GATE EE 2015 Set 1 — Question 14
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Engineering Mathematics → Vector Calculus → Gradient, Divergence & Curl
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Question
Consider a function , where is the distance from the origin and is the unit vector in the radial direction. The divergence of this function over a sphere of radius , which includes the origin, is
Correct answer
(C) 4π
Solution
The function is given as . According to the properties of the Dirac delta function in three dimensions:The question asks for the divergence 'over a sphere', which implies the volume integral of the divergence over the sphere of radius that includes the origin.Alternatively, using the Gauss Divergence Theorem:For a sphere of radius , the surface element is .
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