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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 volume, dx dy dz .
***
Here d(sigma) is a vector surface element, V is a vector field, and d(tau) is a infinitesimal volume element.
Well, from the right side of the equation is clear that derivatives of V will appear, but I can't do the same on the left side, where I only get components of the vector field multiplied by infinitesimal area elements.
Using the lower part of the fraction, some of these elements "disappear", but no hint of the derivatives of V appear to me. Any ideas?
By the way, is there any way to put images inside the message?
Thanks!
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 volume, dx dy dz .
***
Here d(sigma) is a vector surface element, V is a vector field, and d(tau) is a infinitesimal volume element.
Well, from the right side of the equation is clear that derivatives of V will appear, but I can't do the same on the left side, where I only get components of the vector field multiplied by infinitesimal area elements.
Using the lower part of the fraction, some of these elements "disappear", but no hint of the derivatives of V appear to me. Any ideas?
By the way, is there any way to put images inside the message?
Thanks!
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