A circular ring of radius r made of a non-conducting material is placed with its axis parallel to a uniform electric field. The ring is rotated about a diameter through 180°. Does the flux of electric field change? If yes, does it decrease or increase?
No, the flux will remain the same.
We know, Flux = 
Where
E = electric field vector, ds = small area element.
Now, ds = n.da,
where n is the unit normal in the direction of the area, and da is a small area element.
By the law of dot product in vector calculus,
E.ds = |E||ds|cosθ
Where
θ is the angle between the normal to the area and the electric field.
|E| = magnitude of electric field vector,
|ds| = magnitude of small area element.
In the first case, since the axis of the ring is parallel to the electric field, the angle θ between the normal to the surface is 0°, since the normal is parallel to the axis.
When θ=180o
Φ=|E||ds| cos(180o) =|E||ds| (-1) =-|E||ds|
Therefore, the flux is just |E||ds|. When it is rotated about its diameter by 180°, the normal just rotates by 180°, and thus the angle changes to 180°. The flux becomes negative, but its value remains the same.