$A$ charge $q$ is placed in the middle of a line joining two equal and like point charges $Q$. For what value of $q$ will the system be in equilibrium?

Six charges are placed at the corners of a regular hexagon as shown. If an electron is placed at its centre $O$,the force on it will be:

Two fixed charges $+4\,Q$ and $-Q$ are located at $A$ and $B$ respectively,with the distance $AB = 3\,m$.

Given below are two statements:
Statement $I$: An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero,but the electric field is not zero anywhere in the sphere.
Statement $II$: If $R$ is the radius of a solid metallic sphere and $Q$ is the total charge on it,the electric field at any point on a spherical surface of radius $r$ ( < R ) is zero,and the electric flux passing through this closed spherical surface of radius $r$ is also zero.
In the light of the above statements,choose the correct answer from the options given below:

Point charges are placed at the vertices of a regular hexagon with center $O$ and side length $L$ as shown in the figure. Given $K = \frac{q}{4\pi \epsilon_0 L^2}$,which of the following statements is correct?

Two small spheres each carrying a charge $q$ are placed $r$ metre apart. If one of the spheres is taken around the other one in a circular path of radius $r$,the work done will be equal to