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if you haven't done so yet please pause the video and attempt to solve the question on your own before listening on we know that the work required to set up the arrangement of charges shown in the picture is equal to the change in electrical potential energy which we can write as the final electrical potential energy minus the initial electrical potential energy because the charges initially are infinitely far apart that means that their initial electrical potential energy is actually zero joules so we can eliminate this term from the equation thus in order to calculate the work all we need to do is figure out the final electrical potential energy of this arrangement we know that the electrical potential energy between two point charges is given by this formula but of course this arrangement shows four point charges so it might not be obvious how to work with this formula what we can do is imagine that initially none of these charges are present so we can empty the space here now what we can do is bring in the first charge maybe we can bring in the one that was in the upper left-hand corner so we'll just draw a charge there the work required to move that charge in is actually zero because there were no other charges present we then move in the next charge so maybe we can bring in this one now notice that we're going to have to calculate the electrical potential energy between these two charges so perhaps we can call that u 1 we next bring in the third charge and we would have to calculate the electrical potential energy between those two charges which we could call you two and those two charges which we could call u 3 finally we bring in the fourth charge maybe I'll change colors here so we would have to calculate the electrical potential energy between those two charges those two charges and finally these two charges so actually we have to use this expression for the electrical potential energy 6 times we can remind ourselves that here we had a positive charge this was negative this was positive and this was negative so for u 1 we can plug into the formula we'll have a positive charge and a negative charge and when we multiply that positive times that negative we'll overall come out to be a negative electrical potential energy here's our expression for u1 notice that the distance between the charges was symbolized by a as that was the distance represented in the diagram for you two we're going to have to find this diagonal distance right here and because this is a square we should know that the diagonal distance would be a radical two so let's set up our expression for u two we're multiplying a positive by a positive so it should come out positive overall we're going to continue in this manner we're going to set up expressions for u three through u six when you do so just be mindful of whether it's a positive charge and a negative charge or whether it's a negative and a negative etc also be mindful of your distances so we'll go ahead and set up the rest of the expressions here so there they all are to get the overall electrical potential energy we simply need to sum these together remember that energy is a scalar quantity so we don't have to worry about components all we need to do is add all six of these together algebraically it's a bit of a lengthy equation but maybe what we could do if we look carefully is factor out a common factor now each term has a KQ squared as well as an a so let's factor that out we could then combine the negative ones as well as the one over root two s and at this point all we need to do is plug in the known values we know that K is a constant q is given to us in Pico Coulomb so we'll have to multiply it by 10 to the minus 12 to convert it into coulombs and then a is given to us as well we'll have to multiply that by 10 to the -2 to convert to meters and when you plug all that into your calculator you should get a value of approximately negative 1.9 2 times 10 to the negative 13 joules so that would be the work required to set up that arrangement of charges thanks for taking the time to watch the video if you like to please subscribe to the channel also you are welcome to send in your own question to the email address on the screen and I'll do my best to post a solution on YouTube