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23IA half cylinder of radius R and length L >> R is formed by cutting & cylindrical pipe made of an insulating material along a plane containing its axis....

Question

23IA half cylinder of radius R and length L >> R is formed by cutting & cylindrical pipe made of an insulating material along a plane containing its axis. The rectangular base of the half cylinder is closed by a dielectric plate of length of length L and width 2R. Acharge Q on the half cylinder and charge q on the dielectric plate are uniformly sprinkled Electro- static force between the plate and the half cylinder is closest to 0b (a Ob (6) 260' RL 2teoRL 9Q (c 9Q 460' RL 8e

23 IA half cylinder of radius R and length L >> R is formed by cutting & cylindrical pipe made of an insulating material along a plane containing its axis. The rectangular base of the half cylinder is closed by a dielectric plate of length of length L and width 2R. Acharge Q on the half cylinder and charge q on the dielectric plate are uniformly sprinkled Electro- static force between the plate and the half cylinder is closest to 0b (a Ob (6) 260' RL 2teoRL 9Q (c 9Q 460' RL 8e RL



Answers

23 IA half cylinder of radius R and length L >> R is formed by cutting & cylindrical pipe made of an insulating material along a plane containing its axis. The rectangular base of the half cylinder is closed by a dielectric plate of length of length L and width 2R. Acharge Q on the half cylinder and charge q on the dielectric plate are uniformly sprinkled Electro- static force between the plate and the half cylinder is closest to 0b (a Ob (6) 260' RL 2teoRL 9Q (c 9Q 460' RL 8e RL

So we have a cylindrical rod off land Elf are not. We want to find a field, so let's go in the field for an hour. That is greater than our Not that is any point outside this cylinder. So for that we'll use a costume service that looks something like this. It's another cylinder in closing our cylinder. Why do you use this? The reason is because our system is cylindrical is symmetry. We expect the electric field Toby a radial e outwards on, depend only on the distance from the cylinder it is. We don't expect it to depend on who were these out on the cylinder. So sit on, such as Gaussian surface on these two services, the two circular surface onto ends. The electric field would be worth a call to the coast interfaces, and there will be no contribution to the flux, whereas the center circle the center surface, the electric field will be perpendicular to the area on. Hence, our we could find the electric field body easily. No, let's say that this really is off the cylinder is our as we've seen already. The flex on the two side service's will be zero so the total flux will be only do tow center surface. Let's say this Gaussian surface has excellent on you know that the radius is our the really is off this circular surface off the cynical surface would be x times the rate, the circumference of a circle. This would be to buy our This will be the area we need to multiply with electric field and we expect the electric field with seem all over the cylinder because of our political symmetry. We know that this is going to charge in closed be weighted by That's it. I'm not so if he extend this so if we extend this cylindrical surface all over the our cause in service all over the cylinder on we ignore the changing effect and we put X is equal to hell. We will see there e in tow to bite our and is equal to queuing. Yes, it or not. Now the charge enclosed is simply the charged density times the volume enclosed and you know that the volume in close will be the volume wealthy broad that is enclosed. That would be the area off the road that is fire north square times the distance so that would be road times. I are not square. Not so canceling you Common terms. We see that the electric field Israel are not scared by tow, vessel or not are And it's a directive Really upwards for Barbie be considered Art is less than are out Then we use the same gods and surface and we have The flux is equal. Do in tow Ellen to two pi r But this is a call to charge. Enclosed, derided by accident I'm in this case the charge in close will be. Let's say this is our cylinder with radius are not Let's say we're considering the distance. Distance are so we considered another surrender in this radius. So they were charged in clothes will be rolled times I ask Weird s it on? I'm sorry. And so that is rope. I ask where l by SL or not? No canceling. The comment comes. You can see that our is out until get scattered giving us He's a weirdo. Hello. I'm sorry. This is an r squared So through our by a salon Not again. This field is also director really over words

