontal we’d just get pushed away if we’re a positive test charge.0383

We just get pushed away. However if we were on the inside we’d get pushed away but eventually we’re going to start getting closed to that positive other charge.0390

It’s going to start pushing us away, it’s going to start pushing away. Now they’re both pushing us away, the only direction we have left to go is up to get away from them.0398

If we started on one side it’s going to push up and away from us. It’s going to be stronger at first but as it gets farther and farther away the other guys are going to start having an effect we’re going to wind up getting pushed with both of the forces put together.0406

These are the ideas we’re working with. If we have two parallel plates where one is full of positive charge and ones full of negative charge, between the two it’s just going to be a straight electric field.0418

We’re going to get pushed from one into the other. All of the positives on this side are all going to push in and we’re going to get pushed this way.0427

Simultaneously all the negatives on this side are going to pull us in and we’re just going to shuttle along directly.0435

If we’re at very edge we’ll wind up having this curved effect because we’re going to get pushed up and away but then we get sucked back in by the negatives on the other side and so on.0440

Finally if we had a positive bar and a single smaller positive charge in a point, if we were only on this side of the bar we wind up getting pushed basically directly out.0450

Actually if we were down here we might wind up getting pushed and curved just a little bit by the extra force of the circle of the smaller charge, but we don’t have to worry about that too much.0460

But if we were over here say we’d start going forward. As we got closer to it, it would wind up some effect and curving us away. If we were coming directly at it as first as we get closer to it it’s going to repulse us and get really strong.0469

So it’s going to push us off course by quite a bit. As we come towards it, it gets stronger and stronger. Remember divided by r² so as you get really close to it, it gets way more power.0482

It gets way more force involved. As it gets stronger force the closer you get it’s going to push you even farther off course, have more effect on where you’re going.0493

Remember, important thing to note here, all this was done from the point of view of a positive charge motion. Electric field lines are always drawn from the positive point of view.0503

Not the negative point of view. Even though you might think that’s you expect because electrons are the ones really moving around. It’s all done from the positive point of view, the sort of phantom positive charge that follows in the wake of a move, of a gone electron charge.0512

Little bit more. A faraday cage, an amazing property of electricity is if you completely enclose a space with a conducting surface, external electric fields will have no effect inside the conductor.0538

This happens with any shape. You could do it with an egg shape; you could do it with a weird vase shape with a top on top. Anything so long as it’s fully enclosed. A fully enclosed conductor is called a faraday cage.0539

Fully enclosing conductor we call it a faraday cage. It can also be done with wire that is tightly woven together enough. If you basically….a thick gauge cage could work. Hence part of the reason we call it a faraday cage.0551

This idea allows us to have electric shielding. You might wonder and you’d wonder quite rightly, why this works. Imagine if we placed a conductor inside an electric field.0565

The electrons would wind up being rearranged or if we wound up putting some charge on this conductor. Say we’ve got all this charge will show up, the charge is going to cluster, try to get as far away from each other as it possibly can.0578

It’ll wind up actually clustering at the corners because that’s where it can get the farthest away. It can be shown mathematically, that’s the case.0589

In any case we’re going to get some motion of the charges around until eventually they come to stop. They come to an equilibrium. Once they’re at equilibrium they’ve managed to cancel out either the charge, they’re in static equilibrium we’ve managed to find just the right configurations that they don’t have to keep moving around anymore.0595

Or they’ve managed to deal with the electric field in such a way so as to have dealt with it so they’re now once again in static equilibrium.0612

Once they’re in static equilibrium that means everything on that conductor must not feel any force. Well that means if everything on the conductor doesn’t feel any force, everything inside the conductor must also not feel any force.0619

They’ve arranged themselves in a static equilibrium. Since they’re at equilibrium they’ve canceled out the effect of the field or the effect of the charge on that conductor.0632

Since they done this on the conductor it has to similarly have the same effect on anything inside the conductor.0640

So they’ve canceled out, they’ve put things on static equilibrium for the conductor so anything inside of the conductor has the exact same experience. It’s also now going to be in static equilibrium because of the motion of those charges.0647

The electric field is still present but it’s now canceled out perfectly by the conductor around us. This is really cool, it allows for electric shielding. This is a really useful thing if you’ve got background interference and you want to say have a really clean pure signal.0657

They have electric shielding around important lines such as a good TV signal or if you had a mic signal that you cared about a lot.0671

If you’ve ever dealt with good audio equipment you might know that they have shielding inside of the cable to prevent any outside electrical interference from being able to effect the signals going through that cable.0682

