5

15 20The electrical potential over certain region of space is given by V _ 2x Srey 3yz? , Find expressions for the x,Y and components of the electrie field in this ...

Question

15 20The electrical potential over certain region of space is given by V _ 2x Srey 3yz? , Find expressions for the x,Y and components of the electrie field in this region. What is the magnitude of the electric field (in units of Volts/meter) at point P whose coordinates are given as (1. 0. -21in units of meters?4) 5vz b) 153 c) v193 d 4 e v333

15 20 The electrical potential over certain region of space is given by V _ 2x Srey 3yz? , Find expressions for the x,Y and components of the electrie field in this region. What is the magnitude of the electric field (in units of Volts/meter) at point P whose coordinates are given as (1. 0. -21in units of meters? 4) 5vz b) 153 c) v193 d 4 e v333



Answers

Over a certain region of space, the electric potential is $V=$ $5 x-3 x^{2} y+2 y z^{2} .$ (a) Find the expressions for the $x, y,$ and $z$ components of the electric field over this region. (b) What is the magnitude of the field at the point $P$ that has coordinates $(1.00,0,-2.00) \mathrm{m} ?$

Expression me equals five x Last three x squared. Why plus two. Why c square via Way E at 10 maybe two. Taking first e with respect acts, he said. Backs take partial drew The with respect X that gives us five plus six x. Why so evaluate? Because this negative five plus six times one time zero Because that's negative. Five. E some Why Pasta River v with respect to Why gives us positive. Three X squared minus two z squared so evaluated three times one square minus two times name too square equals negative. Five for e subsea Partial Drew movie with respect to see Here's us Negative four. Why Z? Because us before time zero. Come see me, too. Excuse us zero I've I waiting e equals square root Oh, east of X Square. Plus, he said, Why square we'll see subsea square square where it that gives us square root of a five square plus negative five square plus zero square that gives us at the square root everything. 7.0 seven millions perform for me. The electric field

Okay, so we're in Chapter 23 Problem 51. So we have in a certain region of space. The electric potential was given by be equaling y squared, plus 2.5 x y plus or minus 3.5 x y z and it says, determine the electric field vector. Okay, well, he is given by the negative Grady Inspector off potential so we can find E X as negative, deep partial The partial X that comes out to being 2.5 Live minus 3.5 y z. Let's now find you why that's made a partial. The partial. Why, which comes out of being too? Why plus 2.5 x minus 3.5 x z. And lastly, we have easy, of course. Negative partial. Be partial Z miss. It comes out the negative 3.5 x y and that's everything. So just write this out. We have 2.5. Why? Minus 3.5 y Z. That's all the ex components. That's kind of the I, Huh? Plus, too I plus 2.5 x minus 3.5 x Z. That's the J component. It must leave. What's at Argo que component Negative 3.5 x y. This is all in the K hat direction. There is our concert.

It was about this question. We know the potential function is 100 times X squared, minus y squared voltage. So when, uh, you potentially see with the naked 400 votes will have ax squared minus twice where you see Kootenay before there will have asked a white square over four minus X squared over 46 to 1. And this is the graph for a white square over four, minus X squared, ovoid, even one. Okay. And then we know when on the potential function is even connected. 100 votes would have export mines. Y square is even connected. One. So, therefore, why score minus export is a good one. And this is the graph for y squared minus acts. Where is he? The one and when the potential become zero x squared minus y squared Just become zero. Okay, so have acts. Words to the wise where which means that positive, negative, accessible positively. Why? And it's give us four combinations here. But eventually he's asked us to come nations which is wise flu acts and why is he connected? Acts. So this is a graph. But why is he going to act and wise equals connective X and that's plugging 100 well here. So when we plug in the 100 boat will have X squared minus y squared. It's a good one. And this is the graph we'll explore minus y squared equals one. And when the potential is cool, 400 votes will have expert minus y squared is equal to four there, four x squared over four minutes. Weisbrot force you could want. And this is the graph for X squared minus twice were equal to one. So now let's at all these graphs together into one graph a one coordinates. Okay, so issue looks something that is so I marked the potential, uh, lines with the different potentials on each lines. And this will be the, uh, contour map off the all potential together. Okay, well, next question, while we know in his case, it after a few cervical to degrade in off the potential which is a Grady in 100 AC Square, Maya's 100 y square. Okay. And Grady means taking derogative on multiple variables, respectively. So in this case, we're taking the reserve Oh, accent. Why, respectively, which means that that review she'll be equal to D over DX guys 100 square minus 100 y square. And it's that ah factor component is that I've actor. Because if we're talking about the de Rosa off acts, okay? And then plus the there is a total of who I was d over the why? Which is an end times 100 ac square minus 100 y square with the tractor components over the factors, the same factors A Okay, so therefore, this will give us that review should be equal to 200 X I a vector minus 200. Why? Jabe actor. So if we take 200 out, we have 200 multiply x I minus Why, j okay. And for the last question, this is the graph I drew. So they put the realize are the potential lies with basic. So I basically copied the potential line's front question. They okay, So you was looking something ideas and how I truly after a few lines? Well, we know that it every few allies this was always programmed Equilar to potential eyes. So I need to do just try to draw the lines that are perpendicular to the rail lines, which is the green eyes here. Okay. And, uh, these are my answers for this question.

