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Answer carefully: <br> (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? <br> (b) If Coulomb’s law involved 1//r^(3) dependence (instead of 1//r^(2)), would Gauss’s law be still true ? <br> (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? <br> (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? <br> (e) We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there? <br> (f) What meaning would you give to the capacitance of a single conductor? <br> (g) Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (= 6).

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Answer Text

Solution :
(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. <br> (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. <br> (d) whenever the electron completes an orbit, either circular or elleptical , the work doen by the field of a nucleas is zero. <br> (e) no <br> Electric field is discontinous across the surface of a charged conductor. however, electric potential is continous. <br> (f) the capacitance of a single conductors is considered as a parallel plate capacitor with one of its two plates at infinity. <br> (f) the capacitance of a single conductor is considered as a parallel plate capacitor with one of its two plates at infinity. <br> (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.

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