Divergence Definition and 775 Threads

Hi everyone! I am having some trouble with this particular problem on Vector Calculus from Griffith's book. The question is: Check the divergence theorem for the vector function(in spherical coordinates) \vec v = r^2\cos\theta\hat r + r^2\cos\phi \hat \theta - r^2\cos\theta\sin\phi\hat...

Why does the series of 1/n! diverge in the p-adic metric?In other words, how do I show that the lim of 1/n! (in the p-adic metric) does not equal 0 because it is >1

Im having a bit of a problem understanding the crucial part of the divergence theorem from Electromagnetic Fields and Waves by Lorrain and Corson. Ill try descibe the set up of the problem 1st and see if anyone can help me in any way before i continue with the electromagnetism course I am doing...

so we know that the divergence theorm, was proved by Gauss, and also proved by ostrogradsky. but infact, the divergence theorm was discovred by Lagrange...correct? now, did these 3 guys prove it differently? I'm sure it couldn't be exactly the same way right? basically, I've been...

Given a vector field: \vec F= (x^2-xy)\hat x +(y^2-yz)\hat y +(z^2-xz)\hat z Find the conditon for the divergence to be equal to zero.

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.

1+(1/2)+(1/3)+(1/4)+(1/5)...+(1/n) can sum one prove this series is divergent? or just tell me what the expression for sum to infintiy in terms of n is?

Hi, I'm doing a problem of finding the divergence of a radius vector from the origin to any point in Cartesian, cylindrical, and spherical coordinates. The answers look kind of strange to me. I just want to make sure what I did was correct. To find: \nabla\cdot \vec{r} Cartesian: r = (x...

Something we did in electrostatics that's a source of confusion for me: We learned to use caution when taking the divergence of the (all important) radial vector field: \vec{v} = \frac{1}{r^2} \hat{r} Applying the formula in spherical coords gave zero...a perplexing result. The...

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...

I want to find which values of n make the vector field \underline{F} = {|\underline{r}|}^n\underline{r} solenoidal. So I have to evaluate the divergence of this vector field I think, then show for which values of n it is zero? Im starting by substituting: \underline{r} = \sqrt{x^2...

I have \sum_{n=1}^\infty{\frac{1}{n^2+n+1}} and I need to show that it converges or diverges. I choose to do the comparison test making A_n=\sum_{n=1}^\infty{\frac{1}{n^2+n+1}} and B_n=\sum_{n=1}^{\infty}\frac{1}{n^2+n} so far so good? Okay well \lim_{n\rightarrow0}B_n=0 so does A_n...

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...

I'm not sure why this question comes to mind now, since I haven't had an E&M class for a few months now, but nonetheless. Place some charge at the origin. Surround the charge with a spherical Gaussian surface and calculate the surface integral. You obviously get a non-zero result(Gauss's...

ok this probley seems simple but i just need to see how to do it, ok well how do u evaluate this... find the flux of the vector field... \vec{F}=<x,y,z> throught this surface above the xy-plane.. z = 4-x^2-y^2 how do u evaluate this with surface integrals method and the divergence...

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

Could I get a demonstration of why they are the same? I have the two equations which the two theorems reduce to in two dimensions, and it's pretty tantalizing because they are virtually the same, but differ in a nice symmetrical way. But I can't for the life of me show that they are the same (I...

I have read that you can limit the divergence of a laser by sending it backwards through a telescope. I have not yet been able to do this with my telescope, but seem to have some success using less powerfull lenses. Would anyone be willing to help me conduct this expiriment. The problem I am...

Hi! We are nearing the end of our course --- culminating in Stokes and Divergence Theorems for surface integrals, and I am having some difficulty with the following 1. F(x,y,z) = <x^3y, -x^2y^2, -x^2yz> where S is the solid bounded by the hyperboloid x^2 + y^2 - z^2 =1 and the planes z...

I was wondering if someone could give me a hand here with 2b) on the following link. http://www.am.qub.ac.uk/users/j.mccann/teaching/ama102/2003/assignments/assign_8.pdf For part a) I got it to be equal to 3x^2+3y^2+3z^2+2y-2xy, and I'm hoping that's right! However, for part b) I can't...

Hey there, one of our h/work questions is to prove that a certain sequence is divergent, where xn=(-1)^n for every natural n. I started off by assuming that it was infact convergent so wrote that mod(xn/l)<e where e is any real number greater than zero, and this holds for any n>no. But from...

I need help evaluating both sides of the divergence theorem if V=xi+yj+zk and the surface S is the sphere x^2+y^2+z^2=1, and so verify the divergence theorem for this case. Is the divergence theorem the triple integral over V (div V) dxdydz= the double integral over S (V dot normal)dS? If so...

I need help evaluating both sides of the divergence theorem if V=xi+yj+zk and the surface S is the sphere x^2+y^2+z^2=1, and so verify the divergence theorem for this case. Is the divergence theorem the triple integral over V (div V) dxdydz= the double integral over S (V dot normal)dS? If so...

hi. how can I prove that if A is a converges and B diverges that the Sum of these series (A +B) diverges.. ( A = a1 + a2 + a3 + ... B = b1 + b2 + b3 + ...) if the series start from n=1