Two small plastic spheres are given positive electric charges. When they are 15.0 cm apart, the repulsive force between them has magnitude 0.220 N. What is the charge on each sphere (a) if the two charges are equal and

Video transcript

Welcome back everybody. We are taking a look at two glass spheres here that we are going to rub with silk in order to give them both an equal positive charge. Since we are told that they're going to have equal positive charges. I'm just going to assign their magnitude of charge to both Q. Now we are told that at a distance of 22 cm from each other or .22 m, there is a repulsive force of 0. Apologies. Newtons. And we are tasked with finding what is the magnitude of charge for each glass sphere. What we're going to do is we are going to use cool. Um Law to find this magnitude of charge law states that the force felt is equal to a constant times the charge of the first fear times the charge of the second sphere all over R squared. Now, since they both have the same magnitude of charge, this just simplifies down to K. Q squared over R squared. But we do need to isolate this Q term right here. So what I'm gonna do is I'm going to multiply both sides of our equation by R squared over K. Here are squared over A. You'll see that these terms will cancel out and we are left with that Q squared is equal to F. R squared over K. We finally then isolate Q. We are going to take the square root of both sides and we get our formula for Q being the square root of F. R squared over A. So now let's go ahead and plug in all of our values. To find the magnitude of charge. We get that Q equal to the square root of our force 0.32 newtons times the distance away from each other, which is 0.22 m squared, all over columns constant, which is nine times 19th. When you plug this into your calculator, we get a magnitude of charge of 1.31 times 10 to the negative six columns, which corresponds to our answer choice of the Thank you all so much for watching. Hope this video helped. We will see you all in the next one.