Flux integrals - determining dS for a tetrahedron

[deheerbeer]

Hello heroes,

I have been trying to wrap my head around this exercise for the last two days.


I understand everything, except one vital part.



For s4, why is dS given by ? Why is the dot product of N^chosen with j here?

I must admit my understanding of dS is not thorough, but that is the objective of such exercises.

Thank you for your help.

 

[LCKurtz]

I think it is just a typo. On [MATH]S_4[/MATH] you have [MATH]\vec F \cdot \hat N = \frac{x + 2z}{\sqrt{14}}[/MATH], so it will be easiest to express [MATH]dS[/MATH] in terms of [MATH]x[/MATH] and [MATH]z[/MATH]. So the line should just read [MATH]dS = \frac{dxdz}{|\hat N \cdot j|} =\frac{\sqrt{14}} 2 dxdz[/MATH]. Not sure why the line is repeated twice nor why they try to include x and y.

 

[deheerbeer]

I think it is just a typo. On [MATH]S_4[/MATH] you have [MATH]\vec F \cdot \hat N = \frac{x + 2z}{\sqrt{14}}[/MATH], so it will be easiest to express [MATH]dS[/MATH] in terms of [MATH]x[/MATH] and [MATH]z[/MATH]. So the line should just read [MATH]dS = \frac{dxdz}{|\hat N \cdot j|} =\frac{\sqrt{14}} 2 dxdz[/MATH]. Not sure why the line is repeated twice nor why they try to include x and y.

Thank you so much for your reply. I could not wrap my head around why they chose to include y here.