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Tha electric fiald at a distan ofo 157 From tha sunace radiug0 371 1750 N/C_scld inulatno schare wntYcu ma waniderie" Page)Lan?Forreluted Roblen-sohno lipg und srutloiay Sollian Lnilcamk churocd sphclcMu wunivier 4 Video Tulc:AasminjSpnere : chaneIlfomk dislricule d Knailscharg: densty Ins Je 4?AzPC/m'SubiulProviolls Answers FJueSensentIngoitsce Iuy Aq*in; 2 #uriad} rsialnimgPar &FZaularaclactric Fel inside Ihe spharedistarce of0 219centarAEdNICSuhuttHunvloualan ucm EqquetLAnaIngo

Tha electric fiald at a distan ofo 157 From tha sunace radiug0 371 1750 N/C_ scld inulatno schare wnt Ycu ma wani derie" Page) Lan? Forreluted Roblen-sohno lipg und srutloiay Sollian Lnilcamk churocd sphclc Mu wuni vier 4 Video Tulc: Aasminj Spnere : chane Ilfomk dislricule d Knails charg: densty Ins Je 4? AzP C/m' Subiul Proviolls Answers FJueSensent Ingoitsce Iuy Aq*in; 2 #uriad} rsialnimg Par & FZaulara clactric Fel inside Ihe sphare distarce of0 219 centar AEd NIC Suhutt Hunvloualan ucm EqquetLAna Ingonege In Aazin; % >Mrnons rmain'm Provide Feedback



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Consider a transcranial magnetic stimulation (TMS) device containing a coil with several turns of wire, each of radius $6.00 \mathrm{cm} .$ In a circular area of the brain of radius $6.00 \mathrm{cm}$ directly below and coaxial with the coil, the magnetic field changes at the rate of $1.00 \times 10^{4} \mathrm{T} / \mathrm{s}$. Assume that this rate of change is the same everywhere inside the circular area. (a) What is the emf induced around the circumference of this circular area in the brain? (b) What electric field is induced on the circumference of this circular area?

High in the given problem. The magnitude off electric plugs at the surface off Planet Mars is given US electric flux at the surface off Planet Marce is five is equal to 3.63 into 10 days of R 16 Newton meters square for colon. In the first part of the problem, we have to find the charged a total charge present over the surface off this planet mask for which using Gaza store um as we know, the total flux is given as one upon Absalon off times the total charge and closed. So using this, the expression for charge will become five times Absalon, not there. The fire is This is 3.63 into 10 days. Part 16 Newton meters square for Coulombe multiplied by absolute note, which is 8.854 in tow. 10. The super minus 12 Tsunami square for Newton intermediary square. So then the calculated the magnitude of discharge comes out to be three point one into 10 reached five colon and it becomes the answer for the first part off the problem Now, in the second part of the problem, first of all, we have to find we have to search for the radius off Planet Mars and using the data or Internet. The radius off planet Mars is 3000 389 0.5 kilometer or approximately. We can say this is 3.4 into tenders for 6 m, so the expression for electric field at the surface off Mars is one by 45 Absolute not into Q by R squared so plugging in all the values. This is nine into 10 or nine Newton meters square or Fulham Square multiplied by the charge, which is three point 21 into 10 days for ¥5 divided by the square off distance, which is 3.4 into 10. Dish for six square into meter square. So mhm, the final answer for this electric field here comes out to be 2.5 in tow. 10. They should part to Newton per column, and it becomes the answer for the second part off the problem. No. In the third part of the problem, we have to find the surface charge density off the surface off planet Mars, for which we will use the expression for electric field as the ratio off surface charge density with the absolute for negativity. So using that the surface charge density off the planet comes out to be the product off electric field with the absolute or victim ity. Hence it becomes 2.5 into stand their support to multiplied by 8.854 into 10. Rich bar minus Well, so calculating them, we get a value for surface charge density as 2.2 or one into 10. Dish the power minus nine, Golan, where meter is square and it becomes the answer for the third part of the problem. Thank you.

