Solid metal sphere of radius a is surrounded by a concentric metallic shell of r

Question

Solid metal sphere of radius a is surrounded by a concentric metallic shell of radius b. The space between them is fully filled with the isotropic conducting medium with electrical conductivity . Find electric resistance R between the metal electrodes.

Solid metal sphere of radius a is surrounded by a concentric metallic shell of radius b. The space between them is fully filled with the isotropic conducting medium with electrical conductivity ?. Find electric resistance R between the metal electrodes.

Explanation / Answer

By do you maybe mean resistivity? That's the traditional symbol for resistivity, usually for conductivity. Anyway I am going to use it as resistivity and if it is actually conductivity, just use the reciprocal.

R = (l/A).    Consider an infinitesimal spherical shell located at radius r between A and B. Its length is dr and its area is 4r2.   Now integrate from A to B:

R = (/4)r-2 dr = (/4)(1/A - 1/B)

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