A cylindrical capacitor has two co-axial cylinders of length $20 \,cm$ and radii $2 r$ and $r$. Inner cylinder is given a charge $10 \,\mu C$ and outer cylinder a charge of $-10 \,\mu C$. The potential difference between the two cylinders will be

The capacity of a spherical conductor in $ MKS$ system is

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 $(=6)$

The distance between the circular plates of a parallel plate condenser $40\,mm$ in diameter, in order to have same capacity as a sphere of radius $1\;metre$ is….$mm$

A $500 \,\mu F$ capacitor is charged at a steady rate of $100\, \mu C/sec$. The potential difference across the capacitor will be $10\, V$ after an interval of…..$sec$