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Using Gauss divergence theorem to evaluate $\int\int\limits_s\bar F.\hat n \space ds,$ where $\bar f=x\bar i+y\bar j +z\bar k $ and 's' is sphere $x^2+y^2+z^2=9$ & $\hat n$ is outward normal to 's'
written 8.9 years ago by gravatar for teamques10 teamques10 ★ 70k modified 3.9 years ago by gravatar for krithikkm200 krithikkm200 • 10

Mumbai university > Electronics and telecommunication engineering, Electronics engineering > Sem 3 > Applied mathematics 3

Marks : 04

Years : MAY 2016
engineering mathematics
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written 8.9 years ago by gravatar for teamques10 teamques10 ★ 70k

Gauss-Divergence Theorem $\int\int\limits_s\bar F.\hat n \space ds =\int\int\limits_v (\triangledown.\bar F) dv \\ \triangledown \bar F =\dfrac {dF_1}{dx}+ \dfrac {dF_2}{dy} + \dfrac {dF_3}{dz}=1+1+1 = 3 \\ \therefore \int\int\limits_s \bar F. \hat n\space ds =\int\int\limits_r\int 3.dv =3 [\text { volume of sphere }] \\ =3[\dfrac 43\pi (3)^3] =108\pi$
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