Until the electric people can be defined by the following equation. So E is equal to the derivative of the potential over the derogative Off the position far. So now if you substitute the the potential that were given, which is the musical positive A explain why must be x squared b y squared. So if we substitute that let me hold on Let me just get that down on paper first p is equal to X squared. Why minus b x y squared So now you see that and bring it into the potential into this equation. So then you enter in back so be the are That's a really long line every lunch And now go back to Penn now A Let us be x y squared tonight he compute this, uh, so now we need to come computed for each of the components. So if you computed for E X and B now the whole for the position that X he x who would respect to X and now the mistress being straight down here. All right, Uh, we take this year. I believe that, uh, let me just make it easier. So if we can do this quicker. So you move this down here and, uh, differentiated with respect to X. Beginning at that belly is equal to two times exp i minus. And since this excellent power one was the coefficients of the White Square And now we know the conference teacher just given to us in equation in the and the question. So if you substitute that like, I don't think I need to write it. But if you plug it straight into a calculator, substitute the values that getting the question we're going to get that yeah, is equal to negative 6.72 both for meter. Now, that's potentially so I mean to caucus potential. Why? So if you do the same thing, so the differentiated. But this time with this respected why interior cooperating percent feel that way. Oh, she bring this year. Bring it down here. So now if you differentiated with respect the wire, you're gonna get the equal distances y to the power line here it just becomes a coefficient. So x squared. And since is what part two? Here it just be bring to theaters and then subtract power. So it's minus to be a why Now I see so city the values that we get from the question straight into this, uh, into the corn that we can get that it's equal to negative 7.2. Okay, go screw meter square number. Always remember the unit on finally, the potential, etc. I actually don't think I need to read it out. We can just look at the about the equation. And our remember we're different to you than respect, is he. But just by looking at this, we can notice that there is no variable for them to differentiate with respect. Disease just equals zero to the potential. That easy sequence there. So now, to find the net magnitudes off the electric field, we can use this foreign formula. So let me let me write this in the different colors. Easy quote, too. So this is the net magnitude of Flex Field, which is equal to X squared. Plus he y squared plus e c. Ever. So now we substitute the values that we just computer to above. We can get that this is equal to negative. Six point 72 squares negative 7.2 squared. And since it's just zero for a concert Easy. We don't eat right the You know, if you compute this and I call clear, we're gonna get that meant potential. The Net electric field is a put 9.8 over 9.8 both from here. So not defined the direction off the electric field that you can just use this falling for me. So let me get that in between. So the pita You mean like a better feed it there. The angle. The sequel to the pan and worse uh, e y over e x. This is justified direction. Since these two are the heads of the triangle, If you could imagine like, So now, if you just substitute the values that we got from the previous equation, it's time negative one that's equal to negative. This is the very, very calculated up here in black. So now it's over. Think it is six point seven to now. If you compute this, you're gonna find that is equal to 47 degrees. So now we're cooking with the magnitude in that naked huge here and direction here, and that's it for this question. Thank you for


