Electric Potential Vs Electric Potential Energy

Let's review a little bit ofwhat we had learned many, many videos ago about gravitationalpotential energy and then see if we can draw the analogy,which is actually very strong, to electrical potentialenergy. So what do we know about gravitational potential energy? If we said this was the surfaceof the Earth- we don't have to be on Earth, butit makes visualization easy. We could be anywhere that hasgravity, and the potential energy would be due to thegravitational field of that particular mass, but let'ssay this is the surface of the Earth. We learned that if we have somemass m up here and that the gravitational field at thisarea- or at least the gravitational acceleration- isg, or 9.8 meters per second squared, and it is h- we couldsay, I guess, meters, but we could use any units. Let's say it is h meters abovethe ground, that the gravitational potential energyof this object at that point is equal to the mass times theacceleration of gravity times the height, or you could viewit as the force of gravity, the magnitude of theforce of gravity. You know, it's a vector, butwe can say the magnitude of the vector times height.

• Electrical Potential Vs Potential Difference
• Electric Potential Vs Electric Potential Energy Examples

And so what is potentialenergy? Well, we know that if somethinghas potential energy and if nothing is stopping itand we just let go, that energy, at least withgravitational potential energy, the object will startaccelerating downwards, and a lot of that potential energy,and eventually all of it, will be converted to kineticenergy. So potential energy is energythat is being stored by an object's situation or kind ofthis notional energy that an object has by virtueof where it is. So in order for something tohave this notional energy, some energy must havebeen put into it.

And as we learned withgravitational potential energy, you could viewgravitational potential energy as the work necessary to movean object to that position. Now, if we're talking about workto move something into that position, or whatever, wealways have to think about, well, move it from where?

You must be able to calculate the electric potential for a point charge, and use the electric potential in work-energy calculations. Electric potential and electric.

Well, when we talk aboutgravitational potential energy, we're talking aboutmoving it from the surface of the Earth, right? And so how much work is requiredto move that same mass- let's say it was here atfirst- to move it from a height of zero toa height of h? Well, the whole time, theEarth, or the force of gravity, is going tobe F sub g, right?

So essentially, if I'm pullingit or pushing it upwards, I'm going to have to have- andlet's say at a constant velocity- I'm going to have tohave an equal and opposite force to its weightto pull it up. Otherwise, it would acceleratedownwards.

I'd have to do a little bit morejust to get it moving, to accelerate it however much, butthen once I get it just accelerating, essentially Iwould have to apply an upward force, which is equivalent tothe downward force of gravity, and I would do it for adistance of h, right? What is work? Work is just forcetimes distance. Force times distance, and ithas to be force in the direction of the distance.

So what's the work necessaryto get this mass up here? Well, the work is equal to theforce of gravity times height, so it's equal to the gravitational potential energy. Now this is an interestingthing. Notice we picked the referencepoint as the surface of the Earth, but we couldhave picked any arbitrary reference point. We could have said, well, from10 meters below the surface of the Earth, which could have beendown here, or we could have actually said, you know,from a platform that's 5 meters above the Earth. So it actually turns out, whenyou think of it that way, that potential energy of any form,but especially gravitational potential energy- and we'llsee electrical potential energy- it's always inreference to some other point, so it's really a change inpotential energy that matters. And I know when we studiedpotential energy, it seemed like there was kind of anabsolute potential energy, but that's because we always assumethat the potential energy of something is zero thesurface of the Earth and that we want to know thepotential energy relative to the surface of the Earth, so itwould be kind of, you know, how much work does it take totake something from the surface of the Earthto that height?

But really, we should be saying,well, the potential energy of gravity- like thisstatement shouldn't be, you know, this is just the absolute potential energy of gravity. We should say this is thepotential energy of gravity relative to the surface of theEarth is equal to the work necessary to move something, tomove that same mass, from the surface of the Earth toits current position. We could have defined some otherterm that is not really used, but we could have saidpotential energy of gravity relative to minus 5 metersbelow the surface of the Earth, and that would be thework necessary to move something from minus 5 metersto its current height.

And, of course, thatmight matter. What if we cut up a hole andwe want to see what is the kinetic energy here? Well, then that potentialenergy would matter. Anyway, so I just wanted to dothis review of potential energy because now it'll makethe jump to electrical potential energy all thateasier, because you'll actually see it's prettymuch the same thing. It's just the source of thefield and the source of the potential is somethingdifferent. So electrical potential energy,just actually we know that gravitational fields arenot constant, we can assume they're constant maybe near thesurface of the Earth and all that, but we also know thatelectrical fields aren't constant, and actually theyhave very similar formulas. But just for the simplicity ofexplaining it, let's assume a constant electric field.

Electrical Potential Vs Potential Difference

And if you don't believe me thatone can be constructed, you should watch my videos thatinvolve a reasonable bit of calculus that show that auniform electric field can be generated by an infiniteuniformly charged plane. Let's say this is the side viewof an infinite uniformly charged plane and let'ssay that this is positively charged. Of course, you can never geta proper side view of an infinite plane, because youcan never kind of cut it, because it's infinite in everydirection, but let's say that this one is and thisis the side view. So first of all, let's thinkabout its electric field. It's electric field is going topoint upward, and how do we know it points upward? Because the electric field isessentially what is- and this is just a convention.

What would a positive chargedo in the field? Well, if this plate is positive,a positive charge, we're going to want toget away from it. So we know the electric fieldpoints upward and we know that it's constant, that if thesewere field vectors, that they're going to be the samesize, no matter how far away we get from the sourceof the field. And I'm just going to picka number for the strength of the field. We actually proved in thosefancy videos that I made on the uniform electric field of aninfinite, uniformly charged plane that we actually provedhow you could calculate it. But let's just say that thiselectric field is equal to 5 newtons per coulomb. That's actually quite strong,but it makes the math easy.

