Answer carefully:

$(a)$ Two large conducting spheres carrying charges $Q _{1}$ and $Q _{2}$ are brought close to each other. Is the magnitude of electrostatic force between them exactly given by $Q _{1} Q _{2} / 4 \pi \varepsilon_{0} r^{2},$ where $r$ is the distance between their centres?

$(b)$ If Coulomb's law involved $1 / r^{3}$ dependence (instead of $1 / r^{2}$ ), would Gauss's law be still true?

$(c)$ $A$ small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?

$(d)$ What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical?

$(e)$ We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there?

$(f)$ What meaning would you give to the capacitance of a single conductor?

$(g)$ Guess a possible reason why water has a much greater dielectric constant $(=80)$ than say, mica $(=6)$

What physical quantities may $X$ and $Y$ represent ? ($Y$ represents the first mentioned quantity)

A particle of charge $Q$ and mass $M$ moves in a circular path of radius $R$ in a uniform magnetic field of magnitude $B$. The same particle now moves with the same speed in a circular path of same radius $R$ in the space between the cylindrical electrodes of the cylindrical capacitor. The radius of the inner electrode is $R/2$ while that of the outer electrode is $ 3R/2.$ Then the potential difference between the capacitor electrodes must be

Sixty-four drops are jointed together to form a bigger drop. If each small drop has a capacitance $C$, a potential $V$, and a charge $q$, then the capacitance of the bigger drop will be

A parallel-plate capacitor is connected to a resistanceless circuit with a battery until the capacitor is fully charged. The battery is then disconnected from the circuit and the plates of the capacitor are moved to half of their original separation using insulated gloves. Let $V_{new}$ be the potential difference across the capacitor plates when the plates have moved. Let $V_{old}$ be the potential difference across the capacitor plates when they were connected to the battery $\frac{V_{new}}{V_{old}}=$……