At a certain distance from a point charge,the field intensity is $500 \, Vm^{-1}$ and the potential is $-3000 \, V$. The distance to the charge and the magnitude of the charge respectively are

$(a)$ Consider an arbitrary electrostatic field configuration. $A$ small test charge is placed at a null point (i.e.,where $E = 0$) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.
$(b)$ Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

$A$ ring of radius $R$ is charged with a charge $Q$. The electric field at a point on its axis at a distance $r$ from the circumference of the ring is:

An infinitely long uniformly charged string is placed along the $z-$axis. Its linear charge density is $\lambda$. $A$ point charge $q$ is moved from position $(a, 0, 0)$ to $(2a, 0, 0)$. The work done by the external agent is:

Why is an electric force conservative?

$A$ uniform electric field of $500 \ Vm^{-1}$ is directed at $30^{\circ}$ with the positive $X$-axis as shown in the figure. The potential difference $(V_B - V_A)$ if $OA = 3 \ m$ and $OB = 5 \ m$ is