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)//4pi epsilon_(0) r_(2)`, where r is the distance between their centers?
(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).

Explanation

(a) the force between two conducing spheres is not exactly given by the expression, `Q_(1)Q_(2)//4nin_(0)r^(2)` , because there is a non-uniform charge distribution on the spheres. (b) Gauss's law will not be true, if coloumb's law involved `1//r^(3)` dependence, instead of `1//r^(2)` , on r.
(c) Yes, if a small test charge in released at rest at a point in an electrostatic field configuration, then it will travell along the field lines passing through the point, only if the field lines are straight . this is because the field lines give the direction of acceleration and not of velocity.
(d) whenever the electron completes an orbit, either circular or elleptical , the work doen by the field of a nucleas is zero.
(e) no
Electric field is discontinous across the surface of a charged conductor. however, electric potential is continous.
(f) the capacitance of a single conductors is considered as a parallel plate capacitor with one of its two plates at infinity.
(f) the capacitance of a single conductor is considered as a parallel plate capacitor with one of its two plates at infinity.
(g) water has an unsymmetrical space as compared to mica. since it has a permanent dipole moment, it has a greater dielectric constant than mica.