Vector field Definition and 382 Threads

Question 1: solved! Question 2: Why it's zero? I think we cannot get zero unless it's an exact differential form? Many thanks.

Given 2 vectors, say x and y with a relationship of barXx-barYy (barX =1,0,0 and barY=0,1,0) calculations for the vector field in x and y plane are: Magnitude = sqrt(x2+y2) tails of vectors begin at input points (IE: if I choose 1,0 or 0,-1 etc) and the magnitudes are calcluated from these...

Hi guys, I would like to construct 2 vectors on a coordinate grid.(or a vector field for only one t) of the forces between 2 point particles on a certain moment t. Can I do that? When I try the VectorPlot function and insert all values instead of also inserting a variable it gives the error that...

the divergence and the curl of a vector field "A" are specified everywhere in a volume V. The normal component of curl A is also specified on the surface S bounding V. Show that these data enable one to determine the vector field in the region

I want to graph this vector field -^r/r^2 but I don't know how to do. Any help would be appreciated.

Hi I thought about putting this topic in physics subforum, but I think it's overall more fitting here. So, I'm having problems understanding some basic stuff, and I'm kinda embarassed. I'm an engineer and I'm trying to sort things I already know but on a more rigorous mathematic foundation...

I am trying to turn a 3D parametric equation into a vector field for an experiment, but I am not having much luck. [x,y,z]=[r*cos(u),r*sin(u),a*u] is the equation, I'm using grapher on the Mac. I want it all going in a helix, which is what the equation is for. Thanks!

Homework Statement Yeah I've been pondering over that, my book doesn't really do the justice of nailing it down for me. Does having 0 divergence means having "absolute convergence", like maybe at every point (or at a certain point) all the vectors are pointing towards a point? Like...

Homework Statement Find the work done by the force field F in moving an object from P to Q. F(x,y,z)=10y^(3/2)i+15x\sqrt{y}j P(1,1), Q(2,9)Homework Equations W = \intF dot drThe Attempt at a Solution I have no clue how to do it

Homework Statement For \mathbb{R}^{3} find the integral curves of the vector field B = xy\frac{\partial }{\partial x} - y^{2}\frac{\partial }{\partial y}. Homework Equations The Attempt at a Solution I am having a hard time understand just how to set up the differential equations in order to...

We are given a vector field: F=\frac{-y}{x^2+y^2} , \frac{x}{x^2+y^2} Then asked if F is conservative on R2 \ (0,0). I just solved the partial derivatives of each part of the vector field and they did indeed equal each other, but I don't under stand what the "\(0,0)" part means. We are then...

Homework Statement Compute the flux of the vector field, , through the surface, S. \vec{F}= 3xi + yj + zk and S is the part of the surface z + 4x + 2y = 12 in the first octant oriented upward. Homework Equations by definition from my book the integral is \intF(x,y,f(x,y)\circ<-fx,fy,1>dxdy...

Homework Statement Find the work done by the force field F(x,y) = x sin(y)i + yj on a particle that moves along on the parabola y = x^2 from (-1,1) to (2,4). Homework Equations Work = line integral of the dot product of Field vector and change in the path The path is parabola equation...

Homework Statement Let f be a vector function, f = (xz, 0, 0), and C a contour formed by the boundary of the surface S S : x^2 + y^2 + z^2 = R^2 , x ≥ 0, y ≥ 0, z ≥ 0 , and oriented counterclockwise (as seen from the origin). Evaluate the integral (Closed integral sign) f · dr , directly as...

In my book, it says that gravity can be thought of as a force in the form of this vector: F= (-GMm)/(x2+y2+z2)*u where u is a unit vector in the direction from the point to the origin. How would this be represented as a vector field (this is not a homework problem, just me wondering...)? Is...

I cannot find the meaning of the uniform vector field. I know \hat z k_x+\hat y k_y +\hat z k_z is a uniform vector field if k_x,k_y,k_z are constants. Does this means a uniform vector field: 1) Points to the same direction in all locations? 2) Have the same magnitude in all...

I'm researching General Relativity and have stumbled upon a bit of Hamiltonian mechanics. I roughly understand the idea behind the Hamiltonian of a system, but I'm utterly confused as to what the hell a Hamiltonian vector field is. I've taken ODE's, PDE's, Linear Algebra, and I'm just being...

