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# Electric potential energy

## Video transcript

let's review a little bit of what we had learned many many videos ago about gravitational potential energy and then see if we can draw the analogy which is actually very strong to electrical potential energy so what did we know about gravitational potential energy if we said this was the surface of the earth and we don't have to be on earth but it makes visualization easy we could be anywhere that has gravity and the potential energy would be due to the gravitational field of that particular mass but let's say where this is the surface of the earth we learned that if we have some mass m up here some mass m and that the gravitational field at this area or at least the gravitational acceleration is G or 9.8 meters per second squared and it is H we could say I guess meters but you know we could use any unit let's save is H meters above the ground that the gravitational potential energy of this object at that point is equal to the mass times the acceleration of gravity times the height or you could view it as the force of gravity the magnitude of the force of gravity it's a vector but we could say the magnitude of the vector times height and so what is potential energy well we know that if something has potential energy and if nothing stopping and we just let go that energy well we put with gravitational potential energy the object will start accelerating downwards and a lot of that potential energy and eventually all of it will be converted to kinetic energy so potential energy is energy that is being stored by an object situation or not or a kind of this notional energy that an object has by virtue of where it is so in order for something to have this notional energy some energy must have been put into it and as we learned with gravitational potential energy you could view gravitational potential energy as the work necessary to move an object to that position now if we're talking about you know work to move something into that position or whatever we always have to think about well move it from where well when we talk about gravitational potential energy we're talking about moving it from the surface of the earth right and so how much work is required to move this that same mass let's say it was here at first to move it from a height of zero to a height of H well the whole time the earth or the force of gravity is going to be F sub G right so essentially if I'm pulling it or pushing it upwards I'm going to have to have and let's say at a constant velocity I'm going to have to have an equal and opposite force to its to its weight to pull it up otherwise it would accelerate downwards I'd have to do a little bit more just to get it moving to accelerate it however much but then once I get it just accelerating essentially I would have to apply an upward force which is equivalent to the downward force of gravity and I would do it for a distance of H right what is work work is just Force Times distance Force Times distance and it's four it has to be forced in the direction of the distance so what's the work necessary to get this mass up here well the work the work is equal to the force of gravity times height so it's equal to the gravitational potential energy now this is an interesting thing notice we picked the reference point as the surface of the earth but we could have picked any arbitrary reference point we could have said well from I don't know 10 meters below the surface of the earth which could have been down here or we could have actually said you know some from a platform that's 5 meters above the earth so it actually turns out when you think of it that way that potential energy of any form but especially gravitational potential energy and we'll see electrical potential energy it's always in reference to some other point so it's really a change in potential energy that matters and I know when we study the potential energy it seemed like there was kind of an absolute potential energy but that's because we always assume that the potential energy of something is zero at the surface of the earth and that we want the know the potential energy relative to the surface of the earth so it would be kind of you know how much work does it take to take something from the surface of the earth to that height but really we should be saying well the potential energy of gravity like this should this statement shouldn't be you know this is just the absolute potential energy of gravity we should say this is the potential energy of gravity relative to the surface of the earth is equal to the work necessary to move something to move that same mass from the surface of the earth to its current position we could have said you know we could have defined some other term that is you know not not really used but we could have said you know potential energy of gravity relative to minus five meters below the surface of the earth and that would be the work necessary to move something from minus five meters to its current to its current height and of course that might matter what if you know we cut up a hole and we wanted to see what what is the kinetic energy here well then that potential energy would matter anyway so I just wanted to do this review of potential energy because I want because now it'll make the the jump to electrical potential energy all that easier because you'll actually see it's it's pretty much the same thing it's just the source of the field and the source of the potential is something different so electrical potential energy just just when you know actually we know that gravitational fields are not constant we can assume they're constant maybe near the surface of the earth and all that but we also know that electrical fields aren't constant actually they I have very similar formulas but just for simplicity of explaining it let's assume a constant electric field