$A$ spherical shell of radius $10 \,cm$ is carrying a charge $q$. If the electric potential at distances $5 \,cm$, $10 \,cm$, and $15 \,cm$ from the centre of the spherical shell is $V_{1}$, $V_{2}$, and $V_{3}$ respectively, then:

Calculate the potential energy of a point charge $-q$ placed along the axis due to a charge $+Q$ uniformly distributed along a ring of radius $R$. Sketch the potential energy $(P.E.)$ as a function of axial distance $z$ from the centre of the ring. Looking at the graph,can you determine what would happen if $-q$ is displaced slightly from the centre of the ring along the axis?

$A$ charge $Q$ is distributed over two concentric conducting thin spherical shells of radii $r$ and $R$ $(R > r)$. If the surface charge densities on the two shells are equal,the electric potential at the common centre is

Consider a sphere of radius $R$ with uniform charge density and total charge $Q$. The electrostatic potential distribution inside the sphere is given by $V(r) = \frac{Q}{4 \pi \varepsilon_{0} R} \left( a + b(r/R)^c \right)$. Note that the zero of potential is at infinity. The values of $(a, b, c)$ are

Ten electrons are equally spaced and fixed around a circle of radius $R$. Relative to $V = 0$ at infinity,the electrostatic potential $V$ and the electric field $E$ at the centre $C$ are

Write an equation for the electric potential due to a system of charges.