The nuclei of large atoms, such as uranium, with 92 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately 7.4×10−15 m. (c) The electrons can be modeled as forming a uniform shell of negative charge. What net electric field do they produce at the location of the nucleus?

Video transcript

Welcome back everybody. We have a small ball with a net positive charge that it is inside of a spherical casing with a net negative charge. And we are tasked with finding what is the net electric field produced by the shell at the surface of the ball. So we're gonna have to use God's Law for this. That says the electric flux is equal to the net electric field times the surface area of our shell. Now this is just going to be the electric field times four pi R squared. We also know from God's law that the electric flux is equal to the charge enclosed by the cell. The net charge all divided by the electric Perma titty constant. So we're going to combine these two equations and then we're gonna isolate our E. Term to figure out what our net electric field is that we have E times four pi R squared is equal to our Q enclosed, divided by our electric electric purgative itty constant. Gonna divide both sides by four pi R squared, or pi R squared. And you'll see that all of this cancels out on the left, giving us that our net electric field is equal to Q enclosed divided by our electric Perma titty constant times four pi R squared. But what is Q enclosed? Well, we are told that the small ball on the inside has a positive 50 nano Coolum charge and we're going to add this to the net negative, the uniform negative charge of the outside, which is neck 50 nano columns. When you add this together, we just get that our Q. Enclosed is equal to zero, which means that our electric net field will be equal to zero. And this, of course, corresponds to our answer choice of B. Thank you all so much for watching hope this video helped. We will see you all in the next one.