2.31 (a) Two large conducting spheres carrying charges ${\mathit{Q}}_1$ and ${\mathit{Q}}_2$ are brought close to each other. Is the magnitude of electrostatic force between them exactly given by ${\mathit{Q}}_1{\mathit{Q}}_2$ /4 $\mathit{\pi }{\mathit{\epsilon }}_0{\mathit{r}}^2$ , where r is the distance between their centres?

(b) If Coulomb's law involved 1/ ${\mathit{r}}^3$ dependence (instead of 1/ ${\mathit{r}}^2$ ), 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).