Curl Definition and 371 Threads

Homework Statement I have a field w=wφ(r,θ)eφ^ (e^ is supposed to be 'e hat', a unit vector) Find wφ(r,θ) given the curl is zero and find a potential for w. Homework Equations I can't type the matrix for curl in curvilinear, don't even know where to start! I've been given it in the form...

Dear All, I am studying electrodynamics and I am trying hard to clearly understand each and every formula. By "understand" I mean that I can "truly see its meaning in front of my eyes". Generally, I am not satisfied only by being able to prove or derive certain formula algebraically; I want to...

Homework Statement Prove that the vector field F = (2xyz + 1, x^2 z, x^2 y) is irrotational. Find the potential φ associated with F (i.e. find the function φ for which ∇φ = F). Homework EquationsThe Attempt at a Solution I figure for the first part I just calculate the curl, but for the...

Is the time derivative of a curl commutative? I think I may have answered this question... Only the partial time derivative of a curl is commutative? The total time derivative is not, since for example in cartesian coordinates, x,y,and z can themselves be functions of time. In spherical and...

Homework Statement Proove it Iam supposed to change coordinate system, and proove that the result depends on coordinate system. The Attempt at a Solution My attempt was to start from definition of cross product using levicivita. I already prooved that divergence of a vector is a scalar. But...

Hi all, I am very confused on how to define the vector product or cross product in a physical sense. I know the vector product is a psuedovector, and that it is the area of a parallelogram geometrically. However, I know it used used to describe rotation in physics. As with torque, magnetism and...

Homework Statement }[/B] Find the divergence and curl of the vector field \vec{V}=x^2y \hat{i} + xy^2 \hat{j} + xyz \hat{k} then for both, evaluate them at the point \bar{r} = (1,1,1) Homework Equations div(\vec{F})= \nabla \cdot \vec{F} \\ curl(\vec{F})= \nabla \times\vec{F} The Attempt...

Homework Statement Working in Cartesian coordinates (x,y,z) and given that the function g is independent of x, find the functions f and g such that: v=coszi+f(x,y,z)j+g(y,z)k is a Beltrami field. Homework Equations From wolfram alpha a Beltrami field is defined as v x (curl v)=0 The Attempt...

Hi, I'm trying to determine ##\vec{\bigtriangledown }\times \vec{a}## , where ##\vec{a}=\vec{\omega }\times \vec{r}##, being ##\vec{\omega }## a constant vector, and ##\vec{r}## the position vector, using this definition: ##\vec{curl}(\vec{a})=\lim_{V\rightarrow 0}\frac{1}{V}\oint...

Hello, I'm having some difficulty with a conceptual question on a practice test I was using to study. I have the answer but not the solution unfortunately. 1. Homework Statement "For every differentiable function f = f(x,y,z) and differentiable 3-dimensional vector field F=F(x,y,z), the...

I am thinking about the curl of the electric field and want to make sure I have something straight: Say you have a charged particle moving along some prescribed path. The electric field propagates outward at speed c, leading to a "retarded" time that you need to calculate in order to get the...

Homework Statement There is a sphere of magnetic material in a uniform magnetic field \vec H_0=H_0\vec a_z, and after some calculations I got the magnetic moment vector \vec M_0=M_0\vec a_z, where M_0 is something that isn't important to my question. I am unsure if this magnetic moment vector...

I'm trying to become reacquainted with basic electromagnetics. From my understanding a changing magnetic field induces a changing electric field and visa versa, through the equation: $$ \overrightarrow{\bigtriangledown } \times \overrightarrow{B} = \mu_{0} \left [ \widehat{J} + \varepsilon _{0}...

Hello, I am a beginner in electromagnetism. I am trying to find a vector field whose rotation equals 1 with a curl operator. If I say that the vector field is defined by V(y;2x;0) does it work? As a result, I find (0;0;1), am I right?

Two quick questions. Does the Coriolis effect mean that in the northern hemisphere the curl will always have a negative value and in the southern hemisphere a postive one? Is the curl in the eye of the cyclones equal to zero? Thanks.

Homework Statement Use the LC symbol to calculate the following: $$\nabla \times \frac{\vec{m} \times \hat{r}}{r^2}$$ Where ##\vec{m}## is just a vector, and ##\hat{r}## is the unit radial vector and ##r## is the length of the radial vector. Homework Equations On the Levi Civita symbol...