Similar Solved Questions

5 answers
Xids with cell phones: marketing manager for pnone comoany clalms less than 5900 of children aged &-12 have cell phones. In survcy 822 children aged 8-12 by natanz consumers group, 460 them had cel phones, Can Yau conclude that the manager' $ clalm Inie? Usc the 0.01 level s gnificance and the P-value method with thc tablc Part: 0 / 5Part 1 0f 5State the approprlate null and alternate hypotheses:Ho:Hj:This hypothesis test is a (Choose one)test,
Xids with cell phones: marketing manager for pnone comoany clalms less than 5900 of children aged &-12 have cell phones. In survcy 822 children aged 8-12 by natanz consumers group, 460 them had cel phones, Can Yau conclude that the manager' $ clalm Inie? Usc the 0.01 level s gnificance and ...
5 answers
Question1.5.35Construct a 3x 3 nonzero matrix such that the vectorsolutlon of Ax = 0
Question 1.5.35 Construct a 3x 3 nonzero matrix such that the vector solutlon of Ax = 0...
5 answers
Lemmnntya,15777II ~hch mciad Cuir borFAanODuntnLallx=ra anbrannnolenentmaameIeneaneenahentrial Hbt Mmeent etnn euemeeelut tanetDmnurul n Ittuun 5 a untMneh mhealennlaua entnntenetnecnlulnn]Lollr eala [nt el ama tcmanddenman&
lemmnntya, 15777II ~hch mciad Cuir bor FAanO Duntn Lallx=ra anbrannnolenent maame Ieneaneena hentrial Hbt Mmeent etnn eue meeelut tanet Dmnurul n Ittuun 5 a unt Mneh mhealennlaua entnntenetnecnlulnn] Lollr eala [nt el ama tcmand denman&...
5 answers
Determine tne [orque (In Nm) appnia [ to the shaft of DOur car that transmus GO000/44xspeed Ipower] KW anu rolnies ponna Axspeed Vou 60000/44xspeed Dowet Gooo/speed[speed] !pmn_
Determine tne [orque (In Nm) appnia [ to the shaft of DOur car that transmus GO000/44xspeed Ipower] KW anu rolnies ponna Axspeed Vou 60000/44xspeed Dowet Gooo/speed [speed] !pmn_...
5 answers
Question 12Which of the following mixtures can be efficiently separated using simple distillation?Choose all that apply:Warning: Incorrect choices will decrease your score for this question Ethanol (bp 78OC) and Cyclohexane (bp 810C)Benzene (bp 80OC) and Isopropanol (bp 820C)Pentane (bp 360C) and Isopropanol (bp 82.50C)Water (bp 1OOOC) and Ethylene Glycol (bp 1970C) Dichloromethane (bp 40PC) and Pentane (bp 360C)
Question 12 Which of the following mixtures can be efficiently separated using simple distillation? Choose all that apply: Warning: Incorrect choices will decrease your score for this question Ethanol (bp 78OC) and Cyclohexane (bp 810C) Benzene (bp 80OC) and Isopropanol (bp 820C) Pentane (bp 360C) a...
5 answers
Sec? I tan' d.15
sec? I tan' d. 15...
5 answers
Question0.882 g CzHs (g) sample is kept in a constant-volume container at - 239 € I. The gas sample contains 1.20 x 1023 atoms_ II: Effusion time of CzHg (g) molecules is 0.797 times that of Nz (g) molecules at the same temperature_III If the gas was heated to 2270 C, its pressure would be twice the value at - 230 €. Which of the given statements is/are false for this gas sample?Your answer:Only II Onlyandand IllIland IlI
Question 0.882 g CzHs (g) sample is kept in a constant-volume container at - 239 € I. The gas sample contains 1.20 x 1023 atoms_ II: Effusion time of CzHg (g) molecules is 0.797 times that of Nz (g) molecules at the same temperature_ III If the gas was heated to 2270 C, its pressure would be t...
5 answers
Queston 8By hand compute the sample corrclation coefficient for the following daba:Can vou be 95% conhdent thar linear relhton exlsts between the variables? I $0.is thc: relation posirive & negattve? Justify YoU anxwer0 pts
Queston 8 By hand compute the sample corrclation coefficient for the following daba: Can vou be 95% conhdent thar linear relhton exlsts between the variables? I $0.is thc: relation posirive & negattve? Justify YoU anxwer 0 pts...
5 answers
