Answer carefully: (a) Two large conducting spheres carrying charges Q1 and Q2 arebrought close to each other. Is the magnitude of electrostaticforce between them exactly given by Q1 Q2/4pe0r2, where r isthe distance between their centres? (b) If Coulomb’s law involved 1/r3 dependence (instead of 1/r2),would Gauss’s law be still true ? (c) A small test charge is released at rest at a point in anelectrostatic field configuration. Will it travel along the fieldline passing through that point? (d) What is the work done by the field of a nucleus in a completecircular orbit of the electron? What if the orbit is elliptical? (e) We know that electric field is discontinuous across the surfaceof a charged conductor. Is electric potential also discontinuousthere? (f ) What meaning would you give to the capacitance of a singleconductor? (g) Guess a possible reason why water has a much greaterdielectric constant (= 80) than say, mica (= 6).
a)
When two large conducting spheres carrying charges Q 1 and Q 2 are brought close to each other then the force between the these spheres will not be equal to Q 1 Q 2 4 π ε 0 r 2 as per the given expression because on the spheres, there will be a non-uniform charge distribution.
b)
If coulomb law involved 1 r 3 dependence, instead of 1 r 2 then Gauss’s law will not be true.
c)
The electric field lines give the direction of acceleration not of the velocity. Therefore, when a small test charge is released in an electrostatic configuration at rest then the particle will travel along the field lines that are passing through the point, only when the field lines are straight.
d)
The work done by the field of a nucleus is zero when an electron completes an orbit, either circular or elliptical.
e)
The electrical field is discontinuous across the surface of a charged conductor so the electric potential is not discontinuous across the surface of a charged conductor.
Thus, the electrical potential is continuous.
f)
The capacitance of a single conductor is treated as a parallel plate capacitor and the plates of the capacitor are at infinity.
g)
The dielectric constant of water is 80 and for mica is 6 , water has an unsymmetrical space as compared to mica. Since water has a permanent dipole moment, so water has a greater dielectric constant than mica.
a)
When two large conducting spheres carrying charges
b)
If coulomb law involved
c)
The electric field lines give the direction of acceleration not of the velocity. Therefore, when a small test charge is released in an electrostatic configuration at rest then the particle will travel along the field lines that are passing through the point, only when the field lines are straight.
d)
The work done by the field of a nucleus is zero when an electron completes an orbit, either circular or elliptical.
e)
The electrical field is discontinuous across the surface of a charged conductor so the electric potential is not discontinuous across the surface of a charged conductor.
Thus, the electrical potential is continuous.
f)
The capacitance of a single conductor is treated as a parallel plate capacitor and the plates of the capacitor are at infinity.
g)
The dielectric constant of water is