Homework Statement A.) Show that \epsilon_{ijk}A_{k,j} represents the curl of vector A_k B.) Write the expression in indicial nottation: \triangledown \cdot \triangledown \times A 2. The attempt at a solution I'm hoping that if I can get help on part A.) it will shed light on...

i really lost with this. i see two possibilities: (1) something like, \epsilon_{abc}\partial_{a}A_{b}e_{c} with a,b,c between 1 and 5 or (2)like that \epsilon_{abcde}\partial_{a}A_{b} one of the options nears correct? thank's a lot

According to wikipedia, "The moving magnet and conductor problem", I stopped at the equation shown in the attachment. It said that the curl of the E` ( electric field in the frame of the conductor) is equal to minus of the dot product of the velocity of the conductor and the del multiplied by...

Hi, Could someone please guide me with this question? I'm unsure as to what the curl has to do with finding flux.. PS. This isn't actually assessed work, it's from a past question paper that I am using to revise. Thanks heaps!

please go to "Wolfram Alpha" website, (google the term) and copy paste the following formula: curl ( (-y/(x^2+y^2), x/(x^2+y^2), 0) you can see the result is zero I think that's the expression of H surrounding a current. what am I missing?

Here's the setup: I'm trying to write a PHP script to spam my buddy's website. He has given me full permission to try and do so. I have a very rudimentary understanding of HTTP protocols and am probably doing something wrong, because my attempt hasn't been working. Here's my PHP script...

Hey pf! I was thinking about how div(curl(f)) = 0 for any vector field f. However, is this true for div and curl in spherical coordinates? It doesn't seem to be. If not, what needs to happen for this to be true in spherical coordinates?? Thanks all!

Umm what just happened? I understand as far as u=x+y and v = y/x and when he does the 2d curl. What I don't get is the step thereafter when he flips it. How does he know to flip it? Further, when he flips it wouldn't that make the dvdu inside the integral cancel and hence leave him with dxdy?

If the direction of the gradient of f in a point P is the direction of most/minor gradient, so a direction of the curl of f in a point P is the direction of most/minor curl too, correct? Also, if the gradient of f in the direction t is given by equation: ∇f·t, so the curl of f in the...

hey pf! i have a few question about the physical intuition for divergence, gradient, and curl. before asking, i'll define these as i have seen them (an intuitive definition). \text{Divergence} \:\: \nabla \cdot \vec{v} \equiv \lim_{V \to 0} \frac{1}{V} \oint_A \hat{n} \cdot \vec{v} da...

Vector, by definition, have 2 or 3 scalar components (generally), but the curl of a vector field f(x,y) in 2D have only one scalar component: \left ( \frac{\partial f_y}{\partial x} -\frac{\partial f_x}{\partial y} \right )dxdy So, the Curl of a vector field in 2D is a vector or a scalar?

Homework Statement For some reason I can't find anywhere online that gives a good example of the curl of a vector function in spherical coordinates. I need to compute ∇ X A where A = \frac{ksinθ}{r^{2}}\widehat{ϕ} If anyone can point me in the right direction of a good video or text...

Hello, I'm a bit stuck with a case in which the curl gives a vector that does not transform under rotation. As an example, let's have a field with only \hat{x} direction (but this does not mean that it's a scalar field!). The field has this expression: F(x,y,z)=...

Homework Statement Evaluate ∇ x \overline{F}, with \overline{F}(\overline{r}) = \overline{r}lnr, where \overline{r} = (x; y; z) is the position vector and r is the modulus of the position vector. Homework Equations The curl of a vector The Attempt at a Solution I recognise I am...

If I can compute the divergence over an closed curve (or an area) and too over an closed surface (ie, an volume) so I can, actually, to compute the divergence over a n-manifold. \nabla \cdot \vec{F} = \lim_{\Delta V → 0} \frac{1}{\Delta V} \oint_{S} \vec{F} \cdot \hat{n} dS\nabla \cdot \vec{F}...

Is correct to affirm that: | \nabla \times \vec{f} | = \nabla \times \vec{f} \cdot \hat{n}? I asked thinking in this definition: http://en.wikipedia.org/wiki/Curl_%28mathematics%29 Ie, if the affirmation above is correct, so, is correct to express the definition aboce as...

