The electric field in a certain region is acting radially outward and is given by $E=Aa.$ A charge contained in a sphere of radius $a$ centered at the origin of the field will be given by:

What is the flux through a cube of side $a,$ if a point charge of $q$ is placed at one of its corners?
1. $\dfrac{2q}{\varepsilon_0}$
2. $\dfrac{q}{8\varepsilon_0}$
3. $\dfrac{q}{\varepsilon_0}$
4. $\dfrac{q}{2\varepsilon_0}$

Two positive ions, each carrying a charge $q$, are separated by a distance $d$. If $F$ is the force of repulsion between the ions, the number of electrons missing from each ion will be:
($e$ is the charge on an electron)

A square surface of side $L$ (metre) in the plane of the paper is placed in a uniform electric field $E$ (volt/m) acting along the same plane at an angle θ with the horizontal side of the square as shown in the figure. The electric flux linked to the surface in the unit of V-m is:
     

The electric field at a distance $\frac{3R}{2}$ from the centre of a charged conducting spherical shell of radius $R$ is $E$. The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is:
1. $E$
2. $\frac{E}{2}$
3. $\frac{E}{3}$
4. zero