Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

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

flux=0⇔ inside=outside

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

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

iknow just elden Ring

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

Terms of Service

Privacy Policy

Contact: info@tinkutara.com