5

The circular region with radius R = 7.45 cm shown in the figure has an electric field directed upwards and perpendicular to the region_ The amount of electric flux ...

Question

The circular region with radius R = 7.45 cm shown in the figure has an electric field directed upwards and perpendicular to the region_ The amount of electric flux @DE through a circle of radius around the center of the region at time is given by the expressionDE (r) (27s_) - rt2 What is the magnitude of the displacement current ia at a time 0.315 through the circular area with a radius 5.35 cm from the center of the circular region?What is the magnitude B of the induced magnetic field about the

The circular region with radius R = 7.45 cm shown in the figure has an electric field directed upwards and perpendicular to the region_ The amount of electric flux @DE through a circle of radius around the center of the region at time is given by the expression DE (r) (27s_) - rt2 What is the magnitude of the displacement current ia at a time 0.315 through the circular area with a radius 5.35 cm from the center of the circular region? What is the magnitude B of the induced magnetic field about the perimeter of the same circular area at the same time?



Answers

Shows a circular region of radius $R=3.00 \mathrm{~cm}$ in which an electric flux is directed out of the plane of the page. The flux encircled by a concentric circle of radius $r$ is given by $\Phi_{E, \text { enc }}=(0.600 \mathrm{~V} \cdot \mathrm{m} / \mathrm{s})$ $(r / R) t,$ where $r \leq R$ and $t$ is in seconds. What is the magnitude of the induced magnetic field at radial distances (a) $2.00 \mathrm{~cm}$ and (b) $5.00 \mathrm{~cm} ?$

This problem covers the concept of Maxwell of induction. And first we need to calculate the reach of the rate of change of dielectric flux through the region. So d by D. T. Of five E enclosed equals 0.6 volt four m/s Into the distance of the point from the axis of symmetry upon the radius of the region. Let's say this is a question one. Okay from Maxwell of induction. For a point within the region, you can write the magnetic field magnitude uh from the Maxwell equation equals mu. Not absolutely not upon to buy our and to defy a by duty divide et of five E enclosed. And from question when we can write the magnitude of the magnetic field is we're not absolutely not Upon to buy capital art into zero six volt four m/s. Let's say this is a question for a point outside the region that is smaller greater than capital are the magnitude of the magnetic field equals mu Not absolutely not upon to buy our Dubai duty off fi enclosed and in this case then close electric flux is only through the Senate region. So from this we can write the magnitude of the magnetic field equals mu. Not absolutely not upon to buy our Into 0.6 World four m/s and two capital are upon or the magnetic field magnitude is may not explain. Not upon two pi R. into 0.6 volt four m/s. Let's say this equation three. Now for part A Where are? It's less than capital r. and its value is two cm. Mhm. So at that point the magnitude of the magnetic field equals full by Into Tenders -7 Tesla meters. Poem peer into 8.85 In to Tenders -12. Cool um squared poor newton four m squared into 0.6 bold parameters per second upon mhm upon to buy Into the value of capital and there is three cm. Or we can write 0.03 meters are the magnitude of the magnetic field equals 3.54 In to Tenders -17 Tesla. Now for part B. Here, the value of our is greater than R&R equals five cm. So at that point from question three, the magnitude of the magnetic field equals full by Into 10 days -7 Tesla meters. Poem peer into 8.85 in two tenders -12 Cool. Um Square for newton four m squared into 0.6 Volt four m force again are born Two pi into the value of smaller and that is five cm. Or we can write 0.05. Meet us are the magnetic field magnitude at this point is 2.12 into tenders -17 Tesla.

