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## Video transcript

before we move on I want to clarify something that I've inadvertently done I think I was not exact with some of the terminology I use so I want to make a 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 on learning what voltage is I think it's important that I highlight the difference because initially this can be very confusing I remember when I first learned this I found I often mixed up these words and and didn't quite understand why you know there was a difference so the two words are electrical or sometimes you'll see electric instead of electrical so electric potential energy and electric potential I think even in the last video I used 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 with a a charge it's associated with a you know with out with a particle that has some charge only only that particle can have energy electrical potential or electric potential this is associated with a position so for example if I have a charge and I know that if it's at some point with a 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 infinite uniformly charged plate so that we don't have to do calculus we can have a uniform electric field let's say that this is the plate let's say I'll make it vertical just so we get a little bit of change of pace and let's say it's positively charged positively charged plate and let's say that the electric field you know it's constant right it's constant no matter what point we pick these should these field lines should all these field vectors should all be the same length because the electric field does not change in magnitude it's pushing out because we assume when we look at when we draw a few lines that we using a test charge with a positive charge that's pushing outward so if I wanted to ask you let's say I have a a 1 Coulomb charge actually make it to glooms just to hit a point home say I have a 2 Coulomb charge right here 2 coulombs and it's positive positive two coulombs arge and it starts off I don't know let's say it starts off at 3 meters away and I want to bring it in 2 meters I want to bring it in 2 meters so it's 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 we now as we've learned 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 well we have to apply a force we have to apply a force that directly that exactly lets you know we assume that maybe this is already moving the constant velocity or maybe we have to start with a slightly higher force just to get it moving we have to apply force it's exactly opposite the electric the the force provided by this by Coulomb's law right the electrostatic force and so what is that that force we're going to have to apply well we actually have to know what the electric field is which I have not told you yet I just realize as you can tell right so let's say all of these electric field lines I don't know let's say they are three Newton's per Coulomb so at any point what is the force being exerted from this field onto this particle well the force from the electrostatic force on this particle is equal to the electric field times the charge times the charge which is equal to I just defined the electric field as being three Newton's per Coulomb sorry 3 Newton's per Coulomb times 2 coulombs it equals 6 Newtons so at any point the electric field is pushing this way six Newton's so in order to push the particle this way after completely offset that admit and actually I've get it moving initially I'll keep saying that I just want to make that point at that point home so I have to apply a force of six Newtons in the leftward direction and have to apply it for two meters to get the point here so the total work is equal to six Newton's times two meters which is equal to twelve Newton meters or twelve joules so we could say that the electrical potential energy energy and energy is always joules the electrical potential energy difference between this point and this point is 12 joules or another way to say it is this and which one has a higher potential well this one does right because at this point we're closer to the thing that's trying to repel it so if we were to just let go it would start accelerating in this direction and have and a lot of that energy would be converted to kinetic energy by we get to this point right 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 right this was electric potential energy was just how much total work is needed to move it from here to here electric potential says per unit charge how much work is it does it take to move any charge per unit charge from here to here well in our example we just did the total work to move it from here to here with 12 joules but how much work what did it take to move it from there to there per charge will work per charge is equal to 12 joules for what what was the what was the charge that we move those two coulombs well it equals 6 joules per coulomb that is the electric potential the electric potential difference between this point and this point so it was the distinction electric potential energy was associated with a particle how much energy 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 is independent of the size of the particle it actually just depends on our position so electric potential we're just saying how much how much more potential irrespective of the charge we're 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 for volt for voltage is volts 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 the the analogy to to gravitation you know we said petrova tation potential energy was MGH right this was force this was distance right electric potential is essentially the amount of gravitation you know if we if we if we extend the analogy the amount of gravitational potential energy per mass right so if we wanted to know if we wanted a quick no way of knowing what the potential at what the potential the gravitational potential is at any point without having to care about the mass well we divide by the mass and it would be the acceleration of gravity time sign ignore that if it confused you so what is useful about voltage it sells regardless of how small or big or actually positive or negative a charge is what the difference in potential energy would be if we're at two different points so electric potential we're comparing points in space electric potential energy we're comparing we're comparing charges at points in space hopefully I didn't confuse you in the next video we'll actually do a couple problems where we figure out the electric potential difference or the voltage difference between two points in space as opposed to a charge at two different points space I will see you in the next video