A capacitor is made of two square plates each of side $a$ making a very small angle $\alpha$ between them, as shown in figure. The capacitance will be close to

$1000$ small water drops each of capacitance $C$ join together to form one large spherical drop. The capacitance of bigger sphere is ……… $C$

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 $(=6)$

Capacitance (in $F$) of a spherical conductor with radius $1\, m$ is

Consider the situation shown in the figure. The capacitor $A$ has a charge $q$ on it whereas $B$ is uncharged. The charge appearing on the capacitor $B$ a long time after the switch is closed is