Hi. In the given problem, the Earth's magnetic field has been given ah value off 3.0 into 10 based the power minus seven Tesla in that region where that's true, not wants to run their generator. The time period required to move the coil to 90 degree has been given us 1.2 second area off the coil is having a value off 5000 me to re square the MF. The average MF Toby induced in this much time should be 120 volt, so we have to find the number off turns in the coil off that generator. So, using Faraday's laws off electromagnetic induction, the E M F in used is given by minus and times off d five by D D or we can say this is negative off and times off. The change in magnetic flux means final magnetic flux minus initial magnetic flux divided by the time. So as we know, the magnetic flux is given us the dot product off magnetic field vector with the area vector. So this has given us be a cost theta where theta is the angle between magnetic vector and area vector. Suppose initially the plane off the coil waas perpendicular to the magnetic will soap the area Rector and magnetic will better should have initial angle between them as zero degree and when it is rotated through 90 degree, the angle between them should have become 90 degree. So this is minus n time. Sof B A cost 90 degree minus b a cause zero degree divided by the time so plugging in all known values here minus end the number of turns These are missing. We have to find them for magnetic field. This is 3.0 into 10 Dish par minus seven Tesla for area this is 5000 meter square in the bracket. This is for cost 90 degree. This is zero for cause zero degree. This is one divided by the time which is having a value off 1.2 second and the aim of induced is 120 world. So rearranging the terms, the number of times comes out Toby 120 multiplied by 1.2, divided by three into five in tow. 10 dish par minus four. So finally the number of turns in this supposed generator comes out Toby 96,000. But this much high number off turns will make the generator very heavy. So this generator is not possible. Practically do do the huge number off turns in it which will nikh it quite heavy. And the assumption which we have used here initially the coil off generator waas for perpendicular to the magnetic field. Mhm initially the coil boss for perpendicular to the magnetic field. Thank you.

So looking at this problem, part A. We need to find the bill for the summer. Now we're gonna do that by adding up, um, this summer's totals 3 11 20 300 300.65 in 300 to 0.50. Now we add these up. Let's take a look at these 23 11 0.20 plus 300.55 plus 3 2.50 We're looking at 9 14 35 900 14 35. This is this summer, and that would be part a part B wants to know about last summer. So let's take last summer's 1 79 90 203 40 and 2111. And let's add these up. 1 79 90 those two or 3 40 plus two one 11 and we get 500 $84.41 as part B. So Part C. They want to know if the bill increased 50% more, or less than 50% more or less than 50%. So let's take, um ah, the the last summer's bill. Five. I'll see this over here. Five. 84.41 multiply by 0.5 point 50. So times 0.50 and we get to 92.21 rounded. Now let's add that onto the 5 84 41 So sad, um, to 92.21 plus 5 84.41 And we get 800 76.62 and this is 50 50% mawr. And this right here is more than that. More than 8 76 So? So it did. It did go more than more than 50% Nessie answer some more than 50%.

