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Khan Academy Presents: Difference between electrical potential (voltage) and electrical potential energy
Tags:Learn about Voltage,educational videos,khan academy,khanacademy,math lessons,math tutorials,salman khan,voltage,volts
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Learn about Voltage
Before we move on I want to clarify something that I’ve innevertly done, I think I was not exact with some of the terminology I used so I want to make, I want to highlight the difference between two things that I’ve used almost interchangeably up to this point but now that we are about to embark our learning what voltage is, I think it’s important that I highlight the difference because initially this is can be very confusing. I remember when I first learn this I found—I often mixed up these words and didn’t quite understand why there was difference.
So the two words are electrical or sometimes we’ll say electric instead of electrical, so electric potential energy and electric potential. I think even in the last video I used to, these almost interchangeably and I shouldn’t have, I really should have always used electrical or electric potential energy and what’s the difference?
Electrical potential energy is associated with a charge. It is associated with the particle that has some charge only that particle can have energy. Electrical potential or electric potential, this is associated with the position. So for example, if I have a charge and I know that in some point with the given electric potential I can figure out the electric potential energy at that point by just multiplying actually this value by the charge.
Let me give you some examples. Let’s say that I have an infinite uniformly charge plate so we don’t to do calculus, we can have a uniform electric field. Let’s say that this is the plate, let’ see I’ll make it vertical just we get a little bit of change of pace and let’s say it’s positively charge, positively charge plate. And let’s say that the electric field is constant, it’s constant and no matter what point we pick, these field lines should all of these field vectors should all be the same length because there electric field has not change and magnitude has pushing out because we assume when we draw a field lines, we are using charge with the positive charge that’s pushing upward.
So, if I wanted to ask you, let’s say I have a coulomb charge. Actually let me make it two coulombs just to hit a point home. Say I have a two coulomb charge right here. Two coulombs and it’s positive, positive two coulomb charge and it starts of I don’t know, let’s say it starts off at 3-meters away and I want to bring it in 2-meters, I’m going to bring it in 2-meters so its 1-meter away.
So, what is the electric or electrical potential energy difference between the particle at this point and at this point? Well, the electrical potential energy difference is the amount of work—as we’ve learn in the previous two videos is the amount of work we need to apply to this particle to take it from here to here. So how much work do we have to apply we have to apply a force, we have to apply a force that directly that exactly, let’s assume that maybe this are already moving at a constant velocity we have to start with the slightly higher force to get it moving. But we have to apply force as exactly opposite the electric the force provided by this by Coulomb’s Law, the electro static force.
And so what is that force we are going to have applied? Well, actually we have to know what the electric field is which I have not told you yet, I just realize as you can tell as we not. So let’s say all of these electric field lines, they are 3-Newton’s per coulomb, so at any point what is the force being exerted from this field unto this particle, well the force from the electro static force on this particle is equal to the electric field times the charge, times the charge which is equal to—I just define the electric field as being 3 Newton’s per coulomb, sorry, three units per coulomb times two coulombs it equals 6 Newton’s.
So at any point the electric field is pushing this way, 6 Newton’s so in order to push the particle this way I have to completely offset that and actually I get moving in this way and I’ll keep saying that, I just want to make that point, that point home. So I have to apply the force of six Newton’s in the left ward direction and I have to apply it for 2 -meters to get the point here. So the total work is equal to 6 Newton’s times 2-meters which is equal to 12-meters or 12 joules.
So, we could say that the electrical potential energy, energy and energy is always joules, so electrical potential energy difference between this point and this point is 12 joules or in other way to say it is, this, and which one has a higher potential well this one does because at this point we’re closer to the thing that’s trying to repeal it, so if we were just let go it would start accelerating in this direction and a lot of that energy will be convert to kinetic energy by when we get to this point.
So we could also say that the electric potential energy at this point right here is 12 joules higher than the electric potential energy at this point. Now that’s potential energy. What is electric potential? Well, electric potential tells us essentially how much work is necessary per unit of charge. This was electric potential energy which is how much total work is needed to move it from to here.
Electric potential says per unit charge, how much work is it does it take to move any charge per unit charge from her to here. Well in our example we just did the total work to move from her to here was 12 joules but how much work did it take to move from there to there per charge. We’ll work per charge is equal to 12 joules per what, what was the charge that we move? Well, its two coulombs well it equals 6 joules per coulomb. That is the electric potential difference between this point and this point so it was a distinction.
Electric potential energy was associated with the particle how much more energy did the particle have here than here. When we say electric potential because we essentially divide by the size of the particle, it essentially it’s independent of the size of the particle it actually just depends on our position. So electric potential were just saying how much potential irrespective of the charge we are using, does this position have relative to this position.
And this electric potential that’s just another way of saying voltage. Voltage and the unit fro volt for voltage is volt. So 6 joules per coulomb that’s the same thing as 6 Volts and so if we think of the, if we think of the analogy to gravitation we said gravitational potential energy was MGH this was force this was distance.
Electric potential is essentially the amount of gravitation if we extend the analogy the amount of gravitational potential energy per mass. So is we want to know, if we want to quick know way of knowing what the potential, the gravitational potential is at any point without having to care about the mass, will we divide by the mass and would be the acceleration of gravity times height. Ignore that if it confused you.
So, what is useful about voltage, it tells us regardless of how small or big or actually you’re positive or negative a charge is, what the difference and potential energy would be if it were it two different points. So electric potential, were comparing points and space. Electric potential energy, were comparing charges at point in space.
Hopefully I didn’t confuse you. In the next video will actually do a couple of problems where we figure out the electric potential difference or the voltage difference between two points in space as suppose to a charge at two different points in space. I will see you in the video.