The potential in an electric field varies as $V = (x^2 - y^2)$. The electric lines of force in the $X-Y$ plane are

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.

Four point charges $-q, +q, +q$ and $-q$ are placed on the $y$-axis at $y = -2d, y = -d, y = +d$ and $y = +2d$,respectively. The magnitude of the electric field $E$ at a point on the $x$-axis at $x = D$,with $D >> d$,will vary as:

$A$ half ring of radius $R$ has a linear charge density of $\lambda$. The electric force on a $1\, C$ charge placed at the centre is

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:

An infinite number of electric charges,each with a magnitude of $5 \, nC$,are placed along the $X$-axis at $x = 1 \, cm$,$x = 2 \, cm$,$x = 4 \, cm$,$x = 8 \, cm$,and so on. If the consecutive charges have opposite signs,find the electric field in $N/C$ at $x = 0$. (Given: $\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9 \, N \cdot m^2/C^2$)