This is checked in 21 problem number 84 were given a profitable arrangement, and we are asked to show that the electric field, longest perpendicular by sector, is proportional to one over R to the power, for That's what we want to show at the arbitrary point. So in order to do that, let's is it's drawn here. The the electric fields from the positive point charges Q and the queue on the other side of the excesses. Let's go. These he plus and the electric field at that generated by negative too Q as e negative. So direction of the negative is gonna be towards the negative to cure, obviously. And he positive is gonna be away from because it's due to a positive charge, right? We have two of them, so this is pretty much gonna be the arrangement. So if you want to know the Net electric field, then how are we gonna write it? Let's please pay attention defect at the E. Poor positives. The ex components of these two vectors, they're gonna cancel each other out. What we're gonna have is twice of the positive of the electric field due to the positive charges. Time the sign off this angle. Because if this angle is data, then this angle has to be a favor. Right? So when that's the case, then the white component of this he puffs has to be proportional to sign there. So then, overall, in the positive direction, we have twice the electric field due to a single charge. Times sign off the same ball minus in the negative Y direction. We have B negative, meaning the electric field. Due to this negative to charge. Now let's hear what the positive is again. This is the electric. Due to a positive single charge, it's gonna make a cute over the distance from the charge itself to the point they were interested. So this is a distance you were talking about. Let's call it a D. He squared, right? So what is D in from the hot new stir up the war in there? It's gonna be equal to our story. Plus, elsewhere scare wood off this right and also over at it. Let's figure it was signed today. That would be the divisional scientist is the opposite. Our overhead hot news. D right. So are you. D is far square house, they'll skirt 1/2 our So what is E Negative is K to kill over the distance from the charge to the point average. Interested in It's our square. Right? So we can put all that information in the main equation twice the e plus Que que over instead of the square. Let's put r squared. Plus elsewhere. Scare of this is gonna be cool. To what? It's gonna eliminate the square root sign. Heda heda wien r over r squared plus Hello, squared spear. Ruutel, This right, this is our sign. Data minus que tu que over our square. Right? This is metal. So from now on, we're gonna We're gonna do a lot of eligible. Okay, So the first thing we're gonna do let's look at the common terms that we have in both of these terms. Like to okay and cue. Right. These air common terms. So then, to cake you, um, what we have is the first term to take you is are over, right. The denominators are gonna be multiplied. So then it's gonna be our spirit. Plus else Carrie, three over to write minus long over are square, right when redistribute. We're getting the previous. Now we're gonna do several tricks. What we're gonna do is we're gonna try and quit the denominators here so that we can do this. Subtraction. How are we gonna do it? By extending the first fraction by r squared by expanding the second direction. My Oscar. I'll square three true. Okay, so from here, it's good. Next beach Net Electric field is to take you. Um, now, what did we do? Expanded the first section, but our skirts are times are scared Is gonna give us our cute here. Over the denominator is gonna be our square times Our spirit times our spirit plus small spirit Power three over two for both minus, um, one tens are scared. Plus elsewhere to power three. It was very cross aspirate free, however too, right? So since now we have one denominator what we could do, we can take it out of there. So to cake, you sober are square times are spare parts all screwed. Three over two. And here we have Our cute miners are squared. Plus l spared three or two. No. Let's, um, try to take our cute out from here to take You are cute, and this is gonna be one minus. Right? So what we need to do, we're gonna regroup R squared plus squared. Then if we do, um, r squared here when we take the power of three over two, let's see what this is gonna give us our cute terms. This is gonna give us the previous line, so Okay, that's one right? And in denominated we have are spared our stiff. Plus l squared three over two. Okay, Now we're gonna do the same trick with the denominator here. Okay? To cake. You are cubes over. Someone try and let's just do this. I'm gonna multiplying to denominated by are cute and then behind it by another r cubed. Okay. Have been like what I have is our to the palace Five from this multiplication, right. And then I have are scared. Lost out, squared over are spared to the power of three over to. Okay, this term remains were saying one minus our scarecrow spells. Good morning. Are scared. Three over truth. All right, so then, to cake you are cubes over Harp's power. Five. Let's get what this term equals. Two are scared of last. There is one was false. Whereto are spared. Three over two right here, one minus one. Plus, it'll spiriting her our spears to power three over truth, right? Oh, from here, What we're gonna do is that, um we're going to start using our approximations. So the first first, let's do the binomial extension of remember, this is a different term here. Okay, so from the binomial expansion of this, so one plus health squared over R squared to power through, over to he's gonna give us one plus three over two. Elsewhere are square right extension. So whatever you see, this term, we can equate that one. Plus, the reality all scared are square. So then, if we do that the next electric field, then he's gonna be equal to Thio. More acute soldered onto the tariff. I remember individuated we have this term, so one plus three elsewhere, it over to spare. So we have one. Linus, come on. Plus three over to l squared over our squid because you can see thes wants are gonna cancel each other out, So this is gonna be able to to cake. You are cute over our two power five, um, one plus three spiritual to our squares. So we have negative three over to all spirit over to our square. Right. So now we're gonna do our of the other approximation. We had said that our was actually much, much greater than out Correct. If our is much, much greater than l Look at this turn here this term, if art is too big based on Elvis firm goes to zero. So in denominated, we only have one there. The total the net electric feel is to cake. You are accused over art. If l five times one, I'm writing it, it's a negative three over two squared square. Now these twos, we're gonna cancel each other out. We have our scared. This gonna kill two of the ours. So one R is gonna be a breeze is down to four. Then what we have is negative. Three Que que ele Spared over horror to power or right so well, that's what we wanted to prove. Anyways, that the electric field is decreasing is a function of one of our two power for and then also I want you to pay attention to this negative science which means things towards the magnetic electric. It was towards the negative awards. I get it to you to torch and he is Depending on it is a function of one arrived the barrel for.


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