Curl Definition and 371 Threads

1. If a vector field has zero curl, does it always mean that it is the gradient of some scalar (potential) field? 2. If the vector field is a force field and its curl is zero does that mean that the "potential" scalar field that it is the gradient of is always some form of "potential energy"...

purpose of each of the "operators", divergence, gradient and curl? Hi. Can anybody give me a reasonably simple explanation of what the purpose of each of the "operators", divergence, gradient and curl? (I've been looking but I never found something simple to understand) I know how to evaluate...

Calculate the average value of the curl of the fluid for a rectangular path 15 cm by 10 cm, as shown in the figure (see file attachment). Va=(10i + 5j) Vb = (5i+10j) Vc= (5i + 10j) Vd = (10i + 5j) Could someone help me to get started with this one? Please :smile: Maybe give me an...

Jackson("Classical Electrodynamics", Ch.6) uses the theorem of curl of curl to separate current density into transverse and parallel, \vec J = \vec{J_p}+\vec{J_t} to say, \begin{align*}\vec{J}(\vec{x}) &= \int\vec{J}(\vec{x'})\delta(\vec{x}-\vec{x'})d^{3}x'\\ &=...

A vector field is difined by A = f(r)r. a) show that f(r) = constant/r^3 if divergence A equal to zero. b) show that curl A is alway equal to zero

A fluid rotates with an angular velocity w about the z-axis. The direction of rotation is related to the z-axis by the rigrt hand screw rule. a) Find the velocity v of a point in the fluid, and show that curl v = 2w_k b) If now w is a function of the radius r, show that curl...

I need a physical meaning about "curl" (rotational field) thanks... NOR.

To calculate the divergence of a vectorfield in cartesian coordinates, you can think of it as a dot product, and to calculate the curl, you can think of it as a cross product. But how can you calculate the div and curl when you have spherical or cylindrical coordinates, without explicitely...

Is there any neat way/rule to write: \vec B \times (\vec \nabla \times \vec A) ? I've tried it myself and found (e.g) for the x-component: \left(B_x\frac{\partial A_x}{\partial x}+B_y\frac{\partial A_y}{\partial x}+B_z\frac{\partial A_z}{\partial x}\right)-\left(B_x\frac{\partial...

Hi Guys,, i have just started to study Divergence and curl but this is not at all enetering into my mind...Pls help me out understand this...This also has Divergence and Stokes theorm ..pls help me grasp it...Thx in advance... The Divergence Theorem and Stokes's Theorem provide the...

Hi, I'm having trouble proving the following result: \int_{V} (\nabla\times\vec{A}) dV = -\int_{S} (\vec{A}\times\vec{n}) dS I'm not sure how I should Stokes' and/or the Divergence Theorem in proving this, or if you should use them at all. Thanks in advance.

I'm having a bit of difficulty with this problem: \vec{\nabla} \times \vec{G} = \vec{F} where \vec{\nabla} \cdot \vec{F} = 0 and \vec{F} = <y, z, x> . Find \vec{G} . I'm really at a loss how to solve this. I know the solution must be quick and easy because it was on a quiz. What...

If the curl of a vector field is zero, then we can that the vector field is path independent. But there are cases where this is not true, I was wondering how? Whats the explanation for this? Thanks in advance for any help. - harsh

Hi All, Given electric field E=c(2bxy,x^2+ay^2), I need to determine the constants a and b such that CURL E = 0 and DIV E = 0. I'm also given a path from (0,0) , (1,0) and (1,1). Ok so the curl = 0+0+cx(2-b) = 0 and the divergence = 2cy(b+a) = 0 How do I solve for a and b at this...

Hi, I'm looking for a clear descripion of what a curl is. From what I understand, the curl of a point in flowing water can conceptually be measured by placing the center of a paddle-wheel at the point. The vector direction is then given by the rotation axis when it spins the fastest and...

Can anyone please explain what Diverange and Curl actually physically represent on a 3d surface, i know what the operators are, but what do they actually mean? Thanks all

Can anyone explain to me the concept of div and curl? Of course, I know how to determine the div and curl of a vector, but I don't really understand their physical significance. Any help is greatly appreciated. --Brian

Curl and Surface Integral (help!) Hello people! I've been working on this problem, but I can't find how differentials of V on the left side of the equation appear. *** Show, by expansion of the surface integral, that (see attached image). Hint: choose the volume to be a differential...

Does anyone know if there is an operation that will undo a curl operation?

magnetic flux density B for an infinitely long cylindrical conductor of radius b is know: inside: B = (Mu*R*I)/(2*pi*b^2), R<b outside: B = (Mu*I)/(2*pi*R^2), R>=b I need to determine the vector magnetic potential A using only the relation B = curl A (del X A)

I'm wondering if physics ever uses a differential equation of the form of a curl of a gradient of a scalar function. Or is this too trivial? Thanks.