Potential diff. & negative potentials

just when i thought that i understood potentials i saw weird statements like this electric potential at some point p equals negative 300 volts and my brain was like hey what does that negative sign even mean what does it mean to have negative energy well by the end of this video we will have a much deeper understanding of what electric potentials are and we'll be able to understand what negative potentials mean so just to quickly recall what does it mean to say that potential at a sum at some point is 11 joules per kilogram it just means that if i were to keep a l if a one kilogram object over here then that would have 11 joules of potential energy but i could keep 10 kilogram object over here and it would have 110 joules of potential energy it's an indicator similarly what does it mean to say that at a point the potential is 5 volts well 5 volts is just 5 joules per coulomb and so that means that if i were to keep a coulomb of charge let's say a rock which is positively charged for some reason and let's say it's one coulomb then it would have five joules of potential energy but i could keep a hundred coulomb of charge over here and then you would have 500 joules of potential energy it's an indicator of how much potential energy it would have per coulomb and if you're not familiar with this concept or new refresher we've talked more about this in our previous videos on introduction to electric potential feel free to go back and check that out but let's dig a little deeper this time remember what it what does it even mean to say that potential energy of a kilogram is 11 joules what does that number represent do you remember what does potential energy even mean well we've talked about that what this really means is that if i were to let go of this rock let's say imagine i was holding that rock and let's say i let go of that rock then we know that rock is going to fall down and as it falls down as it falls down its kinetic energy would increase and this means that by the time it reaches the ground all of that 11 joules is now converted into potential sorry kinetic energy that's what it means to have stored energy that much can be converted to kinetic and so this means when that rock comes from here to here it would have lost all that 11 joules of potential energy so do you know what we are really saying over here when we say va is equal to 11 joules per kilogram what we are really saying and this is important is that let me write this down is that if i were to call this point some other name say b then what we're really seeing over here is that potential at this point is 11 joules per kilogram more than potential at this point so let me just write that down and it'll make more sense as we talk more about this so what i'm really saying is that potential at a is 11 per kilogram more than potential at b this is what i'm really saying let me tell you why this is important now imagine instead of a ground there was a table here somewhere now when i let go of this rock it goes and hits the table and stops over there and this time by the time it reaches the table do you think it would have gained 11 joules no it would have gained much less maybe only i don't know maybe only three joules of energy now what i would do is i would define the point over here i would call this point as say i don't know maybe t and now i would say hey potential at point a is only 3 joules per kilogram compared to the potential at point t because this is now a more convenient point to define potential depending upon which reference point we use the potential at any point can change in fact there is no such thing as an absolute value of potential energy potential energy that you mentioned is always always always compared to potential energy at some other point in space and to make sense of this let me give you an example of something that you may be familiar with in maths and that is a number line if i asked you hey what's the position of this point and i don't give you anything else on the number line can you answer this question no you can only find positions relative to some other point for example you could say hey let me call this point as b and now if each one represents one centimeter and to the right it's increasing so we could now say okay one two three four five we can now say hey this point is five centimeters more than b this is how we really represent in our number lines and most often what we would say is this reference is often called the origin and we call it zero and as a result now this would become five centimeter plus zero would become five but what's important is i don't have to call that 0 maybe i could call some other point as 0 and i could call this as i don't know maybe 10 centimeters then this automatically becomes 15 centimeters so notice what the value the actual position really depends upon what you call this position all right but what's important what what doesn't change is that this will always stay five centimeters more than point b and similarly somebody else could say hey you know what no no i don't want to use this reference point i want to use this reference point and we can call this as t now with respect to this reference point what is the value of this position it's now just one centimeter more oops one centimeter more compared to t and so now if somebody likes to call this as my zero and then this would be one centimeter and so on and so forth same idea over here potentials are always with respect to some other point and the exact same thing happens in electric potential as well exactly the same thing and that's why i love gravity okay so when i say potential at some point a is 5 volts or 5 joules per coulomb what i'm really saying is that hey it's 5 volt more compared to potential at some other point some other reference point in this case i may have chosen this as my reference point so long story short potential or potential energy is always represented with respect to some other point if i call the potential here as 0 then the value of potential here is 11 if i call potential here as 0 the value of the potential over here would be 3 in this example and for gravity we most likely always like to choose the lowest point in our experiment as 0 or as our reference point but what about when it comes to charges what's our convenient reference point over here well the most convenient point we like to choose is infinity so in any scenario if the reference point is not mentioned and someone says hey potential at a point let me just write that potential at some point p is 30 volt what does it mean if i don't mention any reference it just means that it is 30 joules per coulomb and that means that the coulomb over here would have 30 joules more potential energy than it would have at infinity all right so we always choose infinity as our reference point so most of the time we like to choose this to be infinity but it doesn't have to be it's just a convenience so that let me now show you a standard way of writing this we often write this as potential at point a with respect to point b that's how we write like to write this so this is my reference point and we can call this as 5 volt directly so this is the same thing as writing it this way and you can also call this so this would be just ba minus vb so you can also write it this way this also means the same thing potential at a how much more it is compared to my reference point with respect to point b and so this means whenever you're talking about potentials you're always talking about the difference between the values of potentials between two points and that's why we can also call this potential difference so whether you call it potential at a point or potential difference between two points it's really really the same thing and so now we can update our definition of potential we could now say hey what does it mean to def what is the definition of potential at point p with respect to some reference point q we can now say hey it is basically potential energy that a charge would have at point p compared to at point q per coulomb per per charge okay and this would be potential energy at point p minus the potential energy at point q you're basically uh calculating how much more potential energy it has compared to point q divided by be divided by the charge q and for charges most often this second point is taken to be infinity so the second point is most often infinity so i think we now have everything to answer our earlier question what would it mean so let me just okay there's no space over here let me go down what would it mean if someone said hey potential at some random point p electric potential was minus 300 volt what is the meaning of this statement can you pause and extra and explain this to someone now all right i would first say it is negative 300 volt is joules per coulomb and what this now means is that potential at a point if i kept a coulomb of charge at this point it would have 300 joules of energy less less compared to how much it would have at infinity because our reference point is infinity so now positives and negatives make a lot of sense because we're always comparing if it's a positive potential it's saying more potential energy compared to how much there will be at infinity if it's a negative potential we are saying hey less potential energy compared to our infinity just like in our number line some positions can have negative values meaning less value than our reference point and some positions can have more values compared to a reference point and finally you can be even more curious and ask hey but how do we calculate the potential energy values in the first place it's got something to do with work and we'll explore all of that fun stuff in the future video