$A$ cube of side $L$ has point charges $+q$ located at its seven vertices and $-q$ at remaining one vertex. The electric field at its centre is found to be $|E|=\alpha\left(\frac{q}{4 \pi \varepsilon_0 L^2}\right)$. The magnitude of constant $\alpha$ is

Consider a circular loop that is uniformly charged and has a radius $R = a \sqrt{2}$. Find the position along the positive $z$-axis of the Cartesian coordinate system where the electric field is maximum,assuming the ring is placed in the $xy$-plane at the origin.

The number of electrons to be put on a spherical conductor of radius $0.1 \ m$ to produce an electric field of $0.036 \ N/C$ just above its surface is $...... \times 10^4$.

Three isolated metal spheres $A$,$B$,and $C$ have radii $R$,$2R$,and $3R$ respectively,and the same charge $Q$. If $U_A$,$U_B$,and $U_C$ are the energy densities just outside the surfaces of the spheres,then the relation between $U_A$,$U_B$,and $U_C$ is:

Two point charges $a$ and $b$,whose magnitudes are the same,are positioned at a certain distance from each other with $a$ at the origin. $A$ graph is drawn between the electric field strength $E$ at points between $a$ and $b$ and the distance $x$ from $a$. $E$ is taken as positive if it is along the line joining $a$ to $b$. From the graph,it can be decided that:

Consider the following statements about electric field intensity and electric potential.
$A$. The electric field intensity due to a charged spherical shell is inversely proportional to the square of its distance from the center for points outside the shell.
$B$. The electric potential due to a point charge is inversely proportional to the distance between the charge and the point.