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 $\frac{3V_0}{2},\frac{{\displaystyle 5V_0}}{{\displaystyle 4}},\frac{{\displaystyle 3V_0}}{{\displaystyle 4}} \text{and} \frac{{\displaystyle V_0}}{{\displaystyle 4}}$ have radius $R_1, R_2, R_3$ and $R_4$, respectively. Then

The region between two concentric spheres of radii $a$ and $b$, respectively (see figure), has volume charge density $\rho =\frac{A}{r}$, where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge $Q$. The value of $A$ such that the electric field in the region between the spheres will be constant, is

(i) Three equal charges $q_0$ each are placed at three corners of an equilateral triangle of side$a$. Find out force acting on one of the charge due to other two charges?

(ii) In the above question, if one of the charge is replaced by negative charge then find out force acting on it due to other charges?

(iii) Repeat the part (i) if magnitude of each charge is doubled and side of triangle is reduced to half.

A solid sphere of radius $R$ is uniformly charged with charge density $\mathrm{\rho }$ in its volume. A spherical cavity of radius $\frac{R}{2}$ is made in the sphere as shown in the figure. Find the electric potential at the centre of the sphere.

A uniform surface charge of density $\sigma$ is given to a quarter of a disc extending up to infinity in the first quadrant of $x-y$ plane. The centre of the disc is at the origin $O$. Find the $z-$component of the electric field at the point $(0, 0, z)$ and the potential difference between the points $(0, 0, d) \& (0, 0, 2d).$