A parallel plate capacitor is charged to a potential difference of $100\ V$ and disconnected from the source of emf. A slab of dielectric is then inserted between the plates. Which of the following three quantities change?

$(i)$ The potential difference
$(ii)$ The capacitance
$(iii)$ The charge on the plates

In the given figure, three capacitors $C_1, C_2$ and $C_3$ are joined to a battery, with symbols having their usual meanings, the correct conditions will be

Four identical capacitors are connected in series with a battery of $emf$ $10\,V$. The point $X$ is earthed, then the potential of point $A$ is.....$V$

Two point charges placed at a distance $r$ in air experience a certain force. Then the distance at which they will experience the same force in a medium of dielectric constant $K$ is

A sphere of radius $R$ and charge $Q$ is placed inside an imaginary sphere of radius $2R$ whose centre coincides with the given sphere. The flux related to imaginary sphere is

If $\vec E = \frac{{{E_0}x}}{a}\hat i\,\left( {x - mt} \right)$ then flux through the shaded area of a cube is