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An electon moveswh Soeed +Or10' I{sint2 directora ahov (Figure (F olte 2) belcw: 0.30 magnejic field pcints Inne postve I-directon...

Question

An electon moveswh Soeed +Or10' I{sint2 directora ahov (Figure (F olte 2) belcw: 0.30 magnejic field pcints Inne postve I-directon

An electon moveswh Soeed +Or10' I{sint2 directora ahov (Figure (F olte 2) belcw: 0.30 magnejic field pcints Inne postve I-directon



Answers

Consider the vector field $\vec{F}$ shown in Figure $18.13,$ together with the paths $C_{1}, C_{2},$ and $C_{3} .$ Arrange the line integrals $\int_{C_{1}} \overrightarrow{\boldsymbol{F}} \cdot d \vec{r}, \int_{C_{2}} \overrightarrow{\boldsymbol{F}} \cdot d \vec{r}$ and $\int_{C_{3}} \overrightarrow{\boldsymbol{F}} \cdot d \vec{r}$ in as- cending order. (FIGURE CAN'T COPY)

Okay. Today I'm going to show you how to draw the the field. So here is the vector. Few function so the right is related by X. And why Uh huh. When you take a look you have There are points three I I Which one is the? So if I go like this way Oh, okay. So if I draw like this way, here is the X And here's why And I use the direction point to the X and J is the direction point to the why I'm sorry. Here is G And here is I So when we take a look here. So it's 0.3 I minus point for Jay and we can use another notation. Which one is 10.3? We use the bracket here, so it's a different notation. Then we we can use the application called the mathematic and we can use like the few. I think the function is the vector plot right on here. Correct her cross and you just need to. This one is so function and you choose the range X from something. And why From something. And you close the bracket. Use this one. You you put a comment in mathematics. You will get this. Thank you

In this problem of line integral. We have given A Figure. 1st, I'm showing you. So this is the figure and for each of the factor field F. So these are the vector fields we have to sketch occur for which the integral say F dot D r along the courtesy should be positive. So for this here I have made another diarrhea. I'm showing you. So this is a figured one. And now for making this to be a line integral to the positive, we have to move along the direction of vector field. So we are moving along this direction. No, for a second we have to move along the same part. So this is the direction and I'll see what I feel is here. So we have to move along this direction. And now since the rector feelings in words, so we have to move in words. So this is the direction For 1, 2, 3 and four. And now, but we in part way it is asked that for which of the factor field is it possible to make your answer of part a closed curve? That means where we can make a closed curve. Since here you can see In part one this vector field is circular, so we can make our part to be closed. So we have the first, the answer is for Graph one. And also as you can see on the left hand side here, director field here is in negative direction and here we have positive direction and as we move further say as we move further, the magnitude is increasing. So that's why we can say here, we can make our path to be closed. So here this part could be closed. Hey, the value would be still positive. So we can say for 1st and 3rd we can make the party will be closed.

In this problem of line integral. So we have to compute line integration of F dot d R along the girl. See where ski age oriented curve in the figure I'm showing you. So this is the courtesy from P to Q. Then Q two R. And then R two S. Now we have given that the vector field F is the victor Constant on each of three straight segment of courtesy. And we have given that the vector field F is so this is equals to simply I on the path pick you. And victor is equals to two. I minus day on Q R. And we have given that this is the vector field F equals three I mark. This is plus J actually plus J on odd S. So we would have to find the value of this term. So this will be the submission say currency would be the submission of the line integral own path pick you then cure than ours. So first we would have to find f dot they are along. Thank you then line integration of f dot along cuba. And then line integration of M dot d R along artist. So after dear. So this is as you can see We are moving from the origin the 00 and this point is X equals to four. And why is it close to two. So 42. And as you can see point R is equal to X equals 23 and y is equal to four and s is equals two. X is one and y is to. Now first we're moving from 00 to 42 and the doctor phillips along I. So the line integral would be contributed by only I component. So we said that the vector field PQ dot say it vector field F. There's a part peak actually my daughter product with. Yes, so pick you message four I plus today and dot product with simply I. So this is equal to simply four. So we have the value S four no from cuba from Q two are so this is will be vector QR dot product with victor. F. No, this is on I we have One minute less so that's where they would be -1. And plus do they? Plus today And don't forget to it. Mhm. F Which equals to I minus J. No when we do the dot product. So this eight equals two. To multiply with -1 which is -2 and two multiples -1. So the stage -2 -2 which is equals 2 -4. And now We are moving from this is three I plus 40 and this is I plus two. J. So we are moving from R two. S so this we will be rs dot with tariff. No When we subject it. So this way they would be too I they said -2. I this is -2 I -2. J. Dot bird with director which is three I plus jay. Now when we do the dot product. So three multiplied with minus two is minus six and minus two. Multiple weight one is equal to minus two. When we added, the city equals two minus eight. No, we have to edit. So F daughter dear, What are we? Equals 2? So we said that f dot d r would be equals two along the car. Z is equal to four minus food and minus eight, which is equals two minus eight. So we have the right answer is minus it. Yeah.

Hello students in this question we have to find the magnetic field at point C. Okay so we have the two disciples that is over and 02. Okay. And the magnetic movement of the first one is and when equals two am not and for the second one M two it is equal to 16. I'm not. So this open is situated at the actual point. So that magnetic field of even will be equals to the you know two divided by 45. And this I'm going to ever buy. These are not Q. Okay so everyone is equals to this. I am not some you not divided by four path blurb. I am not aware they are not cute. And this Magnetic field will be in the direction of the Apple movement. So this will be towards the right. Okay now talking about the magnetic field B2 which is due to the photo. So this will this is on the equatorial position. Sorry. Here we will have another factor too. Yeah. To do excel situation. Okay this is exhale, this is equatorial. So um you know to develop before by and this is um to develop our mhm dash is cute. Okay so you not divided by 45 and M. Two which is equal to 16 and not ever be our dish which is to our not so too are not to the power three. And this disciple after this magnetic field after solving is equals two mu not divided by 45. Yeah who am not where they are not cute and this will be opposed to the double movement because it is in the equatorial situation. So the net magnetic field at once, she will be equals two B one plus B two. Both are equal in magnitude. Okay? But oppose it in the direction. So the net result will be equals to zero. Okay, so this is the answer for the problem. Okay, so from the given options option C. Is the correct answer here. Thank you.


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