Question 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.

Answer

Radius of the inner sphere, r_{2} = 12 cm = 0.12 m

Radius of the outer sphere, r_{1}= 13 cm = 0.13 m

Charge on the inner sphere, q = 2.5 μC = 2.5 x 10^{-6} C

Dielectric constant of a liquid, ∈_{r }= 32

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

Where,

∈_{0 }= Permittivity of free space = 8.85 x 10^{-12} C^{2} N^{-1} m^{-2}

Hence, the capacitance of the capacitor is approximately 5.5 x 10^{-9} F.

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

Hence, the potential of the inner sphere is 4.5 x 10^{2} V.

(c) Radius of an isolated sphere, r = 12 x 10^{-2} m

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.

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(b) Is there a transfer of mass from wool to polythene?

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- Q:-
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- Q:-
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(a) Why does a paramagnetic sample display greater magnetisation (for the same magnetising field) when cooled?

(b) Why is diamagnetism, in contrast, almost independent of temperature?

(c) If a toroid uses bismuth for its core, will the field in the core be (slightly) greater or (slightly) less than when the core is empty?

(d) Is the permeability of a ferromagnetic material independent of the magnetic field? If not, is it more for lower or higher fields?

(e) Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. (This fact is analogous to the static electric field lines being normal to the surface of a conductor at every point.) Why?

(f ) Would the maximum possible magnetisation of a paramagnetic sample be of the same order of magnitude as the magnetization of a ferromagnet?

- Q:-
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(b) What is the force on the second sphere due to the first?

- Q:-
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(b) After the supply was disconnected.

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(d) None of the above.

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(d) 1000 GHz

Amit
2018-07-24 08:37:06

sir define brief about the potential diffrence how it is less for concentric spheres

Gaurav Jewaria
2018-06-24 12:07:57

Thnks saralstudy.com

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