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Homework Help: Surface integral of nndS

  1. Feb 14, 2017 #1
    1. The problem statement, all variables and given/known data

    Let n be the unit outward normal of a spherical surface of Radius R, let the surface of the sphere be denoted by S.
    Evalute Surface integral of nndS

    2. Relevant equations

    3. The attempt at a solution
    I have evaluated the surface integral of ndS and found it to be 0. but am not sure how nn relates to it.
  2. jcsd
  3. Feb 15, 2017 #2


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    If ##\bf nn## is an inner product, it is positive definite and of magnitude 1. What remains is the integral of ##d\bf S## ?
    Can you show how you find the integral of ##{\bf n}d{\bf S } \ ## is zero ?
  4. Feb 15, 2017 #3


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    The area of a sphere is a scalar quantity. If bold letters mean vectors, do not use bold for scalars.
    Presumably dS is also scalar, the area of a surface element. The outward normal of that surface element is n. So dA=ndS is the surface element vector. Yes, its integral for the whole sphere is zero. But ##\int {\vec n \cdot \vec {dA}} ## is not zero, as @BvU pointed out.
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