So that the electric fields won’t be able to effect the conductor and change and jimmy with what you’ve got going through that line.0692

Electric potential energy. Now we’re ready to shift gears into the idea of talking about potential. Let’s say we fix a positive charge in space somewhere.0701

If we place a positive charge somewhere else around it, it’s going to have some electric potential energy due to the force the first charge will exert on it.0710

If we’ve got these two positive things we’re going to have some force pushing up on it. What happens if we place it in a different spot?0718

If we place it in a different spot, boom, we’ve got way more force. Not only that, it’s got all of this distance to cover so we’re going to put more work into as it covers this distance.0726

The force will change as it covers that distance but we’re definitely going to have more force and more distance than the other potential.0736

If we place a second charge even closer it’s going to have more potential energy because it gets a larger force to start off with and then it will have more distance to be accelerated.0744

Eventually it’ll get to that same location as the first one but by that time it will have already picked up a fair bit more speed, a fair bit more energy.0751

Really the thing to talk about isn’t where it is because we’re going to finally manage to exhaust that potential energy when it’s infinitely far away.0761

We can keep putting them a little bit farther or a little bit closer and so as we go farther and farther out we’ll have less and less potential energy but you could always be farther out.0770

Since you could always be farther out you could always have even less potential energy which means that the only time you’re going to finally run out of potential energy is when you’re way out at….arbitrarily infinitely far away, effectively infinitely far away.0779

That’s kind of difficult to work with. The important thing isn’t this infinite far away it’s the difference between this state and this state.0791

The difference between locations. It’s not about considering absolute potential energy. What’s you’re absolute potential energy in you? What it would be…how much energy would you have if ran from here to infinity?0800

That’s going to take a long time to ever get used. Instead what’s more interesting to talk about is the change in the potential energy.0811

How much energy do you have here versus here? How much energy do you have in one location versus another location?0816

That’s what we want to talk about. Just like we did with the idea of a field we can disassociate electric potential energy from the second charge involved.0823

If that second charge we were placing had a little bit of charge it’s going to have a little bit of potential energy.0833

If we had a lot of charge it’s going to have a lot of potential energy. There’s an effect from that, the second charge will affect the amount of potential energy.0838

We could also talk about this in a way were we could get rid of having to worry about what that charge is right now and we can pull it out, we can normalize for that.0847

We can instead look at the energy per charge, per unit of charge. We’ll call this electric potential and we use the capital V to do this.0855

We do that because later we’ll talk about why that comes up; it comes from its units. However, just like with electric potential energy it’s going to be most often be useful to look at the difference between states.0864

We don’t want to talk about the electric potential here versus all the way out to infinity, that’s once again not so useful.0877

Instead what we really want to talk about is what we’re looking at, what’s the change in energy or the work done per unit charge if we’re going to look at electric potential.0883

We want to look at…if we wanted to look at change in electric potential energy; we want to look at change in electric potentials.0892

The change in the electric potential is equal to the work divided by the charge involved. More charge means we’ll have had more work.0898

If we want to normalize it we’re going to have to cancel out that charge that we had in the first place.0908

Electric potential is measured in volts. Joules per coulomb, which would make sense because, work…joules, charge, coulomb.0913

Volts is joules per coulomb which is why we’ve also got electric potential as a big capital V.0924

A volt is also denoted with another big capital V so sometimes they can get a little confusing because you might see something that says ‘Change in V equals 20 V.”0929

Well it’s not that you could divided both sides by V. They mean different Vs. One is the change in the electric potential is equal to 20 volts.0939

Don’t worry about that too much, it’ll make sense whenever you wind up seeing it.0947

Because of this electric potential difference is often simply referred to as voltage. You’ll often hear voltage; something has a voltage of 120 volts or 60 volts.0951

Where the difference between two things is going to be 10 volts. This is an important idea, the idea of voltage.0962

Ground voltage. Since it’s really useful to talk about potential differences we need a reference voltage.0970

When we worked with gravitation potential we arbitrarily set the ground as h = 0. We said “Alright, here it’s h=0, if you go up you’re going to be some other amount.”0978

That doesn’t mean that it’s not possible to get below h=0. We could have been on a hill. If that’s the case, down here we’d have h = negative.0988

Up here we’d have h = positive. It’s not that you can’t have a negative electric potential or a negative gravitation potential.0996

All that matters is that you’ve set something as your reference. You’ve got a base to work off of.1004