So we have a cylinder over. It gets are one Onda cylindrical shell off inner and outer radius are two and on three Now we want to find a field in the various regions most of all I mean, if you been the previous problems, you will remember that the electric field you don't surrender is often form you enclosed You are good Bye bye. Excellent Not are if they are is the really is the radio distance from the cylindrical source? L is the length off the political source and you enclosed is charged in closed Begin your cause in service. No, but Barchi consider a distance less than our one that is within the inner cylinder. So electric field is Q and closed. Do you have a right to what? Not our No que enclosed is simply the Charles density times the volume and the value is simply by our square. I'm cell You want a bite by shor, not ours. Giving this so are by two excellent and over the charts. Justice in both cases are saying so for Barbie. New York in this region in between, the two surrenders so the charge enclosed is always to see here is equal. Do charge the same formula. But here the child in close to simply wrote times the volume of a cylinder We should be I are one squared. I'm still you. What did I do? Buy a slow not getting this through. Auto in squares by two. Excellent are for park Si. We want to consider in between the outer cylindrical shell. So you got in surface? Looks something like this. So when this is the case, obviously the charge enclosed will be rule times the volume Athena cylinder, which is why our one square l That's the volume off these cylindrical shell that is inside the service. It should be high. Our square l minus. I are two square where art is the inner radius and are only three years old. Inertial on. Our three is three years off out the radius of the show. Therefore electric field is grow into I l a times I won't square That's our square minus are too square delightedly two slr not R l it is. It's transferred to be ruled by two by excellent not I don't square. Let's r squared minus are we square way out rd we want to consider outside the hole Silicone shell. So in this case, the charges clothes will always be the seam. Hence electric field will be road signs. The volume of the inner cylinder that will be all right are one square end. Yes, the volume of the all cylindrical shell. Which will be I r three square l minus pi R to square. Help! Do you want in life to buy s it or not? Our bill? It starts out, Toby. Throwing toe. I don't square. Plus our three squared minus are too square. Do you read it? Really? Tuusula or not are No. It is very hard to show you lot. What? You can simply put this piece five function and do any lording software on sentry duty numbers. But I can show you how it probably looks. You are asked to plot under 20 meters. I need fire. 15 on five five 10 and 15 meters. The nature of the graph becomes a different, has a different formless starting at these ones, they feel initially increases linearly and then falls as when they are and increases sort of clearly and then falls off again as when we are the feels are should be off the order off. 10 part for Newton Bakula, where the maximum point should correspond to about eight point two into tend bar for Newton. This is how your final graphic look your X axis will be our in centimeters on by access will be electric field Intend for you to work with him.

So we have. Ah, too cynical Shells 6.5 centimeters on nine city readers on the carry charge off minus 0.88 Micro pullem on 1.56 Michael Kula. We want to find the field in the distance is off 3.7 centimeters, which is inside the inner sitting down seven points of the city We does, which is in between the do cylinders on four point serious injury does, which is beyond the two cylinders. So let's start before we go ahead. Uh, remember that if you don't the last few problems that the eloquent feel for a cylinder is that the form your way by accident. Q. Is its charge enclosed? It is. If you consider a cylinder, we simply draw cards and surface that is another cylinder around it off radius are the 80 off. This course in service will be. Why are I'm still? And once he had this be used, Gaza's Tatum. You see that flux is equal. Do electric field time Syria, which is charged enclosed. Do you read it by its it or not? Using this formula, you get here No for Barbie when you are inside the inner cylinder. The charge enclosed is simply zero. So the electric field will also with zero or Bobby. When you're in between the two cylinders, your charge enclosed. It's simply minus zero point. A dating micro cooler. Hence the electric field will be using this form. Look you enclosed by a person or not, Carol. We contracted us. Took you excellent enclosed. You had it before, but it's not. How did so that we know that one by four banks that are not is 8.98 eight in tow in far nine Newton meters square. Put Coolum square toe in tow. The charge enclosed is 0.8 into tend bar minus six. We also have a minus. Same divided by are is someone simply reduces us with that suit of one single seven meters. I'm still is five meters. By turning this into a calculator, we can see that this is equal to minus 455 to 10 for using for cooling. Similarly, for party, I've used the same formula, but this time be charging closed is the some off the two charges. So one by four by external parties again, 8.988 Entertain part ninth. We have two into charging closed, which is 1.56 minus 0.88 micrograms. Do you want a fight where he gets his first? And they were So that's it. 112 meters times our readers. It's chancellor to be 2.0 into 10 part for Newton Occluded. This is the electrical outside the board, he surrenders. Notice that I've used to significant digits because that's what was used in the question.

Bye. God's law. We know that e d is a girl toa que and closed upon born epsilon. There is a girl too. Limit raw Davey upon Absolutely, um, that is e multiplied by twice by r l is equal to limit zero to our, um, as far. Well, he played very one Minus are twice by r l d R one are absolutely That is a modified by twice by r l is equal to twice by our alfa upon to learn, not limit zero to our ar minus r squared upon the other. Do I spy toys by l l l. So that is equal to twice by our Alfa upon Exelon not squared toe minus three are you know? So he is a girl toe. As for epsilon are I squared? Do minus. I killed three odds that is equal to I'll for upon absolute or not are upon to minus I square upon three are, uh, limit off Interrogation zero to our is equal. Tow us for upon three. It's still a not are I square upon to our cube country are zero to I that is. As for if salon are are square one upon to minus one upon three. That is equal to I swear. Hips Island. Not our three minus two upon six that is is equal toe Alfa R Square upon six salon are


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