The work done by a vector field $\vec F$ in moving along a trajectory C $$\int_C \vec F \cdot d\vec r = \int_C \vec F \cdot \hat T ds$$
Where $\vec r$ is the position vector along C and $\hat T$ is the tangential vector along C
If I have to calculate the flux of the field across C then it is given by
$$\int \vec F \cdot \hat n ds$$
Where the convention used is $\hat n$ is $\hat T$ rotated clockwise. What is the reason behind this clockwise convention?