A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 12.0 cm, giving it a charge of −49.0 μ C. Find the electric field (b) just outside the paint layer;

Video transcript

Welcome back everybody. We are taking a look at a metal spherical ball and we are told that it has a radius of five centimeters. We are told that it carries a charge of 50 nano columns or 50 times 10 to the negative ninth columns. And we are to determine the electric field at a distance of 0. centimeters away from the surface. But we know from Kaos is law that the electric flux is equal to the electric field times the surface area of the sphere, which is simply just four pi R squared. And we also know that the flux is equal to the charge. The net charge divided by the electric permitted the constant dividing both sides here by four pi R squared. We get that these terms on the left will cancel out and we get that are electric field is equal to this term right here. I'm actually gonna split this up in the two fractions and you'll see why I'm doing that a little later on the problem, but I'm gonna split this up into 1/4 pi times the electric productivity constant, times our net charge divided by our desired radius squared. Now that we have our formula, let's go ahead and find the magnitude of our electric field this term right here is also known as columns constant. This is equal to 8.9, 9 times 10 to the ninth. This will be multiplied by our charge of 50 times 10 to the -9. Coolants. All divided by our desired radius squared, but what is our desired radius? Well, we are looking at a distance point oh one centimeters away from the surface and we already know that the radius of the sphere is five centimeters. So our total radius will be five plus point oh one centimeters, giving us five point oh one centimeters. So this will be five point oh one times 10 to the negative second meters squared. Which when you plug this into your calculator yet that the magnitude of our electric field is 1.79 times 10 to the fifth. Newtons per cu. M, corresponding to our answer choice of D. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.