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Consider a cylinder of height h and radius a, closed at both ends, centered at the origin. Let  the position vector and  unit vector normal to the surface. The surface integral  over the closed surface of the cylinder is
  • a)
    2πa2(a+h)
  • b)
    3πa2h
  • c)
    2πa2h
  • d)
    Zero
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider a cylinder of height h and radius a, closed at both ends, cen...
For calculation of surface integral ,we need surface normal on the top surface of the cylinder shown in adjacent figure


Where  is the given position vector. Thus

top surface
 (on top surface)
On the bottom surface of the cylinder

vector  is normal to the current surface of the cylinder and therefore for this surface we have

Thus  a(area of curved surface) 
The value of  are the whole surface of cylinder is then 
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Most Upvoted Answer
Consider a cylinder of height h and radius a, closed at both ends, cen...
For calculation of surface integral ,we need surface normal on the top surface of the cylinder shown in adjacent figure


Where  is the given position vector. Thus

top surface
 (on top surface)
On the bottom surface of the cylinder

vector  is normal to the current surface of the cylinder and therefore for this surface we have

Thus  a(area of curved surface) 
The value of  are the whole surface of cylinder is then 
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Consider a cylinder of height h and radius a, closed at both ends, centered atthe origin. Letthe position vector andunit vector normal to the surface. The surface integralover the closed surface of the cylinder isa)2πa2(a+h)b)3πa2hc)2πa2hd)ZeroCorrect answer is option 'B'. Can you explain this answer?
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