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Let S be a closed surface and let denote the position vector of any point (x,y,z) measured from an origin O. then  is equal to (if O lies inside S). 
  • a)
     3π
  • b)
     2π 
  • c)
     4π
  • d)
     None of these 
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Let S be a closed surface and let denote the position vector of any po...
When origin O is inside S. In this case, divergence theorem cannot be applied to the region V enclosed by S, since  has a point to discontinuity at the origin. To remove this  difficulty, let us enclose the origin by a small sphare Σ of radius ε. 
The function F is continuously differentiable at the points of the region v´ enclosed between S and Σ. Therefore applying divergence theorem for this region V´, we have 
Now on the sphere Σ, the outward drawn normal n is directed towards the centre. Therefore on Σ, we have 
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Let S be a closed surface and let denote the position vector of any point (x,y,z) measuredfrom an origin O. then is equal to (if O lies inside S).a)3πb)2πc)4πd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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