# Surface integral of nndS

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1. Feb 14, 2017

### Xian Xi

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. Feb 15, 2017

### BvU

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 ?

3. Feb 15, 2017

### ehild

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.