Electric charges of $+10\,\mu C, +5\,\mu C, -3\,\mu C$ and $+8\,\mu C$ are placed at the corners of a square of side $\sqrt{2}\,m$. The potential at the centre of the square is:

Derive an expression for the electric potential at a distance $r$ from a positive point charge $Q$.

Eight charges,each of magnitude $q$,are placed at the vertices of a cube placed in a vacuum. The electric potential at the centre of the cube due to this system of charges is . . . . . . . ($\varepsilon_0 = $ permittivity of vacuum,$a = $ length of each side of the cube.)

Four equal charges $Q$ are placed at the four corners of a square of side length $a$. The work done in removing a charge $-Q$ from its center to infinity is

Three particles,each having a charge of $10\,\mu C$,are placed at the corners of an equilateral triangle of side $10\,cm$. The electrostatic potential energy of the system is.....$J$ (Given $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\,N\cdot m^2/C^2$).

$A$ uniformly charged solid sphere of radius $R$ has potential $V_0$ (measured with respect to $\infty$) on its surface. For this sphere, the equipotential surfaces with potentials $\frac{3V_0}{2}, \frac{5V_0}{4}, \frac{3V_0}{4}$, and $\frac{V_0}{4}$ have radii $R_1, R_2, R_3$, and $R_4$ respectively. Then: