Electric field inside a uniformly charged sphere of radius $R,$ is ($r$ is distance from centre, $r < R$)

Charge $q$ is uniformly distributed over a thin half ring of radius $R$. The electric field at the centre  of the ring is 

The plates of a parallel plate capacitor are charged up to $100\, volt$. A $2\, mm$ thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6\, mm$. The dielectric constant of the plate is

Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho _0r^2$ ($\rho _0$ is a constant and $r$ is measure from centre). Consider two points $A$ and $B$ at distance $x$ and $y$ respectively $(x < R, y > R)$ from the centre. If magnitudes of electric fields at points $A$ and $B$ are equal, then 

The equivalent capacitance between $A$ and $B$ is (in $\mu\, F$)

If the distance between the plates of a capacitor having capacity $C$ and charge $Q$ is doubled then work done will be