Q61 of 94 Page 166

A spherical capacitor is made of two conducting spherical shells of radii a and b. The space between the shells is filled with a dielectric of dielectric constant K up to a radius c as shown in figure. Calculate the capacitance.


Lets re-draw the diagram-


We know, capacitance for a spherical capacitance c is given by-


C =



Where,


C: Capacitance


ri: inner radius


ro: outer radius


k: relative permittivity


∈: permittivity of space


Capacitance between c and a-



Similarly, between b and c



From fig, we can see that the two capacitors are connected in series, hence the net capacitance is given by-






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59

A parallel-plate capacitor of plate area A and plate separation d is charged to a potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. Find the work done on the system in the process of inserting the slab.

 60

A capacitor having a capacitance of 100 μF is charged to a potential difference 50V.

a) What is the magnitude of the charge on each plate?


b) The charging battery is disconnected and a dielectric of dielectric constant 2.5 is inserted. Calculate the new potential difference between the plates.


c) What charge would have produced this potential difference in absence of the dielectric slab.


d) Find the charge induced at a surface of the dielectric slab.


 62

Consider an assembly of three conducting concentric spherical shells of radii a, b and c as shown in figure. Find the capacitance of the assembly between the points A and B.

 63

Suppose the space between the two inner shells of the previous problem is filled with a dielectric of dielectric constant K. Find the capacitance of the system between A and B.