At a certain distance from a point charge,the electric field intensity is $500 \ V/m$ and the electric potential is $3000 \ V$. What is this distance in $m$?

Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $-\frac{2q}{3}$ placed at points $A, B$ and $C$,respectively,as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $\angle CAB = 60^{\circ}$.

Two identical metal spheres charged with $+12 \mu C$ and $-8 \mu C$ are kept at a certain distance in air. They are brought into contact and then kept at the same distance. The ratio of the magnitudes of electrostatic forces between them before and after contact is (in $: 1$)

$A$ unit positive point charge of mass $m$ is projected with a velocity $V$ inside a tunnel as shown. The tunnel is made inside a uniformly charged non-conducting sphere of radius $R$ and volume charge density $\rho$. The minimum velocity with which the point charge should be projected such that it can reach the opposite end of the tunnel is equal to

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:

$A$ total charge $q$ is divided into $q_1$ and $q_2$,which are placed at two vertices of an equilateral triangle of side $a$. The magnitude of the electric field $E$ at the third vertex of the triangle is to be depicted schematically as a function of $x = q_1 / q$. Choose the correct figure.