Mathematics · Vector Calculus

Given a function φ = ½ (x 2 + y 2 + z 2 ) in a three-dimensional Cartesian space, what is the value of the surface integral &oiint; S n̂ . ∇φ dS, where S is the surface of a sphere of unit radius and n̂ is the outward unit normal vector on S?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

4π

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