Vector field Definition and 382 Threads

Homework Statement Consider the vector field: F = r/r3 where r = xi + yj + zk Compute the flux of F out of a sphere of radius a centred at the origin. Homework Equations The Attempt at a Solution Hi everyone, I have: flux = \intF.dA I can't use Gauss' Law, because the...

Homework Statement Consider the vector field \vec F=\frac{\vec r}{r^3} with \vec r =x\hat{i} +y\hat{j} +z\hat{k} Compute the flux of F out of the box 1\leq x \leq 2, 0\leq y \leq 1, 0\leq z \leq 1 Homework Equations I can't use the Gauss divergence theorem since the divergence of...

Homework Statement Consider the vector field \vec F=\frac{\vec r}{r^3} with \vec r=x\hat{i}+y\hat{j}+z\hat{k} . Compute the flux of \vec F out of a sphere of radius "a" centred at the origin. Homework Equations The Gauss Divergence Theorem \int_D dV \nabla \bullet F=\int_S F\bullet dA...

HI I was a under a little confusion about vector field. Consider velocity field of fluid flow: V = u i + v j + w k here V is vector and consider a cap over i, j, k (since they represent x,y,z directions) now we know that u,v,w are functions of x,y,z,t. This is where i am confused...

Hi, I'm trying to compute the gradient tensor of a vector field and I must say I'm quite confused. In other words I have a vector field which is given in spherical coordinates as: \vec{F}=\begin{bmatrix} 0 \\ \frac{1}{\sin\theta}A \\ -B \end{bmatrix} , with A,B some scalar potentials and I...

My calculus book states that a vector field is conservative if and only if the curl of the vector field is the zero vector. And, as far as I can tell a conservative vector field is the same as a path-independent vector field. The thing is, I came across this...

I have been trying this problem for multiple hours now, and cannot figure out what I am doing wrong. --Calculate the flux of the vector field F(vector)= 5i + 8j through a square of side 2 lying in the plane x + y + z = 20 oriented away from the origin. I realize that I need the integral...

Homework Statement This is an example in my book, and this is the information in the question. Find the work done by thr force field F(x,y) = (1/2)xy[B] i + (1/4)x^2 j (with i and j vectors) on a particle that moves from (0,0) to (1,1) along each path (graph shows a x=y^2 curve from (0,0)...

Homework Statement Calculate the outward flux of the two dimensional vector field f:\Re^{2}\rightarrow\Re^{2} , f(x,y)=(x/2 + y\sqrt{x^{2}+y^{2}},y/2 + x\sqrt{x^{2}+y^{2}}) through the boundary of the ball \Omega = {(x,y)\in\Re^{2} \left| x^{2}+y^{2} \leq R^{2}} \subset\Re^{2}, R>0...

First I want to greet everyone because I am new here. I have attended to applied electromagnetic course which seems to be pretty hard to understand and issues came up at very first time after I went at calculations. I try to explain this as good as possible. 1. Vectorfield F(x,y,z) =...

Homework Statement verify Stokes's theorem for the given surface and vector field. S is defined by x^2 + y^2 + z^2 = 4, z <= 4, oriented by downward normal; F = (2y-z, x + y^2 - z, 4y - 3x) Homework Equations double integral over S of the curl F ds = integral over S' of F ds...

Homework Statement I'm supposed to sketch the vector field and verify that all the vectors of the following equation have the same length.Homework Equations G(x,y) = \frac{-iy + jx}{\sqrt{x^2+y^2}}The Attempt at a Solution If I start plugging in numbers, for example the point (1,1) into...

Ok so I'm new to vector analysis, just started about a week or 2 ago. I'm using Paul C. Matthews' book, "Vector Calculus". This is an example problem from it which I have difficulty understanding because of integration with partial derivatives. The problem is solved, I just have trouble...

Not exactly a homework problem, a problem from a sample test. I'm boning up for my qualifying exam. Homework Statement Consider the vector field: F = (ax + by)i + (cx + dy)j where a, b, c, d are constants. Let C be the circle of radius r centered at the origin and going around...

I am in real need for a graphical application with 3d plotting capabilities. I need to plot some particles given their space coordinate. This has been well managed using VMD. But i am clueless how to plot associated velocity vector with particles. So basicall i am looking for to plot velocity...