Once we’ve got that base to work off of we can compare things and that’s what we really want to get at.1010

We want to get at the comparison. Worrying about makings sure it’s absolutely nothings ever going to be passed it, it’s the perfect choice. That’s not the best idea.1014

The best idea is to just say “Okay, we’ve got a good base to work from. Something that’s trustworthy that we can rely on being there.”1022

If we can rely on it and it’s going to steady there we’ve got a steady base voltage. Then that’s great. We’ve got that voltage we can measure a difference off of.1031

What matters is that we have a base reference to work from. For voltage, for electric potential we want that base voltage.1040

What we do is we’ll arbitrarily set this as V = 0. We’ll have to set some reference voltage when we’re working with voltage.1048

Generally when we’re working with electricity we set the ground. We use the ground as this voltage. Literally the ground of the Earth, we use the Earth itself.1055

Dirt plunging into the dirt because the Earth functions as one really large conductor. For most intensive purposes we can deal with the Earth as if it’s just one big conductor.1065

If you’ve got excess charge you can ground it, you can put it into the ground because the ground is there and since the ground is basically one big conductor it’s going to have about the same potential everywhere.1078

That means we can just say “Oh hey we need this useful reference voltage, let’s compare it to what the voltage at the ground is.”1091

V = 0 when we’re talking about the ground. It’s also the reason lightning rods connect to the Earth is because they’re trying to get a lightning to Earth itself.1097

It’s trying to give an easy route that the lightning can make as opposed to striking the top of the church or the temple steeple. It’s going to strike the top of a lightning rod nearby where it’s got this wonderful conductor and it’s going to drive into the ground which is where it’s trying to get in the first place.1107

It wants to spread that charge out. In the USA we call it ground, it’s called the ground and you might ground something as a verb, grounding.1123

In the UK on the other hand it’s called the Earth. Something might be Earthed or Earthen. The idea of this is very important in electric circuits.1133

Whether you wind up…whether for you call it ground or you call it Earth, the idea of it winds up being really important to electric circuits and we might talk about this a little bit later down the road.1142

If you ever really study electric circuitry design you’re going to really care about the ground and possibly grounding your object.1150

Electron volt. If we’re dealing with very small charges sometimes it’s really convenient to use the electron volt. Since a difference of one volt would give one joule of energy for one coulomb of charge.1159

We can look at the elementary charge. Remember one volt was the amount of work for one charge…sorry one volt, the difference of one volt means that it took one joule to move one charge over a distance of one volt.1171

That’s great if we’re dealing with large charges like one coulomb. However if we’re dealing with a small one like 1.602 x 10^-19 coulombs the electron or the proton charge amount, we’ll want to talk about the electron volts.1185

An electron volt is a very small unit of energy. Since voltage equals work over charge we can find out what that work is by just multiplying voltage of one times the elementary charge and we get 1ev which is equal to 1.602 x 10^-19 joules.1200

A small, small quantity of energy thus 1ev is the electric energy involved for moving 1 elementary unit of charge across a difference of 1 volt.1220

Echo potential surfaces, inside a good conductor it’s very easy for charge to move around. Inside something like copper or gold it’s so easy that it basically takes no energy to change the location of your charge from one place in the conductor to another place.1231

This isn’t quite true if we’re dealing over huge stretches of distance like many, many kilometers, but if we’re dealing over something like the size of a room, it doesn’t matter.1245

It’s really easy to get around. It’s not hard to shift charge inside of a conductor. If that’s the case we call such a thing an echo potential surface.1255

Since it takes no potential energy there’s no electric potential difference there’s no change in the potential we’re going to have equal potential.1263

So echo potential surface since it will have equal electric potential throughout, no change in voltage throughout the surface.1270

Within a conductor you’re going to have echo potential. We can have this idea in our electric field diagrams from before.1278

If you’re on an echo potential line that means everything on that echo potential line is going to have the same electric potential.1286

Here we’re all the same distance away from that positive thing. You can move your charge anywhere around that circle, anywhere around that circle of that positive charge in the middle and they’re all going to be the same potential.1293

Similarly as long as your anywhere on this line between these two plates, you’re going to wind up being at the same potential. If you want to jump from one to the next or to the next, that’s going to be a change in your potential.1308

As long as you stay on the line you stay the same. If we started off here and then bounced down here and bounced here and then moved up here and then moved here and then moved back here and then moved here, then moved up here and then moved here.1321

We would have changed potential over the course of it? No because we wound up ending at the end. A whole bunch of stuff happened but the total change in the potential; we wound up being on the same echo potential line at the end so there is no change in the electric potential at the end.1334