And this from him. We have a circular region. Off areas are equal to three centimeters in which electric flux is actually going out off the page. So let us draw a circular region. This is a circular region. It has a radius, are there is an electric field which is deserting in a net electric flux. So I'll write as five e in in this case reversed. Oh, the electric field. So this man and this flux is due to the electric field. And as we said that this is actually waiting. So the radiation off electric flux through this office is killing as 0.6 world meet up a second or in six volt meter toe a second and it's dependent on the radial vector are so this is again multiply twit are who are the capital of capitalist over a radius on bearing with time T. Now, as for the problem, we need to find out the magnitude off induced magnetic field at radial distance two centimeters and five centimeters. First we'll write down that our is equal to three centimeters, so we need to find out the magnitude off induced magnetically to the first case is when our is less than our so are is equal to two centimeters. We'll use a formula that the girl closed loop, Peter, the l is the line element representing for the loop. It's equal to mu note I includes. This is the current which is enclosed within the loop. Now, as you can see, there is no current as such within the loop. In this case, however, there is also another part which is called the displacement current and rewrite that last minute I the displacement No idea is actually represented as since this part goes to zero. We write this a zero. This is, um, you know, absolutely not. Partial derivative off electric flux. Well, our name and that's a bit Oh dear. No considering so Vinto first consider our is equal to this. We have one small loop which is insane at a radius off are equal to present images are taking the fact that the magnetic flux in this case it's constant along the water loop with a be outside they get the magnitude off key into steel along the clothes look close group of circular so in particular is to buy our the artist that tedious. This gives us mu notes. Keeps little Lord the elevated off. This with respect to time he cancels out. So did we. Do not started canceling 30 course of a because of the radio, Uh, with calculus. So, as you can see, are now gets cancelled out. So the value off be that we are plain in this case, Yes. So the value of B that we often in this case, it's plain simple mathematics 10 and that men do is now equal to three point food into 10 pervert minus 17 Tesla. So this can be done by substituting for all the other values. Art gets cancelled out. We get a group, I 0.6. You have to substitute the values of these constant and are equal to three. Sentiment doesn't reflect this value for people next to move with the other section. This is friend. Are is equal to five centimeters. Now heavy. You'll have an interesting part. This is when our is actually greater than the capital are. It's which you can draw that neatly again. We go back to the same form, lovey. Right? B Dubai are this time our is after efi centimeters It is outside. The slim pickle surfaced. You not hopes, Eleanor. 16 However, we'll have to. Now consider vote are toe shoes. No. What are should be to lose him now. This represents this valley right here. This term actually represent the displacement, current and displacement current is purely due to the change in the electric field flux. And since the elected field flux exists, will need this region. We should also remember that the electric field exists only within this region, which has a radius off capital. So our can only go all the way from zero to the capital. I cannot go beyond that in this case. So this means our our artist testicle the one and we get the total net maximum changing and electric flux. So So in this case, we will be using. So, unlike the previous case where the art gets cancelled out this way, in this case, we won't have that our will actually be important. And so a solution will be immuno. Absolutely not. 16 They were both Gupta. This is actually equal into saying no. We can also study the whole case, but is hearing that this is you can also assume that this whole structure is actually a wire so elected feeling. And if I want to find out what's the magnetic field outside, I'll consider the entire current which is flowing through the wire, which is only limited till the surface off the wire. But if I want to find out, elect magnetic field, which is inside the surface off the inside the fire, I'll have to consider it will need that part off the wire, which is in second, and Gary separate, and the solution for this is now good point 13 into 10. Power minus 17 dessler.

This problem goes the concept of Maxwell. Love induction. and to solve this problem 1st, we need to find the electric flux enclosed through a region. So to find the electric flux first, we need to consider elementary area which is at a distance of our and has a thickness off dear. So through this elementary ring the Elementary Flux that is G five E. Equals the electric field, which is uh 0.5 Into 1- are upon Capitola. Okay Bold. four m 4 seconds into 19. And do the elementary area and the elementary area, D A. S. To buy us Gs. So the total flux and close by this region, it is D five E enclosed. It's in the grill off this part and that is in cuba into uh 0.5 into goodbye. G into 1-. Are upon capital are R. D. are integral from 0 to our. So we're fine. If I am closed is CUba into by T uh pity our square upon to minus Are killed upon three are. That's how this question. So The value of the rate of change of the flaps and close that is D five E. And close from this equation equals by into r squared upon to minus our cube upon. So yeah. Okay. Now for a reason are less than or equal to capital are from Maxwell. A production V equals well not absolutely not upon to buy up into defy ability. And that is why our square upon to minus our cube upon triage. Or we can write the magnetic field magnitude is equivalent to may not. Absolutely not. Okay may not. Absolutely not. Uh Upon to into are upon to minus r squared up on three. Now for part A we can substitute the value of our in this equation to find the magnitude of the magnetic field. So B equals mu notice full by In to tenders -7 Tesla meters for NPR Absolute notice 8.85 into tenders minus 12. Uh Cool. Um squared for newton for meter square into The value of R. And that is 0.02 needles upon to minus 0.02 meters square Upon three into the value of capital. And that is 0.03 NATO's upon to. Okay so the magnetic field magnitude is a Cuban too 3.09 into Tenders -20 s. La. This is the solution of party now for part B for a point outside the region for part B. Ah B bye DTL. The electric uh employees selected blacks is cuba into bye into for this. The value of smaller will be over and took a patella *** out of spot upon to minus Our Cuba 1 3 years. Or that is the cuBA rental. Bye. Our square upon six. So from this we can right the maximum loss of production. The vehicles will not absolutely not upon to buy us. and to defy by duty that is five Our Square .6. Okay. Now we can substitute the value so the magnetic field induces for by In to tenders -7 Into 8.85 Into and uh -12 In 25 and 0.03 square upon two and 25 and two. Ah that is 0.05 m and to six are the magnitude of the magnetic phase at this point comes out to be 1.67 and two tenders minus 20 s life.

