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AG
AG asked in Science & MathematicsMathematics · 8 years ago

How to calculate this flux integral? HELP PLEASE?

F=xi + yj + zk

and the surface is the whole sphere of radius a centered out the origin orientated outward.

Please help me, I'm quite lost. Thank you so much in advance!

1 Answer

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  • kb
    Lv 7
    8 years ago
    Favorite Answer

    Since the surface is closed, use the Divergence Theorem.

    The flux equals

    ∫∫s F · dS

    = ∫∫∫ div F dV, by the Divergence Theorem

    = ∫∫∫ (1+1+1) dV

    = 3 ∫∫∫ dV

    = 3 * (volume of the sphere)

    = 3 * (4π/3)a^3

    = 4πa^3.

    I hope this helps!

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