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The following surface integral is to be evaluated over a sphere for the given steady vector field, F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j, and k as unit base vectors.
 , Where S is the sphere, x2 + y2 + z2 = 1 and n is the outward unit normal vector to the sphere. The value of the surface integral is
  • a)
    π
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The following surface integral is to be evaluated over a sphere for th...
Concept:
Gauss divergence theorem:
It states that the surface integral of the normal component of a vector function  taken over a closed surface ‘S’ is equal to the volume integral of the divergence of that vector function taken over a volume enclosed by the closed surface ‘S’.
Calculation:
Given:
F = xi + yj + zk
Stokes theorem:
It states that the line integral of a vector field  around any closed surface C is equal to the surface integral of the normal component of the curl of vector  over an unclosed surface ‘S’.
Green's theorem:
 
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Most Upvoted Answer
The following surface integral is to be evaluated over a sphere for th...
Concept:
Gauss divergence theorem:
It states that the surface integral of the normal component of a vector function  taken over a closed surface ‘S’ is equal to the volume integral of the divergence of that vector function taken over a volume enclosed by the closed surface ‘S’.
Calculation:
Given:
F = xi + yj + zk
Stokes theorem:
It states that the line integral of a vector field  around any closed surface C is equal to the surface integral of the normal component of the curl of vector  over an unclosed surface ‘S’.
Green's theorem:
 
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The following surface integral is to be evaluated over a sphere for the givensteady vector field, F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j, and k as unit base vectors.,Where S is the sphere, x2+ y2+ z2= 1 and n is the outward unit normal vector tothe sphere. The value of the surface integral isa)πb)2πc)d)4πCorrect answer is option 'A'. Can you explain this answer?
Question Description
The following surface integral is to be evaluated over a sphere for the givensteady vector field, F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j, and k as unit base vectors.,Where S is the sphere, x2+ y2+ z2= 1 and n is the outward unit normal vector tothe sphere. The value of the surface integral isa)πb)2πc)d)4πCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The following surface integral is to be evaluated over a sphere for the givensteady vector field, F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j, and k as unit base vectors.,Where S is the sphere, x2+ y2+ z2= 1 and n is the outward unit normal vector tothe sphere. The value of the surface integral isa)πb)2πc)d)4πCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following surface integral is to be evaluated over a sphere for the givensteady vector field, F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j, and k as unit base vectors.,Where S is the sphere, x2+ y2+ z2= 1 and n is the outward unit normal vector tothe sphere. The value of the surface integral isa)πb)2πc)d)4πCorrect answer is option 'A'. Can you explain this answer?.
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