Two problems one that I have some idea about solving, the other I have no idea at all about where to start. 1. Find the surface integral of E . dS where E is a vector field given; E = yi - xj + 1/3 z3 and S is the surface x2 + z2 < r2 and 0 < y < b Well Gauss' theorum would be the place...

Homework Statement http://img245.imageshack.us/img245/2353/87006064.th.jpg I need to find the unit vector in the direction of \vec{F} at the point (1, 2, -2). Homework Equations The Attempt at a Solution well first of all I need to find what F is right, which is gradf.. how can I get...

Homework Statement Find the flux of the vector field through the surface of the closed cylinder of radius c and height c, centered on the z-axis with base on the xy-plane. Homework Equations The Attempt at a Solution Can I just use the divergence theorem here? Find the...

Homework Statement http://img16.imageshack.us/img16/9926/fluxs.th.jpg Homework Equations The Attempt at a Solution I really don't know how to solve this, can anyone help me please?

Homework Statement http://img5.imageshack.us/img5/8295/capturewmw.th.jpg Homework Equations The Attempt at a Solution I tried to find the curl first and what i got is y - 3 and then I multiply that by the area of the circle which is 4pi.. am I doing something wrong?

Homework Statement I just need to be able to change a vector field from spherical to cartesian The question is about verifying stokes theorem (curl theorem) for a given vector field within and on a given path. It says not to use spherical coordinates, but the vector field is given in...

Homework Statement div(J)=0 in volume V, and J.n=0 on surface S enclosing V, where n is the normal vector to the surface. Show that the integral over V of J dV is zero. Homework Equations The Attempt at a Solution I can't get anywhere with it! The divergence theorem doesn't...

Homework Statement Given the vector field F=3x^2i-y^3j, show that the flux over any two curves C1 and C2 going from the x to the y axes are the same. Homework Equations Flux = int(F dot n ds) = int(Mdy - Ndx) divF = Ny + Mx The Attempt at a Solution We can show the divergence of...

Hello. I am stuck trying to find an understandable answer to this online: Carry out the following operations on the vector field A reducing the results to their simplest forms: a. (d/dx i + d/dy j + d/dz k) . (Ax i + Ay j + Ax k) b. (d/dx i + d/dy j + d/dz k) x (Ax i + Ay j + Ax k) I...

Hi, How do integrate this? I wish to see it step by step and I'm glad for any help i can get. \int_{ \vec{r}\in{A}} \frac{ \vec{v}+ \vec{\omega}\times\vec{r}}{| \vec{v}+ \vec{\omega}\times\vec{r}|}d^{2}r where A is area of disk with radius R.

Homework Statement For what value(s) of the scalar 'a' is the vector field F(x,y,z)= 2xz i + ay^3 j + (x^2 + y^4) k conservative The Attempt at a Solution F1=2xz F2=ay^3z F3=(x^2 + y^4) I used 3D curl test?? 1)(partial F2)/(partial dx) - (partial F1)/ (partial dy)= 0-0 =...

How do you prove if a vector field is conservative or if it isn't conservative? For example, if we have the vector field F(x, y, z) = x^2yz ı + y  + x^2 k, how do we find out if it is conservative or not conservative?

Homework Statement Find \int\int_{S} F dS where S is determined by z=0, 0\leqx\leq1, 0\leqy\leq1 and F (x,y,z) = xi+x2j-yzk. Homework Equations Tu=\frac{\partial(x)}{\partial(u)}(u,v)i+\frac{\partial(y)}{\partial(u)}(u,v)j+\frac{\partial(z)}{\partial(u)}(u,v)k...

Can somone remind me how to see that the Lie derivative of a vector field, defined as (L_XY)_p=\lim_{t\rightarrow 0}\frac{\phi_{-t}_*Y_{\phi_t(p)}-Y_p}{t} is actually equal to [X,Y]_p?

Hi all, I'm new to the forums so if i do something stupid don't hesitate to tell me. Anyway I'm struggling with this problem: I could do part a ok, but part b has me stumped, I am in the second year of a physics degree and this is a from a maths problem sheet, i haven't done line...

Homework Statement if a vecor A is both solenoidal and conservative; is it correct that A=-▼Φ that is A=- gradΦ Φ is a scalar function thanks

Hello, I am having a lot of trouble finding a definition of a flow generated by a vector field. I can't seem to find a good definition anywhere. I only need a basic definition, and a basic approach to calculating the flow generated by a vector field. For example, Let U = R2 , x = x(u, v, 0)...

