Question

Use the Divergence Theorem to compute the net outward flux of the field F = (3x.y. -22) across the surface S, where is the sphere {x,y,z) x+yz? = 15) The net outward flux across the sphere is (Type an exact answer, using x as needed)

Answer 1

F=234.9 -227 sphere (n?y ? 22:15) Flux ܝܬ I = JF.ds use divergence theorem I =),Fids - Juxo Edi og F 7 7 ala an 02 ) F12,4,7) 3+1 -2 so I JJJQ. du 211) du E て 2 change the integral into spharical Coordinate n=rcos & sino = 15 = r² y = usino sino nt Y + 2 12:15 z=rlos o r = 15 n² + y² + z² = 1² 0! 0 ->15 = 1 Jl dordodo $:0 20 du du ar? sino drdo do 15 ㅈ ai I = wy?sio drdo do 07:0 0-0 INTS 2 er der J.sin odol do و

2 [upya J13C.c05.07." []." [ 15 UTS IS UT5 -07 [-cost + coscos] [at-o N = 1053 x 2XQt T = 40515 486.88