Equal charges are given to two spheres of different radii. The potential will

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

A hemispherical bowl of mass $m$ is uniformly charged with charge density $'\sigma '$ . Electric potential due to charge distribution at a point $'A'$ is (which lies at centre of radius as shown).

Two point charges $-Q$ and $+Q / \sqrt{3}$ are placed in the xy-plane at the origin $(0,0)$ and a point $(2,0)$, respectively, as shown in the figure. This results in an equipotential circle of radius $R$ and potential $V =0$ in the $xy$-plane with its center at $(b, 0)$. All lengths are measured in meters.

($1$) The value of $R$ is. . . . meter.

($2$) The value of $b$ is. . . . . .meter.

The electric potential $V(x, y, z)$ for a planar charge distribution is given by: 

$V\left( {x,y,z} \right) = \left\{ {\begin{array}{*{20}{c}}
{0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,for\,x\, < \, - d}\\
{ - {V_0}{{\left( {1 + \frac{x}{d}} \right)}^2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,for\, - \,d\, \le x < 0}\\
{ - {V_0}\left( {1 + 2\frac{x}{d}} \right)\,\,\,\,\,\,\,\,\,\,\,for\,0\, \le x < d}\\
{ - 3{V_0}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,for\,x\, > \,d}
\end{array}} \right.$

where $-V_0$ is the potential at the origin and $d$ is a distance. Graph of electric field as a function of position is given as

Four electric charges $+q,+q, -q$ and $-q$ are placed at the comers of a square of side $2L$ (see figure). The electric potential at point $A,$ midway between the two charges $+q$ and $+q,$ is