The rate law for the reaction CGHSCH3 + H2 > C6H6+ CH is rate = k[CGHSCH3J[H2|Below are one proposed mechanisms for this reaction. Show that both of these mechanisms are plausible
The rate law for the reaction CGHSCH3 + H2 > C6H6+ CH is rate = k[CGHSCH3J[H2|Below are one proposed mechanisms for this reaction. Show that both of these mechanisms are plausible...
5 answers
Compute the average rate of change of the function on the given interval.$$g(x)=x^{3}-x ext { on }[1,2]$$
Compute the average rate of change of the function on the given interval. $$g(x)=x^{3}-x \text { on }[1,2]$$...
5 answers
Vz7 + 3 _ :5 Problem 2 . Given f(c) find f' (x) . It may be easier to perform some x2 algebra before taking the derivative.
Vz7 + 3 _ :5 Problem 2 . Given f(c) find f' (x) . It may be easier to perform some x2 algebra before taking the derivative....
5 answers
The table below models a particular physical situation_10Find the piecewise linear equation that models the data above. Round to three decimal places if needed:-8 <x<l 1<x<4 4 <x<9
The table below models a particular physical situation_ 10 Find the piecewise linear equation that models the data above. Round to three decimal places if needed: -8 <x<l 1<x<4 4 <x<9...
5 answers
Answer this question ASAP, thanks!A boy imagined a four-digit multiple of 5 with different digits.If the first digit is erased, the obtained number is multiple of 9.If the second digit of the imagined number is erased, the obtainednumber is multiple of 11. If the third digit of the imagined numberis erased, the obtained number is multiple of 7. How many numberssatisfy given conditions?
Answer this question ASAP, thanks! A boy imagined a four-digit multiple of 5 with different digits. If the first digit is erased, the obtained number is multiple of 9. If the second digit of the imagined number is erased, the obtained number is multiple of 11. If the third digit of the imagined numb...
5 answers
The angular momentum, L = Lxi + Lyj + Lzk for a particle with position r = xi + yj + zk and momentum p = pxi + pyj + pzk is defined byL=rxpWhereLx Ypz ZpyLy Zpx XpzLz = Xpy ypxHence, show that[p? , Lx] = [p?,Ly] = [p?,Lz] = 0Where p2 = px2 + py + pz2 and [u,v] is the Poisson bracket of two dynamical variables, u and V_ with respect to a set of n canonical variables qk pkk = 1,. ,n
The angular momentum, L = Lxi + Lyj + Lzk for a particle with position r = xi + yj + zk and momentum p = pxi + pyj + pzk is defined by L=rxp Where Lx Ypz Zpy Ly Zpx Xpz Lz = Xpy ypx Hence, show that [p? , Lx] = [p?,Ly] = [p?,Lz] = 0 Where p2 = px2 + py + pz2 and [u,v] is the Poisson bracket of two d...
5 answers
ApotBooknaragHow are these two ovents rcloted? The two evcnts are Interection: each other Tha two cvants aru the eamc Gvonl The two events pre uniona of cach other; tne entire bamplc #pace Combined; thc twr0 gvents makcShade tha uvent (A n 0)€,
Apot Booknarag How are these two ovents rcloted? The two evcnts are Interection: each other Tha two cvants aru the eamc Gvonl The two events pre uniona of cach other; tne entire bamplc #pace Combined; thc twr0 gvents makc Shade tha uvent (A n 0)€,...
5 answers
Ic.() Fitudl the WWlulx"e Iluatlsti-licz th colitiony o Ilw Mcnn Valun Tworm lor Ilue lunction 9(r) detined ou Ille' iuterval (05].Ic.(ii) Now chraw the Kraph ot 9(r) MuM the NAIIIA axis ssten druw tlw' liuue joining Ilue points Ou (lw' gnph mt the eJlpoiuts AIe | Ml Ilwe' iuterval, Al druw Ihe taugent to %6) which muAll [ t (hix Iiuue , AIld explain wlere ( which /-value) 4his Iitu' (K"HI Ilwe graph:
Ic.() Fitudl the WWlulx"e Iluatlsti-licz th colitiony o Ilw Mcnn Valun Tworm lor Ilue lunction 9(r) detined ou Ille' iuterval (05]. Ic.(ii) Now chraw the Kraph ot 9(r) MuM the NAIIIA axis ssten druw tlw' liuue joining Ilue points Ou (lw' gnph mt the eJlpoiuts AIe | Ml Ilwe' ...

-- 0.069387--