Homework Statement I must determine whether the following vector fields have sources or vortices. 1)\vec A = (\vec x )\frac{\vec a \times \vec x}{r^3} where \vec a is constant and r=||\vec x||. 2)\vec B (\vec x )= \frac{\vec a}{r+ \beta} where \vec a and r are the same as part 1) and \beta >0...

Homework Statement Let \vec{A}(\vec{r})and \vec{B}(\vec{r}) be vector fields. Show that Homework Equations \vec{\nabla}\bullet(\vec{A}\vec{B})=(\vec{A}\bullet\vec{\nabla})\vec{B}+\vec{B}(\vec{\nabla}\bullet\vec{A}) This is EXACTLY how it is written in Ch 3 Problem 2 of Schwinger...

I have a question: hope this fits under "Calculus" topic. I am trying to embed vector graphics in my Word documents. MathCAD does this quite nicely for xy-plots, but MathCAD is awkward for constructing vector fields like those you'd find in electrodynamics. I could use Maple, but those embeds...

Find the curl of the following vector field u = yi+(x+z)j+xy^(2)k Now using the method I've bin taught similar to finding determinant of 3x3 matrix here is my answer i(2yx-1) -j(y^2) +k(0)Just looking for confirmation if this is correct or any basic errors I have made thank you.

I am just curious how you find the divergence of the following vector field Heres my example u = xz^(2)i +y(x^(2)-1)j+zx^(2) y^(3)k Am I right in thinking U take the derivative with respect to x for first term derivative with respect to y for second term... giving me...

I need to solve this general problem. Let's consider the following vector field in cylindrical coordinates: \vec{A}=-J'_m(kr)\cos(\phi)\hat{\rho}+\frac{m^2}{k}\frac{J_m(kr)}{r}\sin(\phi)\hat{\phi}+0\hat{z} where m is an integer, and k could satisfy to: J_m(ka)=0 or J_m'(ka)=0 with a real. (the...

I'm trying to figure out if a given vector field is perpendicular at the surface of a sphere of radius R. The vector field is given in spherical coordinates. I initially attempted to take the cross product of the vector field with the normal vector at the surface of the sphere to see if it was...

Homework Statement A car is driving straight southward, past a service station, at 100 km/h. The surface pressure decreaes toward the southeast at 1 Pa/km. What is the pressure tendency at the service station if the pressure measured by the car is decreasing at a rate of 50 Pa/3h? (Hint: draw...

Homework Statement [PLAIN]http://img84.imageshack.us/img84/5273/questionm.png The Attempt at a Solution How do I go about plotting this?

Homework Statement [PLAIN]http://img130.imageshack.us/img130/8540/vecx.jpg The Attempt at a Solution I've done (i). First of all Poincare's Lemma says that if the domain U of {\bf F} is simply connected then: {\bf F} is irrotational \iff {\bf F} is conservative. So for...

V_{a;b} = V_{a,b} - \Gamma^d_{ad}V_d Now take the second derivative... V_{a;b;c} = (V_{a;b})_{,c} - \Gamma^f_{ac}V_{f;b} - \Gamma^f_{bc}V_{a;f} But I have no idea how to get the parts with the Christoffel symbols. V_{a;b;c} = (V_{a;b})_{,c} - \Gamma^f_{(a;b)c}V_{af} = (V_{a;b})_{,c} -...

What is the value of a surface integral over a closed, continuous surface of a vector field of vectors normal to the surface? The integral of ndS over S. I believe the answer is zero. Can someone direct me to a proof for an aribitrary closed surface?

We can show that any vector field V:M->TM(tangent bundle of M) is smooth embedding of M, but how do we show that these smooth embeddings are all smoothly homotopic? How to construct such a homotopy?

"if a vector field has only nondegenerate zeros then the number of zeros is bounded" With no idea how to show that without using Poincare-Hopf Theorem. Any proof possible without using any concept from algebraic topology?

Homework Statement Assume the vector function A = ax(3x^{2}2y^{2})-ax(x^{3}y^{2}) a) Find \ointA\cdotdl around the triangular contour shown in Fig. 2-36 [it is a triangle with base and height of one on the x and y axis. the curl travels so that the normal vector is in the -z direction] b)...

