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# Coulomb's Law

NGSS.HS:
HS‑PS2‑4
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HS‑PS2‑5
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HS‑PS2.B.1
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HS‑PS2.B
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HS‑PS2

## Video transcript

so we've already started to familiarize ourselves with the notion of charge we've seen that if two things have the same charge so they're either both positive or they are both negative then they are going to repel each other so in either of these cases these things are going to repel each other but if they have different charges they're going to attract each other so if I have a positive and I have a negative they're going to attract each other this charges this property of matter that we've started to observe we've started observe of how these different charges this framework that we've created how these things start to interact with each other so these things are going to these two things are going to attract each other but the question is well what what causes so how can we predict how strong the force of attraction or repulsion is going to be between charged particles and this was a question people have noticed I guess what you could call electrostatics for for a large swath of recorded human history but it wasn't until the 1600s and especially the 1700s that people started to seriously view this as something that they could manipulate and even start to predict in a kind of serious mathematical scientific way and it wasn't until 1785 and there were many that came before Coulomb but it said in 1785 Coulomb formally published what is known as Coulomb's law and the purpose of Coulomb's law Coulomb's law is to predict what is going to be the force of the electrostatic force of attraction or repulsion between two forces and so in Coulomb's law what it states is is if I have two charges so let me so let's say this charge right over here a number make it a white because it could be positive or negative but I'll just make a q1 it has some charge and then I have in coulombs and then another charge q2 right over here another charge q2 and then I have the distance between them being R so the distance between these two charges our goal is going to be R Coulomb's law states that the force the magnitude of the force so it could be a repulsion a repulsive force or it could be an attractive force which would tell us the direction of the force between the the two charges but the magnitude of the force which I'll just write it as F the magnitude of the electrostatic force I'll write the sub e here the subscript T for electrostatic chrome stated well this is going to be and he tested this he didn't just kind of guess this people actually were we're assuming that had something to do with the sat the the products of the the magnitude of the charges and that as the part as the particles got further and further away the electrostatic force dissipated but he was able to actually measure this and feel really good about stating this law he said that the magnitude of the electrostatic force is proportional is proportional to the product of the magnitudes of the charges so I could write this as q1 times q2 and I could take the absolute value of each which is the same thing as just taking the absolute value of the product and here's what I'm doing the absolute value of the product well if they're different charges this will be a negative number but we just want the overall magnitude of the force so we could take its proportional to the absolute value of the product of the charges and it's inversely proportional to not just the distance between them not just to R but to the square of the distance the square of the distance between them and what's pretty neat about this is how close it mirrors Newton's law of gravitation Newton's law of gravitation we know that the force due to gravity between two masses remember mass is just another property of matter that we sometimes feel a little bit more tangible because it feels like you know we can kind of see weight and volume but that's not quite the same or we can we can we feel like we can feel or internalize things like weight and volume which are related to mass but in some ways it is just another property another property especially as you get into more kind of fancy physics our everyday notion of even mass it starts to starts to become a lot more interesting but Newton's law of gravitation says look the magnitude of the force of gravity between two masses is going to be proportional to by the Newton's by the gravitational constant proportional to the product of the two masses actually let me do in those same colors so you can see the colors so you can see the relationship it's it's going to be proportional to the product of the two masses 1m2 it's going to be inversely proportional to the square of the distance the square of the distance between two masses now these proportional personality constants are very different gravitational force we kind of perceive this as acting being stronger and so it's a weaker force in close range but we kind of imagine it as kind of what dictates what happens in the in amongst the stars and the planets and moons while the electrostatic force at close range is a much stronger force it can overcome the gravitational force it very easily but it's what we can consider happening at either an atomic level or or kind of at a scale that we are we are more familiar to operating at but needless to say it's very interesting to see how how this this parallel between these two things it's kind of this this you know these patterns in the universe but what that's it let's actually apply let's actually apply Coulomb's law just to