The initial electric potential was equal to the end electric potential. There might have been some other stuff that happened but assuming it was all done when easy ways we could recoup the force and gain the energy back.1347

We wind up having no change in the energy. Ready for some examples?1358

If we’ve got a charge that’s equal to -4 x 10^-8 coulombs, fairly small amount of charge, and it’s fixed in place. What would be the electric field 1.8 meters to the east?1362

How do we find that out? Electric field is equal to k x q1 / r². Remember because all we have to do, the thing you want to do is be able to just come by later with q2.1374

Multiply q2 in and boom you’ve got a force. Since electric force is equal to k q1 q2 / r ² we just pull off q2 for now and we’ve got the electric field.1387

We plug in the numbers 8.99 x 10^9 for k. Plug in q1 which is -4 x 10^-8. Divide by our distance squared, 1.8 meters squared.1397

Plug that all into a calculator and we’ll get -111 Newtons per coulomb. Now I’d like to make special attention, point special attention to the fact that this is a negative.1413

If it were a positive that would mean we’d be pointing this way. Instead we’re actually pointing the opposite direction.1424

We’re pointing this way. Which makes sense, a positive charge would be pulled into a negative charge.1432

We’re going to get -111 Newtons per coulomb because it’s going to be pulling. It’s a negative thing so the electric field diagram, our electric field, our electric field numbers are going to have to be sucking positive charges towards it.1440

Otherwise we’ve broken the rules of electricity. We’re going to being pulled 111 Newtons per coulomb to the West, or -111 Newtons per coulomb.1455

Next one. If we have a charge 0.03 coulombs and it moves from a starting voltage of 60 volts to 10 volts, what would be the change in energy?1466

Remember change in voltage is equal to the work divided by the charge involved. If we have the change in voltage and we have the charge involved we can figure out what the work is.1477

Charge is 0….well let’s make this a little bit easier to follow. We multiply both sides by q, change in voltage equals work.1492

We substitute things in, 0.03 coulombs, change in voltage is 50 and we’re dropping down.1502

We’ve got 1.5 joules. Now important stuff to notice is we dropped from positive voltage to a smaller positive voltage.1512

We went down in voltage. That means we went from a high electric potential to a lower electric potential. We went from high electric potential to low electric potential.1522

That means we’ve lost some of the electric potential energy. We’ve lost 1.5 joules of electric potential energy. Now there’s one of two things that could have happened.1533

Either our charge did 1.5…well three things. Either our charge did 1.5 joules of work on its environment around it or it took in 1.5 joules of energy in some other form.1543

It converted electric potential energy into some other form of energy or it did a mix of those two things summing up to 1.5 joules.1558

We have to notice that this because we’re going from high potential to low potential. If on the other hand we’d have q = -0.03c, we would have had 1.5 joules but that’s how much it would have had to have taken in.1566

It would have taken in so it would have taken in 1.5 joules. In 1.5 joules, this is out 1.5 joules. Since we’re going from high electric potential to low electric potential with a positive charge, we’re going to be having that much coming out of our electric potential energy bank account.1580

On the other hand if we want to go from a high potential to a low potential but we’re a negative charge then that means we’re going to have be bringing 1.5 joules into our electric potential energy bank account.1602

It’s a little confusing the whole positive and negative thing but it’s important to think ‘high to low just like gravity potential’ you’d be used to but we have to do it from the point of view of positive charge.1612

If we’re not going from the point of view of positive charge we have to flip the way we look at things.1622

Third example. We have a constant electrical field that is 7 x 10^6 Newtons per coulomb, every point over a frictionless surface.1628

It’s always pointing to the right. If we place an object with a mass of 35 kilograms and a charge 10^-5 coulombs, what will be the speed of the object when its 3 meters to the right?1638

The first thing we want to do is we want to figure out what is the force on that object. The electric field is equal to the force divided by the charge.1648

Q times electric field. Well what’s our q? 10^-5 times the electric field is 7 x 10^6.1656

We’ve got 70 Newtons to the right is equal to our force. We’ve got 70 Newtons.1668

If we want to figure how what the acceleration on this object is, f = ma. We’ve got 70 = 35 acceleration.1676

We’ve got 2 meters per second per second is equal to the acceleration.1685

Where is it pointing? It’s pointing to the right. Finally if we want to find out what its velocity is; 3 meters to the right.1691

We know final velocity squared is equal to the initial velocity squared plus 2 x the acceleration times the distance.1698