Homework Statement You are given a vector field A= kx2 x. a. First, calculate the line integral of A from x=-2 to x=2 along the x axis. b. Next, calculate the line integral of A between the same 2 points, but use a semicircular path with a center at the origin. Recall that in cylindrical...

Assume that I know the value of \iint_{S} \overrightarrow{F} \cdot \hat{n} dS over any surface in \mathbb{R}^3, where \overrightarrow{F}(x,y,z) is a vector field in \mathbb{R}^3 and \hat{n} is the normal to the surface at any point considered. Using that I would like to compute...

Homework Statement This two-part problem is from O'Neill's Elementary Differential Geometry, section 2.5. Let W be a vector field defined on a region containing a regular curve a(t). Then W(a(t)) is a vector field on a(t) called the restriction of W to a(t). 1. Prove that Cov W w.r.t...

It's a famous claim that spin-0, spin-1 and spin-2 fields are described by scalar, vector and second-rank tensor, respectively. My question is: why not other objects? For example, consider spin-1 field, we can use a field that carries two left spinor indexes. From the group-theoretic relation we...

Here is an approach for lie derivative. And i would like to know how wrong is it. Assuming lie derivative of a vector field measures change of a vector field along a vector field, take a coordinate system, xi , and the vector field fi along which Ti is being changed. I go this way, i take the...

Homework Statement Find the Flux of the Vector Field <-1, -1, -y> where the surface is the part of the plane region z + x = 1 that is on the ellipsoid {x}^{2}+2\,{y}^{2}+{z}^{2}=1 (oriented in the +ve z direction)Homework Equations Surface Integral The Attempt at a Solution Parametrize the...

One form <-----> vector field How exactly does having a one form yield a vector field in a smooth way? I understand it's a duality relationship, but can anyone give me some more insight into this?

I got the answer! thanks for the help

Hello, I am simply looking for an argument proving the smoothness of the Reeb vector field of a given contact form. If you don't know the relevant definitions, the problem is simply this: Let M be a manifold of odd dimension 2n+1 and let \alpha be a 1-form on M such that 1) \alpha is...

The proofs I have seen that a vector field on the 2-sphere must have a zero rely on the general theorem that the index of any vector field on a manifold equals the manifold's Euler characteristic. How about this for a proof that does not appeal to this general theorem? The tangent circle...

Can line integral of a vector field ever be zero? If can, what is the interpretation of this value (0) ? Thanks.

Homework Statement (The S1 after the double integral is supposed to be underneath them btw, I just can't seem to do it right using LaTeX right now so bear with me please.) Suppose F is a radial force field, S1 is a sphere of radius 9 centered at the origin, and the flux integral...

I'm studying for a test. How do I find the flux of the vector field F = (1,1,1) down through the surface \sigma, given by z = \sqrt{x^2+y^2} and 1 < z < 2. The answer is 3pi but have no idea how to get it. I got it down to\int\int_R x+y/\sqrt{x^2+y^2} +1 dA. Now what?

Homework Statement Describe the following vector field: \bold v (\bold x)=\frac{\bold a \times \bold x}{(\bold a \times \bold x)(\bold a \times \bold x)} with \bold a = \text{constant}. Calculate its divergence and curl. In what region is there a potential for \bold v? Calculate it. Hint...

Hello. How can I show the Divergence of a vector field is a scalar field(in E^{3}) ? Should I show that Div is invariant under rotation? x^{i'}=a^{ij}x^{j},V^{'}_{i}(\stackrel{\rightarrow}{x})=a_{ij}v_{j}(\stackrel{\rightarrow}{x}) then \frac{\partial...

Homework Statement Homework Equations Given above. The Attempt at a Solution I attempted this problem first without looking at the hint. I've defined F(r) as (B+A)/2 + t(B-A)/2, with dr as (B-A)/2 dt . Thus F(r)dr = ((B+A)/2)*((B-A)/2)+((B-A)/2)^2 dt When I integrate this from -1 to 1 I...

Hi, so I scanned an image of the problem statement and my attempt at the solution. I don't know if I am headed in the right direction and need some guidance. This is my first post ever and I hope I am doing this properly. Thank you for any help you guys can provide.

Can all vector fields be described as the vector Laplacian of another vector field?