A point charge $Q$ is located just above the center of the flat face of a hemisphere of radius $R$ as in figure. What is the flux

(a) through the curved surface, and

(b) through the flat face?

(c) Repeat parts (a) and (b) if the charge is exactly at the centre.

In figure, a cone lies in a uniform electric field $E$. Determine the electric flux entering the cone.

(a) A point charge $q$ is located at distance $d$ from an infinite plane. Determine the electric flux through the plane due to the point charge.

(b) A point charge $q$ is located at a very small distance from the center of a very large square on the line perpendicular to the square passing through its center. Determine the approximate electric flux through the square due to the point charge.

Calculate the total electric flux through the paraboloidal surface due to a uniform electric field of magnitude $E_0$ in the direction shown in figure.

Consider a closed surface of arbitrary shape as shown in figure. Suppose a single charge $Q_1$, is located at some point, within the surface and the second charge $Q_2$ is located outside the surface.

(a) What is the total flux passing through the surface due to charge $Q_1$?

(b) What is the total flux passing through the surface due to charge $Q_2$?

A hollow half-cylinder surface of radius $R$ and length $l$ is placed in a uniform electric field $E$. Electric field is acting perpendicular on the plane $ABCD$. Find the flux through the curved surface of the hollow cylindrical surface.

A cone of radius $R$ and height $h$ is placed in an uniform electric field as shown in the figure (a), if the axis of the cone made inclined $\mathrm{\theta }$ with the vertical as shown in the figure (b). Calculate the flux of electric field entering the cone.

Point charge $q$ is placed at a point on the axis of a square non-conducting surface. The axis is perpendicular to the square surface and is passing through its centre. The flux of Electric field through the square caused due to charge $q$ is $\varphi$. If the square is given a surface charge of uniform density $\sigma$, find the magnitude of the force on the square surface due to point charge $q$.