Definition:Flux/Direction

Definition
While flux is a scalar quantity, it does have a direction.

The sign of vector area $\delta S$ through which the flux operates depends upon the right-hand rule according to the direction of rotation around $S$ when describing it.

Hence, having decided on the sign of $\delta S$, the flux through $\delta S$ is either:
 * positive, where the angle $\psi$ between the normal to $\delta S$ is acute
 * negative, where the angle $\psi$ between the normal to $\delta S$ is obtuse.

That is:
 * a positive flux when $\delta S$ is oriented from left to right

is:
 * a negative flux when $\delta S$ is oriented from right to left.