Let $v$ be a vector field defined in $R^3$.
$v(x)=C*x/|x|$ where $C$ is a constant.
Let $S$ be the sphere of radius $a$ and center $(b,0,0)$.
Compute $\int_{S}{F\cdot n \ dS}$ where $n$ is the normal vector to the surface of $S$.
I tried to solve this by using a coordinate transformation so that the origin is in the center of the sphere.
$v'(x)=C*(x+b*e_x)/|x+b*e_x|$ was my new vector field und then I used spherical coordinates. But the integral was pretty difficult and I couln't solve it.
How do I solve this?
2026-03-27 11:45:17.1774611917
Surface integral over a shifted sphere
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