So my question to you is howmuch work does it take to take a positive point charge- letme pick a different color. Let's say this is thestarting position. It's a positive 2 coulombs. Once again, that's a massivepoint charge, but we want easy numbers.

How much work does it take it tomove that 2-coulomb charge 3 meters within this field? How much work? So we're going to start hereand we're going to move it down towards the plate 3meters, and it's ending position is going to beright here, right? That's when it's done.

How much work does that take? Well, what is the force ofthe field right here? What is the force exerted onthis 2-coulomb charge?

Well, electric field is justforce per charge, right? So if you want to know the forceof the field at that point- let me draw thatin a different color. The force of the field acting onit, so let's say the field force, or the force of thefield, actually, is going to be equal to 5 newtons percoulomb times 2 coulombs, which is equal to 10 newtons. We know it's going to be upward,because this is a positive charge, and this is apositively charged infinite plate, so we know this is anupward force of 10 newtons.

So in order to get this charge,to pull it down or to push it down here, weessentially have to exert a force of 10 newtonsdownwards, right? Exert a force of 10 newtons inthe direction of the movement. And, of course, just like we didwith gravity, we have to maybe do a little bit more thanthat just to accelerate it a little bit just so you havesome net downward force, but once you do, you just haveto completely balance the upward force. So just for our purposes, youhave a 10-newton force downward and you apply thatforce for a distance of 3 meters, the work that you put totake this 2-coulomb charge from here to here, the workis going to be equal to 10 newtons- that's the force-times 3 meters. So the work is going to equal30 newton-meters, which is equal to 30 joules. A joule is just anewton-meter. And so we can now say since ittook us 30 joules of energy to move this charge from here tohere, that within this uniform electric field, the potentialenergy of the charge here is relative to the charge here.

You always have to pick a pointrelative to where the potential is, so the electricalpotential energy here relative to here and thisis electrical potential energy, and you could say P2relative to P1- I'm using my made-up notation, but that givesyou a sense of what it is- is equal to 30 joules. And how could that help us? Well, if we also knew the mass-let's say that this charge had some mass.

Electric Potential Vs Electric Potential Energy Examples

We would know that if we let goof this object, by the time it got here, that 30 jouleswould be- essentially assuming that none of it gottransmitted to heat or resistance or whatever- we knowthat all of it would be kinetic energy at this point. So actually, we couldwork it out. Let's say that this does havea mass of 1 kilogram and we were to just let goof it, right? We used some force to bring itdown here, and then we let go. So we know that the electricfield is going to accelerate it upwards, right? It's going to exert an upwardforce of 5 newtons per coulomb, and the thing's goingto keep COUGHS- excuse me- keep acceleratinguntil it gets to this point, right? What's its velocity goingto be at that point?

Well, all of this electricalpotential energy is going to be converted to kineticenergy. So essentially, we have 30joules is going to be equal to 1/2 mv squared, right? We know the mass, I said, is 1,so we get 60 is equal to v squared, so the velocity is thesquare root of 60, so it's 7 point something, something,something meters per second.

So if I just pull that chargedown, and it has a mass of 1 kilogram, and I let go, it'sjust going to accelerate and be going pretty fast onceit gets to this point. Anyway, I'm 12 minutes into thisvideo, so I will continue in the next, but hopefully, thatgives you a sense of what electrical potential energyis, and really, it's no different than gravitationalpotential energy. It's just the source of thefield is different.

See you soon.

Electric Potential and Electric Potential Energy with ExamplesElectric Potential and Electric Potential EnergyWe learned that in work power energy chapter, objects have potential energy because of their positions. In this case charge in an electric field has also potential energy because of its positions. Since there is a force on the charge and it does work against to this force we can say that it must have energy for doing work. In other words, we can say that Energy required increasing the distance between two charges to infinity or vice verse. Electric potential energy is a scalar quantity and Joule is the unit of it. We use following formula to find the magnitude of EP;Be careful!. In this formula if the charges have opposite sign then, Ep becomes negative, if they are same type of charge then, Ep becomes positive.

If Ep is positive then, electric potential energy is inversely proportional to the distance d. If Ep is negative then, electric potential energy is directly proportional to the distance d.In Figure 1 and Figure 2, charges repel each other, thus external forces does work for decreasing the distance between them. On the contrary, in Figure3, charges attract each other, distance between them is decreased by electric forces, and there is no need for other external forces.Example: System given below is composed of the charges, 10q, 8q and -5q. Fin the total electric potential energy of the system.Electric PotentialElectric potential is the electric potential energy per unit charge. It is known as voltage in general, represented by V and has unit volt (joule/C).1C charge is brought to the point A from infinity.

Work done here is called potential of q at A. Electric potential is found by the given formula;V=k.q/dV is a scalar quantity. If q is negative then V becomes negative, or if q is positive then V becomes positive.Surfaces having equal potentials are called equipotential surfaces.Potential of a Charged SpherePotential at surface is equal to the potential inside the sphere. Since there is no force acting inside the sphere, work is not done to bring the charge from surface to the inside of the sphere.

As the distance from the surface of the sphere increase, potential decreases. Picture given below shows the change in the potential of the sphere inside, surface and outside.

As you can see, potential is constant inside and surface of the sphere; however, it decreases with the increasing distance outside it.Potential Difference between Two PointsWork done against to the electric field to move unit charge from one point to another is called potential difference between these two points. This difference is found by differences of potential of last point from initial point. If we take the point charge from A to B, then potential difference is found by the formula;Example: Find the potential difference between points A and B, V AB in terms of kq/r?Example: If the total electric field produced by q and q' is like in the picture given below, find the electric potential of the A.