Hi there. So for this problem we have to figure that is shown in here. An electric field is directed out of the screen within a secular region and the radios art is equal to three cm 30 m is 0.03 m. And the field magnitude is also given So the magnitude ford the electric field it is zero point fi bulls per mature per second and there's times one mine is the ratio between our and the radius of the circular region times the time. T. Yeah, an art lower kids. R is the distance that we know is equal or less than these. The radius of this circular region. Now, what we need to determine is the magnitude of the induced magnetic field at some radial distances. So for the first part a we need to determine the magnitude of the magnetic field when the distance art is equal to two centimeters. No, here the enclosed electric flubs is found by integrating So we will find that the integrating the electric flops is equal to the integral From 0 to our. Since our is less than um the the radius of this um circular region. So we will have that this is equal to the electric field times two pi the radius times the differential in the radius. Now we can take out of this everything that is coming and we put the expression that we have for the electric field in here. So taking out everything that is common. We can take out the time, we can take out the man needed that is given 0.5 bulls per meter per second and Also the two pi turn it is constant. And we will have then the integral from 0 to art of 1- are over capital art times art in the differential. So in here what we are going to have let me let me do the integral separately. We will have, we multiply this by each of these terms. So we will have in here that that is from zero to art of art minus are square over art. It is so the first integral we know that the integral of art is are to the square over to and the integral of r squared is Are to the three over three times 3/3. And these three times the radio. So we know evaluate this from zero to art. And this will give us simply that expression Because at zero is just zero. Now we will find then that the flips of electric field is equal to D times pi times the radius in here that we obtain. Now what we are going to obtain after taking the derivative with respect to time is that the product between the magnetic field And two pi art? It's equal to Absoluteal zero Times Music zero pie the expression that we obtained remember that to obtain this, we need to take the the derivative with respect to time for the flips that we just have obtained. So we will obtain just simply that this is one and we obtain that expression from it. So it is one over to the radius squared minus the radius to the cube three times the capital radius. Now we just need to simples institute all of the values that we know for days we know that these two are constants. You can search for it and after substituting the values for our Which in this case it is given that is 2cm. So it's going to be 0.02 meters. And the radius of capital art of this of this Circular region we have that that radius is three cm that emitters is 0.03 m. So substituting all of those values and the value for the constants and Philip subzero and new subzero. We will obtain that the magnitude of the Magnetic field is 3.09 times 10 To the -20 Tesla. So this is a solution for the first part of this problem. Now for part B what do we need to determine is the magnetic field. But now when art is equal to find centimeters. Now, as you can see in here um art is greater than the radius of the circular region. So the integral that we did before will no longer have our as the upper limit. Now the upper limit for that expression in here for this inter goal we will have the data comes from zero to art to capitol are so we just need to simply substitute in dirt. Capital are for by art. So when we are going to have in here so we substitute that into that expression expression that we just have obtained. So in here you just put capital art and here also capital R. And see what we obtain. So we will have the times pine one half of the radio squared minus the radios to the cube Over three times the radius. So from here we can see that we can simplify this. We obtain that this is to so we will have the disease one over sits T pi their radius to the square. Now using again the equation for the The magnetic field we will have that that is B2 pi. The radius art is equal to. We need to dairy wide the expression before with respect to time. So we will have that. It's simply Absalom subzero music. zero times pi times the radius is square. So in here when we solve for the magnetic field we will have the data is absolute zero. Music zero R squared capital are square over over 12. Yeah times the radius art. So in here we just substitute all of these values We will have for absolute zero. That is 8.85. Times 10 to the -12. The value for music, zero is 4 pi times 10 To the -7. And the right. The greatest capital art is equal to 0.03 to the squared. In all of this, The product between 12 and the radius art that is given five cm that emitters is 0.05. So plugging all this into the calculator, we obtain that the magnetic field, the magnitude for Governor Rick Field, is equal to 1.67 times 10 To the -20 -20 Tesla. So this is the solution for this problem. Thank you.


