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Question Number 216352 by issac last updated on 05/Feb/25

Commented by issac last updated on 05/Feb/25

and what Flux ∫∫_S  F^→ ∙dS^→ = 0 mean??  S is Arbitary Closed Surface

$$\mathrm{and}\:\mathrm{what}\:\mathrm{Flux}\:\int\int_{\mathcal{S}} \:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\centerdot\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathrm{S}}}=\:\mathrm{0}\:\mathrm{mean}?? \\ $$$$\mathcal{S}\:\mathrm{is}\:\mathrm{Arbitary}\:\mathrm{Closed}\:\mathrm{Surface}\: \\ $$

Answered by MrGaster last updated on 07/Feb/25

The flux is zero if the divergence of F^→ is 0 throughout the volume V  boumded by S.

$$\mathrm{The}\:\mathrm{flux}\:\mathrm{is}\:\mathrm{zero}\:\mathrm{if}\:\mathrm{the}\:\mathrm{divergence}\:\mathrm{of}\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\mathrm{is}\:\mathrm{0}\:\mathrm{throughout}\:\mathrm{the}\:\mathrm{volume}\:{V}\:\:\mathrm{boumded}\:\mathrm{by}\:\mathcal{S}. \\ $$

Commented by issac last updated on 07/Feb/25

Thx.....!!

$$\mathrm{Thx}.....!! \\ $$

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