#### Question

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 the electric field change? If yes, does it decrease or increase?

#### Solution

It is given that the circular ring, made of a non-conducting material, of radius r is placed with its axis parallel to a uniform electric field.This means that both the electric field and the area vector are parallel to each other (area vector is always perpendicular to the surface area). Thus, the flux through the ring is given by `vec"E" . vec"S"` = ES cos 0 = `"E"(pi"r"^2).`

Now, when the ring is rotated about its diameter through 180^{0}, the angle between the area vector and the electric field becomes 180^{0}. Thus, the flux becomes - `"E"(pi"r"^2)` .