Surface Integral of Outward Normal Vector over a Spherical Surface

[Xian Xi]

Homework Statement

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

Homework Equations

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.

 

[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 ?

 

[ehild]

Homework Statement

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

Homework Equations

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.

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.