and if you don't believe me that one can be constructed you should watch my my videos that involve a reasonably bit of calculus that show that a uniform electric field can be generated by an infinitely by an infinite uniformly charged plane and let's say this is the side view of an infinitely uniformly sorry an infinite uniformly charged plane and let's say that this is its positively charged of course you can never get a proper side view of an infinite plane because you can never kind of cut it because it's infinite in every direction but let's say so that this one is and this is the side view let's so first of all let's think about its electric field well its electric field is going to point upward how do we know it points upward because the electric field is essentially what is and this is just a convention what would a positive charge do in in the field well if this plate is positive a positive charge is we're going to want to get away from it so we know the electric field points upward and we know that it's constant that you know if these were field vectors that they're going to be the same size no matter how far away we get from the field let's form the source of the field and I just I'm just going to pick a number for the strength of the field we actually proved in in in those fancy videos that I made a on the uniform electric field of an infinite uniformly charge playing that we actually proved how you could calculate it but let's just say that this electric field is equal to I don't know 5 Newton's per Coulomb that's actually quite strong but it makes the math easy so my question to you is how much work does it take to take a positive point charge let me pick a different color let's say so let's say I have so let's say this is a starting position it's a positive I don't know two coulombs once again that's a massive point charge but you know where we want easy numbers how much work does it take it to to move that to cold Coulomb charge I don't know three meters within this field how much work so we're going to start here and we're going to move it down towards the plate three meters and in its ending position is going to be right here right that's where it's when it's done how much work does that take well what is goal what is the force of the field outlet right here what is the what is the force exerted on this two Coulomb charge well electric field is just force per charge right so if you want to know the force of the field at that point let me do that draw that in a different color the force of the field acting on it so let's say the field force or the force of the field actually is going to be equal to five Newton's per Coulomb times two coulombs which is equal to ten Newtons and we know it's going to be upward because this is a positive charge and this is a positively charged infinite plate so we know this upward force of 10 Newtons so in order to get this charge to pull it down or to push it down here we essentially have to exert a force of 10 Newton's downwards right exert a force of 10 Newtons in the direction of the movement and of course just like we did with gravity you have to maybe do a little bit more than that just to accelerate a little bit just so you have some net downward force but once you do you just have to completely balance the upward force so just for our purposes you have a 10 Newton force downward and you apply that force for a distance of 3 meters the work that you put to take this 2 Coulomb charge from here to here is going to be equal to the work is going to be equal to 10 Newtons that's the force times 3 meters so the work is going to equal 30 Newton meters which is equal to 30 joules and a joule is just a Newton meter and so we can now say since it took us 30 joules of energy to move this charge from here to here but within this uniform electric field the potential energy of the charge here the potential energy of the charge here relative to the charge being here you always have to pick a point relative to where the potential is so the the electrical potential energy here relative to here potential energy and this is electrical enter potential energy and you could say you know P 2 relative to P 1 I'm using my made-up notation but that gives you 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 you know this charge had some mass we would know that if we let go of this object by the time it got here that 30 joules would be essentially assuming it you know not we've got transmitted to heat or resistance or whatever we know that all of it would be kinetic energy at this point so I actually you know we could work it out let's say that this does have a mass of I don't know one kilogram let's say it has a mass of of one kilogram and we were to just let go of it right we were you know we we use some force to bring it down here and then we let go so we know that the electric field is going to accelerate it upwards right it's going to exert a force of upward force of five Newton's per Coulomb and the thing is going to keep keep e excuse me keep accelerating until it gets to this point right what's its velocity going to be at that point well all of this electrical potential energy is going to be converted to kinetic energy so essentially we have 30 joules is going to be equal to one-half MV squared right we know the mass I said is one so we get 60 is equal to V squared so the velocity is the square root of 60 so it's you know seven point you know something something something meters per second so if I just pull that charge down it has a mass of one one kilogram and I let go it's just going to accelerate and be going pretty fast once against at this point anyway I'm 12 minutes into this video so I will continue in the next but hopefully that gives you a sense of what electrical potential energy is and and and really it's no different than gravitational potential energy is just the source of the field is different see you soon