So i was wondering how the curl of the magnetic field is derived since Feynman just introduces it from nothing in his second volume of Feynman's lectures on physics: c2∇xB=j/ε0 or the other one where ∇x B=μ0j

Hellow! I'd like to know what results the curl and divergence of unit vectos bellow: https://www.physicsforums.com/attachment.php?attachmentid=65279&stc=1&d=1388593339 I just know that ∇·x = 0 ∇·y = 0 ∇·z = 0 ∇×x = 0 ∇×y = 0 ∇×z = 0

Hello, Its been sometime since I touched calculus so some concepts seem to evade me. I understand all the related maths but can't seem to make an intuitive sense of the curl in this case. Green's theorem relates the line integral of a closed curve to the double integral of the curl of the...

Homework Statement Given a vector field F=-y/(x^2+y^2) i +x/(x^2 +y^2) Calculate the curl of it the line integral of it in a unit circle centered at O Homework Equations The Attempt at a Solution I calculated that the curl is 0 but the line integral is 2π. I don't think this...

I need help understanding the significance of curl and divergence. I am nearly at the point where I know how to use Greene's, Stokes and the divergence theorems to convert line, surface, and iterated double and triple integrals. I know how the use the curl and div operators and about...

I posted the divergence of this earlier but thought I should post the curl separately. Homework Statement Find the curl of ##E=-Cx\hat{z}## Homework Equations...

Homework Statement I have a problem that is the curl of jln(rsinθ) Since this is in spherical, why is there a bold j in the problem? Doesn't that indicate it's a unit vector in cartesian coordinates? Can I do the curl in spherical coordinates when I have a cartesian unit vector in the...

Can anyone give me an intuitive/physical reason for why the divergence of the curl of a vector field is always zero? I know various methods to prove mathematically that it is so, but have not managed to find a physical reason. In other words, why is the curl of a vector field always incompressible.

If ∇ x v = 0 in all of three dimensional space, show that there exists a scalar function ##\phi (x,y,z)## such that v = ∇##\phi##. (from Walter Strauss' Partial Differential Equations, 2nd edition; problem 11; pg 20.) I'm not really sure where to begin with this problem. I asked a few of my...

I am asked to compute the Curl of a vector field in cylindrical coordinates, I apologize for not being able to type the formula here I do not have that program. I do not see how the the 1/rho outside the determinant calculation is being carried in? Not for the specific problem - but for...

Homework Statement Explain whether the divergence and curl of each of the vector fields shown below are zero throught the entire region shown. Justify your answer.https://sphotos-a-ord.xx.fbcdn.net/hphotos-prn2/1185774_4956047513788_517908639_n.jpg Homework Equations N/AThe Attempt at a...

First, this is my first time actually posting anything so hi PF!Second, I have been working out of Div, Grad, Curl and all that. This problem has me stumped for some reason. My answer never comes out to be the same as the books. If you could help me figure out where I am going wrong I would...

Hi PF-members. My intuition tells me that: Given a divergence free vector field \mathbf{F} , then the curl of the field will be perpendicular to field. But I'm having a hard time proving this to my self. I'know that : \nabla\cdot\mathbf{F} = 0 \hspace{3mm} \Rightarrow \hspace{3mm}...

Let ##v(x,y)## be function of (x,y) and not z. \nabla v=\hat x \frac{\partial v}{\partial x}+\hat y \frac{\partial v}{\partial y} \nabla \times \nabla v=\left|\begin{array} \;\hat x & \hat y & \hat z \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z}\\...

Let ##\vec {F}(\vec {r}')## be a vector function of position vector ##\vec {r}'=\hat x x'+\hat y y'+\hat z z'##. I want to find ##\nabla\cdot\frac {\vec {F}(\vec {r}')}{|\vec {r}-\vec{r}'|}##. My attempt: Let ##\vec {r}=\hat x x+\hat y y+\hat z z##. Since ##\nabla## work on ##x,y,z##, not...

Let ##\vec {F}(\vec {r}')## be a vector function of position vector ##\vec {r}'=\hat x x'+\hat y y'+\hat z z'##. Question is why: \nabla\cdot\vec {F}(\vec{r}')=\nabla\times\vec {F}(\vec{r}')=0 I understand ##\nabla## work on ##x,y,z##, not ##x',y',z'##. But what if \vec {F}(\vec {r}')=\frac...

Griffiths's proof of Ampère's Law was probably one of the ugliest things I've seen. All that product rule, integration by parts and what not, really could have brought tears to the eyes of ANY man. I mean, have you LOOKED at this? GAAAAH it's terrible, really, terrible. The simple statement...

I've been reading Griffith's "Introduction to Electrodynamics" and I've got to this part where it says: "When you are asked to compute the electric displacement, first look for symmetry. If the problem exhibits spherical, cylindrical, or plane symmetry, then you can get \vec{D}directly from...