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The space between two concentric spherical shells of radii a and b (a < b) is filled with medium of resistivity $ρ$ .The resistance offered by the medium to the flow of current when a source is connected across the two spheres is $\frac{ρ (b - a)}{x π a b}$ . Find x?

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answer is 4.

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Detailed Solution

Consider an elemental shell of radius $r$ and thickness $d r$ .
Its resistance is
$d r = \frac{ρ d r}{4 π r^{2}}$
The total resistance of shell is

$R = \frac{ρ}{4 π} \int_{a}^{b} \frac{d r}{r^{2}} = \frac{ρ}{4 π} (\frac{1}{a} - \frac{1}{b})$

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