Q29 of 38 Page 88

A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig. 2.36). Show that the capacitance of a spherical capacitor is given by


Where r1 and r2 are the radii of outer and inner spheres, respectively.


Radius of the outer shell = r1


Radius of the inner shell = r2


Charge on the inner surface of the outer shell = Q


Charge on the outer surface of the inner shell = -Q


Potential difference between the two shells,



Where, = Absolute Permittivity of free space = 8.8510-12C2N-1m-2


Since, Capacitance,




Hence, proved.


More from this chapter

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27

A 4 μF capacitor is charged by a 200 V supply. It is then disconnected from the supply, and is connected to another uncharged 2 μF capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?

 28

Show that the force on each plate of a parallel plate capacitor has a magnitude equal to (1/2) QE, where Q is the charge on the capacitor, and E is the magnitude of electric field between the plates. Explain the origin of the factor 1/2.

 30

A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 μC. The space between the concentric spheres is filled with a liquid of dielectric constant 32.

(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 12 cm. Explain why the latter is much smaller.

 31

Answer carefully:

(a) Two large conducting spheres carrying charges Q1 and Q2 are brought close to each other. Is the magnitude of electrostatic force between them exactly given by Q1 Q2/4πε0r2, where r is the 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 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).