Three concentric spherical metallic shells $A$,$B$,and $C$ of radii $a=7 \ cm$,$b=17 \ cm$,and $c$ $(a < b < c)$ have surface charge densities $\sigma, -\sigma$,and $\sigma$ respectively. If $A$ and $C$ are at the same potential,then the value of $c$ is: (in $cm$)

$A$ uniform electric field vector $E$ exists along the horizontal direction as shown. The electric potential at $A$ is $V_A$. $A$ small point charge $q$ is slowly moved from $A$ to $B$ along the curved path as shown. The potential energy of the charge when it is at point $B$ is

Three concentric metallic shells $A, B$ and $C$ of radii $a, b$ and $c$ $(a < b < c)$ have surface charge densities $\sigma, -\sigma$ and $\sigma$ respectively. Find the potentials ${V_A}$ and ${V_B}$.

Two charges $q_1$ and $q_2$ are separated by a distance of $30\ cm$. $A$ third charge $q_3$,initially at $C$ as shown in the figure,is moved along the circular path of radius $40\ cm$ from $C$ to $D$. If the difference in potential energy due to the movement of $q_3$ from $C$ to $D$ is given by $\frac{q_3 K}{4 \pi \epsilon_0}$,find the value of $K$.

Two concentric hollow spherical conductors of radii $R$ and $2R$ have charges $Q$ and $-Q$ respectively. Find the electric potential at a distance of $\frac{3R}{2}$ from the centre. $\left[K=\frac{1}{4\pi\varepsilon_0}\right]$

Two concentric hollow spherical shells have radii $r$ and $R$ $(R \gg r)$. $A$ charge $Q$ is distributed on them such that the surface charge densities are equal. The electric potential at the centre is