A small plane area is rotated in a electric field . In which orientation of the area is the flux of electric field through area is maximum? In which orientation is it zero?

The projection of area element proportinal to E is dS cos A , where, A= angle (theta).

Now, Electric flux = E.dS = E.dS cos A.

When A = 0 , cos A = maximum = 1. So, flux is maximum here, i.e, perpendicular.

When A = 90, cos A = minimum = 0. So, flux is minimum when field lines are parallel to dS and will not cross it.