Similar Solved Questions

5 answers
A) Look the epoxidation reaction and draw the product of epoxidation of the following 10. Be sure to draw the relative stereochemistry of the product as either syn or anti: substrate.m-CPBACHzClz NaHCO}B) Draw out m-CPBA What is the role of baking soda (NaHCO:) in this reaction? (Hint: What acid is being generated that needs to be "mopped" up?)
A) Look the epoxidation reaction and draw the product of epoxidation of the following 10. Be sure to draw the relative stereochemistry of the product as either syn or anti: substrate. m-CPBA CHzClz NaHCO} B) Draw out m-CPBA What is the role of baking soda (NaHCO:) in this reaction? (Hint: What acid ...
5 answers
Given the points 4(4.-2 0) and B(I, 1,2):function for the line thal contiins Lhesc Find Fccton-Falucd points:
Given the points 4(4.-2 0) and B(I, 1,2): function for the line thal contiins Lhesc Find Fccton-Falucd points:...
5 answers
4+ xl:0 YzDeterine H_deneral_SokuHon Of Hq_cliereceaka? e Quation
4+ xl:0 Yz Deterine H_deneral_SokuHon Of Hq_cliereceaka? e Quation...
5 answers
PROBLEMS Write each number in scientific notation. 1) 326 2) 798 3) 2650 4) 14,500 5) 826.4 24.97 7) 0.00413 8) 0.00053 9) 6.443 Write each number in decimal form 8.62 x 104 2) 8.67 x 102 4) 3) 6.31 X 10-4 5.41 X 103 5) 7.68 x 10-1 9.94 * 101 7) 7.77 X 108 8) 4.19 x 10-6 4.05 x 100 The number 0.00123X10 3 can be expressed in scientific notation aS.-
PROBLEMS Write each number in scientific notation. 1) 326 2) 798 3) 2650 4) 14,500 5) 826.4 24.97 7) 0.00413 8) 0.00053 9) 6.443 Write each number in decimal form 8.62 x 104 2) 8.67 x 102 4) 3) 6.31 X 10-4 5.41 X 103 5) 7.68 x 10-1 9.94 * 101 7) 7.77 X 108 8) 4.19 x 10-6 4.05 x 100 The number 0.0012...
5 answers
9.) (3.0LEx (300 Klx (1Oatml = (100.K) x (3.0atm)
9.) (3.0LEx (300 Klx (1Oatml = (100.K) x (3.0atm)...
5 answers
Determine the absolute contigurations tor 'the stereogenlc or clral centers Indicated by the arrows:Hyc-Carbon v [ Select ]Carbon &Carbon € Select ]CHsCHsCH;"CHs
Determine the absolute contigurations tor 'the stereogenlc or clral centers Indicated by the arrows: Hyc- Carbon v [ Select ] Carbon & Carbon € Select ] CHs CHs CH; "CHs...
1 answers
Find all solutions in radians to $\sin x=0.88$. Round to the nearest hundredth.
Find all solutions in radians to $\sin x=0.88$. Round to the nearest hundredth....
5 answers
Question10 PointsFind the volume of the parallelpiped spanned by ~1,21> b =<9,5,7> <2-10,3>and € whereRound t0 2 decimal places:Add your answcr
Question 10 Points Find the volume of the parallelpiped spanned by ~1,21> b =<9,5,7> <2-10,3> and € where Round t0 2 decimal places: Add your answcr...
5 answers
I tha Vauo. Uio (90741m ^ 0,C eubuntuly Xeuu Ule (Aaphie 45m Mu Rqtm | Gch huvu MVa Im Mva U dnu Henet Vuch hulvo Qluu 96Ilqurd UlcululaIollacntvg dolewlfux 4"D
I tha Vauo. Uio (90741m ^ 0,C eubuntuly Xeuu Ule (Aaphie 45m Mu Rqtm | Gch huvu MVa Im Mva U dnu Henet Vuch hulvo Qluu 96 Ilqurd Ulculula Iollacntvg dolewl fux 4"D...
5 answers
Lt {(=) = |4: Draw the guph o v = I(r) tlie Ixc Unclow , tucu I0 }uut grph hclp YOM AsWer tho following questions, Whg elw: Amtage tule Of chtke ol / ou the Iutertal 6; wlute Iiy FNuie Huuiet Hlant ; Cou-bler moblcmWZut U MVENR" iale of &hnge o mnnsltm Mubut /J Interval |-h,0]. wlcreMyDu Yuil IlA4e MNutLa nu ( Yu Malou Ilo Mateilajgullm GuuY alenl Ihc puph e (auigeut huw Ust poiut?ot chuuug" or 0t I =0 Whnt €0u