Final velocity squared is equal to…well we started at rest, 0² + 2 times the acceleration of 2 times a distance of 3 meters.1707

Velocity final is equal to the square root of 12 which is equal to 3.46 meters per second.1720

The only new part that we hadn’t done previously was the fact that we needed to figure out how much force was coming from that electric field.1729

We knew what the charge on the object was, we knew what the electric field was, we knew what direction it should be moving.1737

All we had to do was find out what the magnitude of the force was and we get that by just multiplying the two.1742

Fourth example. What’s the relationship between the electric field and the change in the voltage?1748

We might not have thought about this yet but it makes sense that if we’ve got an electric field and we move through an electric field we’ve picked up force.1754

That means if we’ve picked up force we’ve lost some of our potential energy. Our electric potential has got to change as we pass through an electric field.1762

How can we figure this out? Well let’s start off with some simple unit values.1770

If we’ve got 1 coulomb charge and a 1 Newton per coulomb electric field, so what’s the force of 1 coulomb in 1 Newton per coulomb?1775

Well 1 coulomb times 1 Newton per coulomb. If we’re an electric field of 1 Newton per coulomb and we’ve got a 1 coulomb charge, that means we’ve got a 1 Newton force.1785

If we travel a distance of 1 meter then that means our work is equal to 1 Newton dotted with 1 meter so we’ve got 1 joule of work.1795

We do 1 joule of work over that meter if we’ve got 1 coulomb. What happens instead if our q was 10 coulombs?1809

Same basic idea but now our force is going to be 10 Newtons. Even with the same distance of 1 meter we’re going to now get 10 joules of work.1817

What’s happened here? We’ve got that the amount of charge is going to change the amount of the work, but we’re already used to that.1832

We’re dealing with electric potential, we’ve solved out for that. That isn’t so much an issue.1841

What if we were dealing with a different electric field? Say we had an electric field of 5 Newtons per coulomb.1845

If it acted on a charge of 1 coulomb then we wind up having a force of 5 Newtons. So we’d have a work over 1 meter of 5 joules.1851

As long as we’re traveling 1 meter it’s going to be whatever the electric field is per coulomb.1866

We can figure out that the change in the voltage is equal to the size of the electric field dotted with distance.1875

The distance that we travel and the electric field is going to give our change in our voltage.1887

The voltage is equal to electric field dotted with distance because what we’ve got here is we’ve got the fact that an electric field, we can express as Newtons per coulomb, but that’s the same thing as volts per meter.1893

If we’ve got a 500 Newton per coulomb electric field that’s the same thing as saying we’ve got a 500 volt per meter.1912

If we go 2 meters in that electric field we’ve got 1,000 volts. We’ve got a potential difference and electric potential difference of 1,000 volts, a voltage of 1,000 volts.1920

That’s a really cool connection. Great, now we can have a bonus idea of how we can reexamine example three in terms of voltage and energy.1933

In number three we had an electric field; we had a mass of an object on a frictionless surface. We had charge for that object and we had a distance that it travelled.1945

Now we know that the change in voltage…not change…voltage is a scalar. Change in the voltage is equal to the electric dotted with the distance.1953

That means we’ve got 7 x 10^6 on 3 meters, so we’ve got 21 x 10^6 volts.1965

We’ve got a change in volts of 21 x 10^6. If we want to know the work done is we know change in volts is equal to the work over the charge involved.1976

The charge involved times that change in voltage, our charge involved is 10^-5, the change in voltage is a whopping 21 x 10^6 volts.1987

That’s going to get us 210 joules. We’ve got 210 joules of work is done in that charge moving those 3 meters.2001

We’ve got 210 joules of work put into the system then since we started off at rest we know that our kinetic energy is going to be ½ mv²2011

We don’t have to worry about there being any beforehand so all of our energy went into moving the object on that frictionless surface.2023

We know that those 210 joules went into the kinetic energy equals ½ mv². We start solving it out.2028

We’ve got that 2 x 210 divided by our mass of 35 kilograms. We take square root, is going to equal the velocity we’ve got.2037

We punch that all out through our calculator and we get the exact same velocity we did before, 3.46 meters per second.2052

Two different ways, two very different ways to figure it out but that’s because can connect the movement through our electric field to the change in the electric potential.2065

That’s a really cool idea and that’s got a lot of power for us.2074

Hope that made sense and it’ll be great to see to you for current because that’s when things really get cooking.2077

Alright, we’ll see you at later.2082