Physics Class 12 NCERT Solutions: Chapter 2 Electrostatic Potential and Capacitance Part 14

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Spherical capacitor

Spherical Capacitor

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Q: 30. A spherical capacitor has an inner sphere of radius and an outer sphere of radius. The outer sphere is earthed and the inner sphere is given a charge of. The space between the concentric spheres is filled with a liquid of dielectric constant .

(A) Determine the capacitance of the capacitor.

(B) What is the potential of the inner sphere?

(C) Compare the capacitance of this capacitor with that of an isolated sphere of radius . Explain why the latter is much smaller.

Answer:

Radius of the inner sphere,

Radius of the outer sphere,

Charge on the inner sphere,

Dielectric constant of a liquid,

(A) Capacitance of the capacitor is given by the relation,

Where,

Permittivity of free space

Hence, the capacitance of the capacitor is approximately.

(B) Potential of the inner sphere is given by,

Hence, the potential of the inner sphere is .

(C) Radius of an isolated sphere,

Capacitance of the sphere is given by the relation,

The capacitance of the isolated sphere is less in comparison to the concentric spheres. This is because the outer sphere of the concentric spheres is earthed. Hence, the potential difference is less and the capacitance is more than the isolated sphere.

Q: 31. Answer carefully:

(A) Two large conducting spheres carrying charges and are brought close to each other. Is the magnitude of electrostatic force between them exactly given by , where r is the distance between their centers?

(B) If Columba’s law involved dependence (instead of ), 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 than say, mica.

Answer:

(A) The force between two conducting spheres is not exactly given by the expression, , because there is a non-uniform charge distribution on the spheres.

(B) Gauss’s law will not be true, if Coulomb’s law involved dependence, instead of , on.

(C) Yes, If a small test charge is released at rest at a point in an electrostatic field configuration, then it will travel 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 elliptical, the work done by the field of a nucleus is zero.

(E) No Electric field is discontinuous across the surface of a charged conductor. However, electric potential is continuous.

(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.