radius-r-circle-x-2-y-2-z-2-r-2-F-x-y-z-yze-1-xe-2-xye-3-Find-flux-F-n-dS-

Question Number 198802 by MathedUp last updated on 24/Oct/23

radius r circle ; x^2 +y^2 +z^2 =r^2 F^� (x,y,z)=yze_1 ^� +xe_2 ^� −xye_3 ^� Find flux 𝛒=∫∫_( 𝚺) F^� ∙n^� dS

$$\mathrm{radius}\:{r}\:\mathrm{circle}\:;\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$$\hat {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)={yz}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} +{x}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −{xy}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} \\ $$$$\mathrm{Find}\:\mathrm{flux}\:\boldsymbol{\rho}=\int\int_{\:\boldsymbol{\Sigma}} \:\hat {\boldsymbol{\mathrm{F}}}\centerdot\hat {\boldsymbol{\mathrm{n}}}\:\mathrm{d}{S} \\ $$

Answered by witcher3 last updated on 25/Oct/23

ϱ=∫∫_Σ F.n ds=∫∫∫_V Div(F).dV div(F)=∂_x yz+∂_y x+∂_z .(−xy)=0 ⇒ϱ=∫∫∫0.dv=0

$$\varrho=\int\int_{\Sigma} \mathrm{F}.\mathrm{n}\:\mathrm{ds}=\int\int\int_{\mathrm{V}} \mathrm{Div}\left(\mathrm{F}\right).\mathrm{dV} \\ $$$$\mathrm{div}\left(\mathrm{F}\right)=\partial_{\mathrm{x}} \mathrm{yz}+\partial_{\mathrm{y}} \mathrm{x}+\partial_{\mathrm{z}} .\left(−\mathrm{xy}\right)=\mathrm{0} \\ $$$$\Rightarrow\varrho=\int\int\int\mathrm{0}.\mathrm{dv}=\mathrm{0} \\ $$

Commented by MathedUp last updated on 25/Oct/23

Wow..... Thx...! hmmm...... Flux ∫∫_𝚺 F^� ∙n^� dS=0 .... how do I interpret the Flux=0 ???? Sadly....i′m not physics student.... so I don′t Know that much How should I interpret it If We give meaning mathematically not Just Calculating ... IT′S DILEMMA... oh...and i recently played witcher3 it was really fun G.O.A.T

$$\mathrm{Wow}…..\:\mathrm{Thx}…! \\ $$$$\mathrm{hmmm}……\:\mathrm{Flux}\:\int\int_{\boldsymbol{\Sigma}} \:\hat {\boldsymbol{\mathrm{F}}}\centerdot\hat {\boldsymbol{\mathrm{n}}}\:\mathrm{dS}=\mathrm{0}\:\:…. \\ $$$$\mathrm{how}\:\mathrm{do}\:\mathrm{I}\:\mathrm{interpret}\:\mathrm{the}\:\mathrm{Flux}=\mathrm{0}\:\:???? \\ $$$$\mathrm{Sadly}….\mathrm{i}'\mathrm{m}\:\mathrm{not}\:\mathrm{physics}\:\mathrm{student}…. \\ $$$$\mathrm{so}\:\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{Know}\:\mathrm{that}\:\mathrm{much}\:\mathrm{How}\:\mathrm{should} \\ $$$$\mathrm{I}\:\mathrm{interpret}\:\mathrm{it}\:\mathrm{If}\:\mathrm{We}\:\mathrm{give}\:\mathrm{meaning}\:\mathrm{mathematically} \\ $$$$\mathrm{not}\:\mathrm{Just}\:\mathrm{Calculating}\:… \\ $$$$\mathrm{IT}'\mathrm{S}\:\mathrm{DILEMMA}… \\ $$$$ \\ $$$${oh}…{and}\:{i}\:{recently}\:{played}\:{witcher}\mathrm{3} \\ $$$${it}\:{was}\:{really}\:{fun}\:\mathrm{G}.\mathrm{O}.\mathrm{A}.\mathrm{T}\: \\ $$

Commented by witcher3 last updated on 25/Oct/23

$$\mathrm{flux}=\mathrm{0}\Leftrightarrow\:\mathrm{inside}=\mathrm{outside} \\ $$$$ \\ $$

Commented by witcher3 last updated on 25/Oct/23

Witcher 3 is Good 1 Witcher3 2 Elden Ring 3 red dead Redemption is my toop and You ∫?

$$\mathrm{Witcher}\:\mathrm{3}\:\mathrm{is}\:\mathrm{Good}\: \\ $$$$\mathrm{1}\:\mathrm{Witcher3}\:\:\:\mathrm{2}\:\mathrm{Elden}\:\mathrm{Ring}\:\:\mathrm{3}\:\mathrm{red}\:\mathrm{dead}\:\mathrm{Redemption}\: \\ $$$$\mathrm{is}\:\mathrm{my}\:\mathrm{toop}\:\mathrm{and}\:\mathrm{You}\:\int? \\ $$

Commented by MathedUp last updated on 26/Oct/23

1. Undertale. 2. Spelunky series. 3. Elden ring 3 :⟩

$$\mathrm{1}.\:\boldsymbol{\mathrm{Undertale}}. \\ $$$$\mathrm{2}.\:\boldsymbol{\mathrm{Spelunky}}\:\boldsymbol{\mathrm{series}}. \\ $$$$\mathrm{3}.\:\boldsymbol{\mathrm{Elden}}\:\boldsymbol{\mathrm{ring}}\:\mathrm{3}\: \\ $$$$:\rangle \\ $$

Commented by witcher3 last updated on 26/Oct/23

$$\mathrm{iknow}\:\mathrm{just}\:\mathrm{elden}\:\mathrm{Ring} \\ $$

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