(a) How much excess charge must be placed on a copper sphere 25.0 cm in diameter so that the potential of its center, rela­tive to infinity, is 3.75 kV? (b) What is the potential of the sphere's surface relative to infinity?

Video transcript

Welcome back everybody. We are making observations about a steel ball and we are told that it has a radius of 20 centimeters or 200.2 m. And we are told that the electric potential of the balls center relative to infinity is 1. Kilovolts, which is equal to 1200 volts. And we are tasked with finding what is the value of the charge on the ball as well as the potential at the surface of the ball relative to infinity. So let's go first and try to tackle the charge. Here we know my apologies. We know that the potential is equal to the charge divided by four pi times r electric constant times our radius. What I'm gonna do is I'm gonna multiply both sides by all those value and you'll see that on the right hand side, those values are going to cancel out. This leaves us with that are charged that we are looking for is equal to four pi epsilon, not times our radius times our potential. So let's go ahead and plug in all of our values. And this is for part A. So this is equal to four pi times r electric constant of 8.85 times 10 to the negative 12 times our radius of 120.2 times our potential of 1200 volts. And this when you plug this in your calculator, we get 2.68 times 10 to the negative eight columns. Now we are also tasked with finding what is the potential at the surface of the ball relative to infinity. Well, we're told that the potential at the ball center relative to infinity is 1.2 kilovolts. So, Uh, the potential at the surface of the ball relative to infinity will also be 1.2 kilovolts. So now we have found both the unbalanced charge as well as the potential at the surface of the ball relative to infinity, corresponding to our answer choice of. D. Thank you all so much for watching. We will see you all in the next video.