Two large conducting spheres carrying charges `Q_1, and Q_2,` are brought close to each other. Is the magnitude of electrostatic force between theme exactly given by `(Q_1Q_2)/(4pi epsi_(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 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. No, The given relation is Coulomb.s law which is true for point charges. In the present case, as the spheres are brought closer, the distribution of charge on them becomes non uniform.
b. No. The surface area in space varies as `1/r^2`. Hence `1/r^(2)` dependence is essential.
c. Not necessarily. The motion of charged particle need not be along the line of the field. It does so in the uniform field. The field gives the direction of acceleration and not that of velocity in general.
d. Zero. For any complete path in electrostatic field (the shape does not matter), it is zero.
e. No. Potential is continuous there
f. The single conductor can form condenser with the other conductor at infinity. Hence the meaning of storage of charge retains.
g. Water molecules are polar molecules.