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 in_(0) r^(2))` where r is distance between their centers ?
(b) If Coulomb 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 line of force passing through that point ?
(d) What is the work done by the field of a nucleus in a complete circualr orbits of electron ? What if the orbits is elliptical ?
(e) We know that electric field is discontinnous across the surface of a charged conductor conductor. Is electric potential also discontinous there ?
(f) What meaning would you give to the capacity fo a single conductor ?
(g) Guess a possible reason why water has a much greater dielectric constant `K = 80` than, say mica `(K = 6)`.

Explanation

(a) When the charged spheres are brought close together, the charge distributions on them become non-uniform. Therefore, Coulomb's law is not valid. Hence the magnitude of force is not given exactly by this formula.
(b) No. Gauss's law will not true if Coulomb's law involve `1//r^(3)` dependance instead of `1//r^(2)` dependence.
(c) The line of force given the direction of acceleration of charge. If the electric line of force si linear, the test charge will move along the line. If the line of force is non linear, the charge will not go along the line.
(d) As force due to the field is directed towards the nucleas ,and the electron does not move in the direction fo this force, therefore work done si zero when the orbits is circular. This is true even when orbits is ellipitical as electric forces are conservative forces.
(e) No, electric potential is contionous.
(f) The capacity fo a single conductor implies that the second conductor is at infinity.
(g) This is because a molecule of water in its normal state has an usysmmetrical shape and, therfore it has a permanenet dipole moment.