find-S-F-n-ds-where-F-y-2-i-yj-xzk-and-S-is-the-upper-half-of-the-sphere-x-2-y-2-z-2-a-2-

Tinku Tara June 4, 2023 Vector Calculus 0 Comments

Question Number 128691 by BHOOPENDRA last updated on 09/Jan/21

find∫∫_S ▽×F .n^� ds where F^→ =y^2 i^� +yj^� −xzk^� and S is the upper half of the sphere x^2 +y^2 +z^2 =a^2

$${find}\int\int_{{S}} \bigtriangledown×{F}\:.\hat {{n}ds} \\ $$$${where}\:{F}^{\rightarrow} ={y}^{\mathrm{2}} \hat {{i}}+{y}\hat {{j}}−{xz}\hat {{k}} \\ $$$${and}\:{S}\:{is}\:{the}\:{upper}\:{half}\:{of}\:{the}\:{sphere} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={a}^{\mathrm{2}} \\ $$

Commented by BHOOPENDRA last updated on 09/Jan/21

$${can}\:{anyone}\:{help}\:{me}\:{out}\:{this}?{plz} \\ $$

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