$A$ conducting sphere of radius $R$ is given a charge $Q$. The electric potential and the electric field at the centre of the sphere respectively are

What is the change in kinetic energy of an $\alpha$-particle when it moves from a point at $70\ V$ to a point at $50\ V$?

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 concentric spherical metallic shells $X$,$Y$,and $Z$ of radii $a$,$b$,and $c$ respectively $[a < b < c]$ have surface charge densities $\sigma$,$-\sigma$,and $\sigma$,respectively. The shells $X$ and $Z$ are at the same potential. If the radii of $X$ and $Y$ are $2\,cm$ and $3\,cm$,respectively,then the radius of shell $Z$ is $......\,cm$.

$A$ Van de Graaff generator has a spherical metal shell as an electrode which is at a potential $15 \times 10^6 \,V$. If the dielectric strength of the surrounding medium is $5 \times 10^7 \,V/m$, then the diameter of the shell is (in $\,cm$)

Point charges $q_1 = 2\,\mu C$ and $q_2 = -1\,\mu C$ are kept at points $x = 0$ and $x = 6$ respectively. Electrical potential will be zero at points