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

An imaginary equilateral triangle $ABC$ of side length $2 \ m$ is placed in a uniform electric field $\vec{E} = 10 \ N \ C^{-1}$ as shown. Then,$V_A - V_B =$

$A$ small conducting sphere of radius $r$ is lying concentrically inside a bigger hollow conducting sphere of radius $R$. The bigger and smaller spheres are charged with $Q$ and $q$ respectively $(Q > q)$ and are insulated from each other. The potential difference between the spheres will be

Given below are two statements $:$ one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A :$ Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero,no matter which path is chosen.
Reason $R :$ Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell.
In the light of the above statements,choose the correct answer from the options given below.

In the following diagram, the work done in moving a point charge from point $P$ to points $A, B$ and $C$ is $W_A, W_B$ and $W_C$ respectively. If there is no charge nearby, then:

The electric potential on the surface of a charged spherical conductor of radius $5 \,cm$ is $200 \,V$. The work done in moving a charge of $+5 \,C$ from a point $A$ to another point $B$ situated at distances of $15 \,cm$ and $10 \,cm$ respectively from the centre of the sphere is (in $\,J$)