make sure that we feel comfortable with the mathematics so let's say that I have a charge here let's say that I have a charge here and it has a positive charge oh I don't know let's say it is positive five times ten to the negative three coulombs so that's that's this one right over here that's its charge and let's say I have this other charge right over here and it has a negative charge and it is going to be it is going to be let's say it's negative 1 negative 1 times 10 to the negative 1 coulombs and let's say that the distance between the two let's say that this distance right here is 0.5 meters so given that let's figure out what the what the electrostatic force between these two are going to be and we can already predict that it's going to be an attractive force because they have different signs and that was actually part of Coulomb's law this is the magnitude of the force if these have different signs it's attractive if they have the same sign then they are going to repel each other I know what you're saying well in order to actually calculate it I need to know what K is what is this electrostatic constant what is this electrostatic constant going to actually be and so you can measure that with a lot of precision and we have kind of modern numbers on it but the electrostatic constant especially for the sake of this problem I mean if we were to get really precise its eight point nine eight seven five five one we could keep going on and on times 10 to the ninth but for the sake of our our our our little example here where we really only have one significant digit for each of these let's just get an approximation it'll make the math a little bit easier I won't have to get a calculator out let's just say it's approximately 9 times 10 to the 9th 9 times 10 to the ninth 9 times actually make my make sure it says approximately because I am approximating here 9 times 10 to the 9th and what are the unit's going to be well I'm in the numerator here when I multiply coulombs times coulombs going to get coulombs squared this right over here is going to give me that's going to give me coulombs squared and this down over here is going to give me meters squared this is going to give me a meter squared and I what I want is to get rid of the coulombs in the meters and end up with just Newtons and so the unit's here are actually their units here are Newtons Newton and then meter squared and that cancels out with the meter squared in the denominator Newton meter squared over coulombs squared over over Coulomb squared let me do that in white over over coulombs squared so these meter squared will cancel those those coulombs squared and the denominator is example and encourage you to pause the video and apply this information to Coulomb's law and figure out what the electrostatic force between these two particles is going to be so I'm assuming you've had your go at it so it is going to be and this is really just applying the formula it's going to be 9 times 10 to the 9th 9 times 10 to the 9th and I'll write the unit's here Newton's meter squared over Coulomb squared and then Q 1 times Q 2 so this is going to be let's see this is going to be actually let me just write it all out for this first this first time so it's going to be times 5 times 10 negative three coulombs x times negative 1 times 10 to the negative 1 coulombs and we're going to take the absolute value of this so that negative is going to go away all of that over all of that over we're in kind of the homestretch right over here 0.5 meter squared 0.5 meters squared and so let's just do a little bit of the math here so first of all let's look at the units so we have coulombs squared here then we have coulombs times coulombs there's that's coulombs squared divided by coulombs squared that's going to cancel with that and that you have meter squared here and actually let me just write it out so the numerator in the numerator we are going to have so if we just say 9 times 5 times when we take the absolute values just going to be 1 so 9 times 5 is going to be 9 times 5 times negative 1 5 times negative 1 is negative 5 but the absolute value there so it's just going to be 5 times 9 so it's going to be 45 times 10 to the 9 minus 3 minus 1 so 6 5 so that's going to be 10 to the 5th 10 to the 5th the coulombs already cancelled out and we're going to have Newton meter squared over over 0.25 meter squared these cancel and so we are left with well if you divide by 0.25 that's the same thing as dividing by 1/4 what's the same thing as multiplying by 4 so if you multiply this times 4 45 times 4 is 160 plus 20 is equal to 180 times 10 to the 5th Newtons and if we wanted to write it in scientific notation well we could divide this by we could divide this by 100 and then multiply this by 100 and so you could write this as one point eight zero times one point and I don't want to make it look like a more significant digits than I really have one point eight times 10 to the seventh times 10 to the seventh news I just divided this 500 and I multiplied this by 100 and we're done this is this is the magnitude of the electrostatic force between between those two particles and it looks like it's it's fairly significant and this is actually a good amount and that's because it's actually good amount of charge a lot of charge especially at this at this distance right over here and the next thing we have to think about well if we you know if we want not just so the magnitude we also want the direction well they're different charges so this is going to be an attractive force this is going to be an attractive force on each of them acting at one point eight times ten to the seventh Newton's if they were the same charge it would be a repulsive force or they would repel each other with this force but we're done