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There are two concentric metallic spherical shells of radii $a$ and $b (a < b)$ . The shells are being maintained at a constant potential difference $V$ . The medium between the shells is filled with a material of resistivity $ρ$ . At a distance $r (a < r < b)$ from the centre of the shells

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Electric field is $\frac{V}{(b - a)}$

Current density is $\frac{V a b}{ρ r^{2} (b - a)}$

Electric field is $\frac{V a b}{r^{2} (b - a)}$

Current density is $\frac{V}{ρ (b - a)}$

answer is A, B.

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Detailed Solution

$\int d R = \int_{a}^{b} ρ \frac{d r}{4 π r^{2}}$

$R = \frac{ρ (b - a)}{4 π a b}$

$i = \frac{V}{R}$

$J = \frac{i}{4 π r^{2}} = \frac{V a b}{ρ (b - a) r^{2}}$

$J = \frac{E}{ρ} \Rightarrow E = \frac{V a b}{(b - a) r^{2}}$

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