The JGM3 model of Earth's gravity is expressed in the form of coefficients C and S to Legendre polynomials in r, theta and phi which give the gravitational potential U = \sum\sum CV + SW Can anyone tell me the algorithm for calculating acceleration vector g(r, theta, phi) from the...

Hello I am trying to get my head around what the divergence actually represents physically. If you have some vector field v, and the components of v, vx, vy, vz have dimensions of kg/s ("flow" - mass of material per second) the divergence will have units of kg/(s*m) (mass per time distance)...

Homework Statement A vector field is defined by A=f(r)r a) show that f(r) = constant/r^3 if \nabla. A = 0 b) show that \nabla. A is always equal to zeroHomework Equations divergence and curl relationsThe Attempt at a Solution I tried using spherical co-ordinates to solve this. But I am not sure...

How to plot this vector field on a graph \stackrel{}{\rightarrow} V=(xi+yj+zk)/\sqrt{}(x^2+y^2+z^2)

Homework Statement Write a vector field equation which describes fluid flowing around a pipe of radius r whose axis is a circle of radius R in the (x,y)-plane. Homework Equations x2+y2=r2 Equation of a torus? The Attempt at a Solution What I've gathered from the question: the pipe...

Homework Statement I have this vector field equation, the first part of the question is to find the potential equation for it, I found it. The second part of the question is to find the work of the field through this path. My idea is to plug t in the r equation, because I'm not sure but I...

Dear forum-members, Pestered by many (in my opinion, fundamental) questions and no literature at hand to answer them, I resort to posing my questions here. Let me start with the following. (Hopefully I have the correct subsection.) I am inspecting a dynamical, autonomous and conservative...

Homework Statement I need to find the flux of this vector field (in the pic) that goes through this plan (in the pic) and z goes from 0 to 1. How am I suppose to do that? Homework Equations The Attempt at a Solution

Homework Statement A 160-lb man carries a 25-lb can of paint up a helical staircase that encircles a silo witha radius of 20 ft. If the silo is 90 ft high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top...

Homework Statement I need to find the flux of the vector field F through S (in the pic), when S represent the edges of a cube. My question is, how do I find N (normal)? Do I need to split the curb and to find the flux through each face?Homework Equations The Attempt at a Solution

[SOLVED] Potential function for conservative vector field Homework Statement Find a potential function for the conservative vector field F = <x + y, x - z, z - y> [/color] 2. The attempt at a solution OK, we know that (1) fx = x + y (2) fy = x - z og (3) fz = z - y We...

I don't even know where to start this one. I can do all the other problems in the section, but this one makes no sense

Homework Statement It can be shown that the line integral of F = xj around a closed curve in the xy - plane, oriented as in Green's Theorem, measures the area of the region enclosed by the curve. (You should verify this.) Use this result to calculate the area within the region of the...

Is it possible to have a tangent vector field on the unit 2-sphere x^2+y^2+z^2 =1 in 3D which vanishes at exactly one point? By the Poincare-Hopf index theorem the index of such vector field at the point where it vanishes must be 2. Is that possible? If yes, can one write an explicit formula...

Homework Statement Compute the flux of vector field (grad x F) where F = (xz+x^2y + z, x^3yz + y, x^4z^2) across the surface S obtained by gluing the cylinder z^2 + y^2 = 1 (x is > or eq to 0 and < or eq to 1) with the hemispherical cap z^2 + y^2 (x-1)^2 = 1 (x > or eq to 1) oriented in...

Can anyone tell me whether or not the divergence theorem requires a conservative vector field? On a practice exam my professor gave a vector field that was nonconservative (I checked the curl) and proceeded to perform the divergence theorem to find the flux. On one of my homework problems I...

Homework Statement Picture is attached. I am trying to find the work done by F (gradient vector field) in moving an object from point A to point B along the path C1. Homework Equations Work = the line integral of F along the curve C of F dot dr. The Attempt at a Solution Just...

Homework Statement Suppose that the isotherms in a region are all concentric spheres centered at the origin. Prove that the energy flux vector field points either toward or away from the origin. Homework Equations J = - k (del)T The Attempt at a Solution so I know that -(del)T is...