All right. So it's considered are to be the radius with cylinder. The electric field e are due to the solid sonar distance are when the simple are less than our is less than or equal to the greater our can be defined by the following equation. So electric field off the small radius R ID equals lambda are over two pi times tentatively of peace face have the radius of the cylinder So this is just so this simple Ah, represents a small this is and the the large are here represents the radius. So, uh, so this is when this is are this less than or greater than the capital are And now for when it's smaller. So the other case this is true then e r is that equal to you, Amanda Times longer over two pi times primitive ity of peace base. And this time it's a simple are so on the surface of the cylinder potential B is zero. Now, if you move on to part a. So to calculate the electric potential inside the cell in urban, so inside the folder means, uh, the first. The first scenario, because it's inside similar. So the smaller radius is mess in the radiance of the sun. So let's consider the potential. So give our my next we are So that's the potential at the surface is equal to the minus, uh, into go off radius. So from the outer surface through the distance, all right, and then the electric potential e r in treated with respect to d r. So if you substitute uh for you are here, we're gonna get that equal to negative our And so we need to substitute the first situation that would spread the both such lambda are over to party e o times, uh, really cylinder square and integrated with Just respected er So if he integrated, we're going to get, uh Since this whole thing is ah, enforcing these are constants, You can actually bring it outside the the internal. And since our is the only one that's being integrated, all you need to do is to integrate that. So if you do that great, any kid, the final actor, as so these were the constant that can be moved outside the integral First, let me write that so and since it's just one are so just are over one. So if you integrate that, that becomes r squared over two. And if he also include the, uh, and points, then it will turn into so oh, are so it's r squared. Minus are? Yeah. So now, uh, let's go back into the main equation so you can actually simplify this further. Andi, uh, do it like this. Like looking to party primitive iti. And since this whole thing is, he waited by our recon Just if I divided since this this expression here is being divided by are here, so we can just simplify so it will become one minus r squared over a capital are square Sorry for that. Uh, they were called, but we know that BR the capital r is equal to zero. So from this equation here, this is a capital R. That's five that so therefore directly potential. So since media this is equal to fierce of them, this just equal the rz 40 Let me separate that. So this is just we are and it's equal to this. So this is electric potential inside the cylinder because we know at the surface electric tens of zero to this whole thing becomes zero. Just make sure that we know that this is equal to zero because of the potential there is that the surface of the cylinder there is no potential. So this is the electric potential when our isn't had seven. So now, to calculate the potential when on on the other case on the radius is outside the cell in there. So in this case, it would be Are So this case, second cheese Now you'd have to calculate the potential again. So what we are I must be at the lower is equal to negative they had to go from are to our And this time it's just Landau Two pi times primitively afi space time simple are which you're then interested of its respective er So now if they integrate this, we can move all of this. That means do that in a different color. We can move all of this. What side? The introductions There are constants and we just need to integrate one over Are exchanging alone are so now I fi right, The final answer. Get that lander over, Uh, two pi relativity Times a couple are And this this whole thing is times long capital are over our Yep. So and now we know that we are is equal to zero. So this is the potential. This is this is a mondo. Yeah, you can. So the electric potential outside the cell in there is equal to this. Sorry. There is a square here. Yeah, and that's it. First part A So the part B. So the graph of he as the function are given So here. Uh so this is the This is a function off he as a function of our. So let me draw that real quick. This would be at one are and to our and then it just keeps decreasing as the radius increases. And this the peak is at when it's equal to the radiant source. So this is E. This is the electric potential on this is the distance that you all know Onda. This is equal to as he described up here. So the grass off V as a function of our can be shown like this this this is electric electric fields. And now we're gonna do the potential. The potential can be shown by this following graph. So the potential here So let's do the do the x cornett again So that one raise two radius on three radius So one at zero it's gonna be two pi. So this is Venice departed from the surface and inside the 70. So the potential increases and goes to zero potential decreases goes to zero. And then now here we are at Lander so long to this negative black land along to over two pi primitive ity free space and let's do another one. So this negative lander this time it's gonna be a long three for three are so it's two pi times the primitive ity. So now we're gonna have it go down 23 are remember this potential against the radius and that's it for this question.