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Question Number 20058 by Tinkutara last updated on 21/Aug/17

$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{difference}\mathrm{between}\oint \mathrm{and}$$$$\int ?\mathrm{Where}\mathrm{is}\oint \mathrm{used}?$$

Answered by dioph last updated on 21/Aug/17

$$\oint \mathrm{indicates}\mathrm{the}\mathrm{integral}\mathrm{is}\mathrm{calculated}$$$$\mathrm{in}\mathrm{closed}\mathrm{path}.\mathrm{For}\mathrm{instance},\mathrm{for}$$$$\mathrm{a}\mathrm{conservative}\mathrm{field}A,\oint A\mathrm{d}s=0.$$$$\mathrm{Works}\mathrm{for}\mathrm{any}n-\mathrm{dimensional}$$$$\mathrm{closed}\mathrm{surface}\mathrm{as}\mathrm{well}.{\mathrm{Gauss}}^{\prime }\mathrm{law}$$$$\mathrm{for}\mathrm{electrostatics}\mathrm{states}\mathrm{that}$$$$\oint D\mathrm{dS}=Q,\mathrm{which}\mathrm{means}\mathrm{that}$$$$\mathrm{the}\mathrm{integral}\mathrm{of}\mathrm{the}\mathrm{electric}\mathrm{field}\mathrm{density}$$$$\mathrm{through}\mathrm{any}\mathrm{closed}\mathrm{surface}\mathrm{equals}$$$$\mathrm{the}\mathrm{charge}\mathrm{encapsulated}\mathrm{by}\mathrm{the}\mathrm{same}$$$$\mathrm{surface}.\mathrm{Hope}\mathrm{that}\mathrm{helps}$$

Commented by Tinkutara last updated on 21/Aug/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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