i would like to know how to calculate the capacitance due to two concentric hollow spherical shells of radii r1 and r2 with r1

Dear STUDENT NAME,

Ans:- The thing is that if you want to calculate the capacitance then first of all you have to give it some charge. Now let's give a charge Q to it. and it is given to the inner sphere. As from the Gauss's law we know that there can not be any charge inside a hollow sphere and hence the entire charge will come out to the external surface of the outer sphere.So the potential of the inner sphere will be V1=Q/Kr1 -Q/kr2+Q/kr2 = Q/Kr1..............(1)                                                           

(Because the charge appearing in the inner and outer surface of the outer sphere is Q && -Q respectively. Thus to calculate the potential in the inner sphere, we must consider all the charges.

But if we consider the outer hollow sphere then the total charge inside this is 0 hence it's potential is V2=Q/Kr2 .....(2)

potential difference = V1-V2=Q/K(1/r1 - 1/r2)=ΔV

Now the capacitance is Q/ΔV=Kr1r2/(r1 - r2)

Hence C=Kr1r2/(r1-r2)

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Soumyajit Das IIT Kharagpur