Point charges q_1 = +2.00 μC and q_2 = -2.00 μC are placed at adjacent corners of a square for which the length of each side is 3.00 cm. Point a is at the center of the square, and point bis at the empty corner closest to q_2. Take the electric potential to be zero at a distance far from both charges. (a) What is the electric potential at point a due to q_1 and q_2?

Video transcript

Hey everyone in this problem, we have a rectangle that is 0.4 m by 0.5 m. Can we have particles with charges plus four nano columns and negative four columns. Sorry, negative for Nanako bombs that are placed on two adjacent corners separated by the shorter length and we are asked to find the electric potential at the center of the rectangle. Okay, be due to those two charges were told that we can take the potential to be zero at infinity. Let's just draw out our rectangle here. So we have a rectangle And the length of the longer side is 0.05 m. The length of the shorter side, 0.04 m. Can we place two charges on the adjacent corner separated by the shorter length. So the particles we're going to be placed on the corner like this. The first has a charge of four Nano columns and the second has a charge of negative four nan equivalents. And we want to find the electric potential at the center of this rectangle. So this is our point of interest. Now let's think about this. This point at the center of a rectangle, it's going to be the same distance from this negative charge as it is from this positive church. So we call this distance r this is also our Alright, so we have two charges, they have the same magnitude four with opposite signs, one positive one negative and they're the same distance from a point. That means that at that point the potential will be zero. Okay, those two charges kind of cancel each other out. And we're gonna have a zero potential at that point. Alright, so that's thinking about it conceptually. Let's go ahead and write down the math. You can see how that works out when we have these same magnitude opposite signs, charges that are the same distance from our point of interest. Alright, first thing let's recall that the electric potential V can be written as 1/4 pi epsilon not times is some of I from one in this case we have two charges so from 1 to 2 of the charge Q divided by the distance. Ri Okay, alright. Now we know the charges but we don't know this distance. Okay, so let's try to work this out. Now we can draw a triangle like this where we have our charge in the corner, we have our point of interest down on the right hand side. And this distance R is going to be the hypotenuse of this triangle. Now we know this small length is going to be half Of the side of the rectangle which is 0.04 m. So this smaller side is 0.02 m. And similarly this longer side it's going to be half of our length, 0.05 m. And so we're going to have 0.025 m. Okay, so pythagorean theorem we're going to have R squared is equal to 0.2 m squared plus 0.25 m squared. We get r squared is equal to 0.00 to 5 m squared. Taking the square root when we take the square root, we're going to get a positive and negative value for our let's just go ahead and write down the positive because we know we're talking about a distance. So we want that positive route. We get 0.32 m. Okay, So we have our distance are now and remember the distance from the first charge and the distance from the second charge to our point is the same. So we found one R. And that's gonna be the distance for both of them. Okay, so going back to our equation, we're going to get this 1/4 pi epsilon naught is 9.0 times 10 to the nine unit. Newton meter squared per column squared. Okay. You can look that up in a table in your textbook or that your professor provided we get the first charge, which is four and let's put this into Cool. Um Okay. The nine times 10 to the nine has a per Cool. Um so we want the units to be the same. So let's stick with columns. So we get four times 10 to the negative nine columns Divided by R 0.032 m. And then we're gonna add the same for the second church negative four times 10 to the negative nine cool homes Divided by R., which is the same. 0.032 m. Okay. And so what you see is that this big term in brackets? Four times 10 to the negative nine columns divided by 0.32 m minus four times 10 to the negative nine columns divided by 0.32, sorry, meters. This is going to be equal to zero. And so the whole thing the is going to be equal to zero volts, just like we predicted when we talked about it conceptually. Okay. And so the answer to this one is going to be D the electric potential at the center of that rectangle is zero volts. Thanks everyone for watching. I hope this video helped see you in the next one.