Okay, so we're in Chapter 23. Problem 21 here. So says the volume charged density wrote e within a sphere of radius are not It's just me. Then I wrote the function of our is not are one minus R over r not squared. So this is our function for row E and where are is measured from the center of this year, ro not as a cost four point p inside the spear inside this year. So that means are less than are not determine the electric potential the and the infinity equals zero. Okay, so we first need to find the electric field. Since the charge distribution is fiercely since symmetric, we know the unused Alison's law where e dot d A is just the times of surface area of a sphere. Miss equals the charge and closed over. Absolutely not. So the charge and clothes now given as 4/3 pi r cubed times wrote e of are all over absolutely not. The total value for third pie are not cute. Okay, but this is actually not the case. Actually, we can't just take the ratio of the volumes, your times the volume density, because It's not constant. It was constantly could do that. But now it depends on our. So, actually, we have to take another step here. So we need to calculate what charge and closed is and this is given. But when we don't have a constant row E oven integral. We want to integrate from zero toe are row e of a function of our d. Okay, so let's do that. So charging clothes is integral from zero to Are we change? D v d r we're left with for pie are prime squared. And now we have ro not one minus our prime squared over r not square. Yeah. Okay, so let's solve this. We have or pie Rhona. Now we have r squared on the first becomes R cubed over three, and then we subtract off are to the fourth. So this is our fifth part of the five. Over five are not squared. So this is what our charging closed is. So let's take this back into our houses. All equation. And we should see that e is now one over for pie. Absolutely not One over r squared times for pi ro, not R cubed over three minus our five part of the fest over five are square. So it's cancelled out these four pies and some of these are there gonna cancer out. And we're left with the answer of of our e field being row not over. Absolutely are. Then we have our over three minus r cubed over five are not squared. Cool. So that's our e. Another thing we need to find out is what the total charges, which is the same as integrating what we had before from zero all the way to are. Not if we do that. We see something very similar to this equation, but it all simplifies out being ate pie. No, no. Are not Cube all over. Okay, we're almost there. We're almost have what we need. We know E for inside the sphere. We know what pew enclosed inside the sphere is a function of our is and we know the total. So now we're trying to figure out the potential O. R You can subtract off potential are not and see that this is the same as negative, Integral of ee dot The l from are not Oh, okay. So why don't we do this in a girl. So this becomes negative and a roll from Are not our of Rhona Over. Absolutely not. Are over three finest r cubed over five are not squared. We are. And let's calculate that, then this becomes negative. Ro, not over. Absolutely not. We have our squared over six minus R to the fourth over 20 are not swear Mrs Evaluated from are not our Okay, So what's out of page here? We're trying to solve he r which is be as a function of our less than on our This isn't how being ahed Plus the answer. We have time there. We haven't evaluated it yet, but we just had be not over. So this is B r equals R and r plus our answer from before. So we are. Let's figure out what Veena is. Well, Veena is just the potential from a point charge with the total charge. So this is que total over more pie Absolutely are not. So this is enough. So if we plug in what we got for Q total, we can simplify things more and this comes out to being to row, not are not squared over 15. Okay, Lastly, we plug our stuff, There's a view not And we add on our answer. All evaluated from or not are so now we can just plug this in must pull out our run on over Absolute merit We should see real efforts are not squared over four minus r squared over six plus part of the fourth over 20 are not cute. Oh, Miss equals the of our less than art out. Finally we got there lots of any girls, but we made it.