Lt {(=) = |4: Draw the guph o v = I(r) tlie Ixc Unclow , tucu I0 }uut grph hclp YOM AsWer tho following questions, Whg elw: Amtage tule Of chtke ol / ou the Iutertal 6; wlute Iiy FNuie Huuiet Hlant ; Cou-bler moblcm WZut U MVENR" iale of &hnge o mnnsltm Mubut / J Interval |-h,0]. wlcre My ...
1 answers
In Exercises 37–52, use a graphing utility to graph the polar equation. Describe your viewing window. $$ r=\cos 2 \theta $$
In Exercises 37–52, use a graphing utility to graph the polar equation. Describe your viewing window. $$ r=\cos 2 \theta $$...
5 answers
Cellular division in both plant and animal cells. While they are similar in many ways, some key differences occur late in the mitotic division. Describe the similarities and differences between the cytokinesis mechanisms found in animal cells versus those in plant cells
cellular division in both plant and animal cells. While they are similar in many ways, some key differences occur late in the mitotic division. Describe the similarities and differences between the cytokinesis mechanisms found in animal cells versus those in plant cells...
5 answers
Question 110 ptsWhat is the direction of the magnetic force on a negative charge that moves as shown in the figure?into the pageright (East)left (West)out of the page
Question 1 10 pts What is the direction of the magnetic force on a negative charge that moves as shown in the figure? into the page right (East) left (West) out of the page...
2 answers
([Ab16, p.140, Ex. 4.5.6).Letf: [0,1]→Rbe continuous withf(0) =f(1).(4.4a) Show that theremust existx, y∈[0,1] satisfying|x−y|=12andf(x) =f(y).(4.4b) Showthat for eachn∈Nthere existxn, yn∈[0,1] with|xn−yn|=1nandf(xn)=f(yn).(4.4c) Ifh∈(0,12) is not of the form1nthere does notnecessarily exist|x−y|=hsatisfyingf(x) =f(y). Provide an examplethat illustrates this usingh=25.
([Ab16, p.140, Ex. 4.5.6). Letf: [0,1]→Rbe continuous withf(0) =f(1).(4.4a) Show that there must existx, y∈[0,1] satisfying|x−y|=12andf(x) =f(y).(4.4b) Show that for eachn∈Nthere existxn, yn∈[0,1] with|xn−yn|=1nandf(xn) =f(yn).(4.4c) Ifh∈(0,12) is not of the fo...
5 answers
Howwax Lo L Find Fk eihca ( Fuin^ cnd idh{y ex +tmt buinta Guepl H< Tunt6u1 X4 _ 2x 2 (4) 4= Uimif^ (A/Ny ! Hobilal % Pule) Final U ' 2 x2 Von (m X) U Xit %Gtex ) (62) Xt X (i-x) Vr
Howwax Lo L Find Fk eihca ( Fuin^ cnd idh{y ex +tmt buinta Guepl H< Tunt6u1 X4 _ 2x 2 (4) 4= Uimif^ (A/Ny ! Hobilal % Pule) Final U ' 2 x2 Von (m X) U Xit %Gtex ) (62) Xt X (i-x) Vr...
5 answers
For the system in equilibrium below, find the unknown Tl and mass: [3 T] Ty Xty Tz 7 60YT3 80 N Tz sin 0 T; ces6 Tx 80 sinbo" Tz &b 60" Tiz 69 N Uon = 1424o 7691Fot = Fn1 -Fj Fg = Fzz 5 ~g Fn Ft m? 22 9 7.0 *9Tz 69NT, = %.0 */o Me 1.0e1
For the system in equilibrium below, find the unknown Tl and mass: [3 T] Ty Xty Tz 7 60YT3 80 N Tz sin 0 T; ces6 Tx 80 sinbo" Tz &b 60" Tiz 69 N Uon = 142 4o 7691 Fot = Fn1 -Fj Fg = Fzz 5 ~g Fn Ft m? 22 9 7.0 *9 Tz 69N T, = %.0 */o Me 1.0e1...
5 answers
Question 26newborn infants' weight at & community hospital is that the mean is 10 pounds A sample of 34 infants iS randoml} A hypothesis regarding sample weights at birth are 13 and the standard deviation is 6 The statistic test IS (answer to three cecima places)Moving to anotner question will save this response:
Question 26 newborn infants' weight at & community hospital is that the mean is 10 pounds A sample of 34 infants iS randoml} A hypothesis regarding sample weights at birth are 13 and the standard deviation is 6 The statistic test IS (answer to three cecima places) Moving to anotner question...

-- 0.024461--