Recent content by advphys

That is right. I didn't think using that for cross product. After that I can use (a) to prove the given relation. It seems this was a little bit dummy question. Thank you very much!

Homework Statement The problem is given in the following photo: Actually I did the first proof but I couldn't get the second relation. (Divergence of E cross H). Homework Equations They are all given in the photo. (a) (b) and (c). The Attempt at a Solution What I tried is to interchange...

Hmm, ok. I choose as F= Fx i + 0j+0k ∇.F=Fx then the right side becomes also integration of (Fx ds sub x) so, for the x component i think i can say ∇ψ=Fx but here ∇ψ is a vector quantitiy but Fx is scalar now. How could it be?

Hi to all Homework Statement ∫∫∫∇ψdv = ∫∫ψ ds over R over S R is the region closed by a surface S here dv and ψ are given as scalars and ds is given as a vector quantitiy. and questions asks for establishing the gradient theorem by appliying the divergence theorem to each component...

ok, drawing the region, transforming into volume integral and subtracting three additional surface integrals; i finally found 3/4 with only pencil and paper. thanks anyway.

Hmm, ok then, thanks.

Hi to all, Homework Statement Evaluate the surface integral of the vector F=xi+yj+zk over that portion of the surface x=xy+1 which covers the square 0≤x≤1 , 0≤y≤1 in the xy plane Homework Equations ∫∫F.ndσ n=∇g/|∇g| maybe transformation to the volume integral The Attempt at a...

Homework Statement ∫∫∫∇.Fdv over x2+y2+z2≤25 F= (x2+y2+z2)(xi+yj+zk) Homework Equations ∫∫∫∇.Fdv = ∫∫ F.n dσ n=∇g/|∇g| The Attempt at a Solution g(x,y,z)=x2+y2+z2-25 taking the surface integral and replacing all (x2+y2+z2) with 25 i got 125 * ∫∫ dσ = 12500π But...

Oh, yes. Definitely. Thanks a lot, i got that.

Because i may not know any other identity. :D I thought for (ψv)k term i may have one more levi civita symbol.

Homework Statement prove, ∇x(ψv)=ψ(∇xv)-vx(∇ψ) using levi civita symbol and tensor notations Homework Equations εijkεimn=δjnδkm-δknδjm The Attempt at a Solution i tried for nth component εnjk (d/dxj)εklm ψl vm εknjεklm (d/dxj) ψl vm using εijkεimn=δjnδkm-δknδjm...

ok from there, ajcjbkdk-ajdjbkck and i assume, similar form can be obtained for j and k components by just replacingg j s with k s, i s with j s and k s with i s. And in total i have 6 terms, 2 terms from each component. Am i right? But, on the right had side i think i should have more...

Ok, thanks, in future i will be more careful. What about the dot product on the left side, how can i use Levi Civita symbol to represent it. Actually, the identity that you wrote and the cross product representation are all i know about the Levi Civita symbol but i couldn't use them.

Dear all, Any idea for the proof of the Lagrange's identity using tensor notations and Levi Civita symbol? (a x b).(c x d)=(a.c)(b.d) - (a.d)(b.c) x: cross product a,b,c,d: vectors Thanks

Thanks for replies. But still can't figure out how to conclude the last scalar triple product gives 0. Edit: I got that it is obvious. I have the same vector in both parts. Again thank you for your help.