Question

Find the upward flux of F vector=<x,y,z> across: a. x^2+y^2+z^2=1, z$\geq$0 and b. z=1-x^2-y^2, z$\geq$0.

Please be detail thanks.

Answer 1

ZI-Xy? ñ ( x +49-2-1) (xy-- 220, 26, Jacahay?) IT Fiña <a, y, z). <28, 29,17 202 + y ²) #2 नाये Jumtah+T s Fonds = SS (Fin) dady inal SS (2 (2²4 y2) + 2) dady. 2² y 21 st 42 (9179)1- (alty2)dn dy. Is (+ y² + 1) dady, ehtyzl into r=0 8-o polar - 211 S...?" (8²+1) r drdo (changing coordinates) s (rar) dr. [ + ]= required flux, 21 211 3 3 42 is the 2 Note: This can be done using "Grauss divergence theorem". It might be easy to do using divergence theorem. (Try it !!!)

= (x, y, z). unit normal on the hemisphore, bety+221,2>,0 ū (x+y +224) 117 () 22x, 24, 227 √ Q x 1764 gr +(2212 & Luy, z) Flux IS (7.5) de IS (<2,0, 2), (2, 4, 28) dx dy Z SS (Sty?4 p? Woudy SI n²ty 2 y 2 + (1 - 22 y 2) V - Cattyh] du dy = ss I paliny Indy, put, a= reaso, y=rsino 20 rder do. ( -12 00 0 rdr vingt d (1-83 1 -82 1 250g +7 21.
Hey!!! You can also use the divergence theorem to evaluate the flux.I am suggesting you to attempt it using Gauss divergence theorem. Thank you