Within a spherical charge distribution of charge density $ρ (r)$ , N equipotential surfaces of potential $V_{0}, V_{0} + Δ V,$ $V_{0} + 2 Δ V, ... V_{0} + N Δ V (Δ V > 0),$ are drawn and have increasing radii $r_{0}, r_{1}, r_{2}, ... r_{N},$ respectively. If the difference in the radii of the surfaces is constant for all values of $V_{0}$ and $Δ V$ then

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$ρ (r) \propto \frac{1}{r}$

$ρ (r) \propto r$

$ρ (r) \propto \frac{1}{r^{2}}$

$ρ (r) = constan t$

answer is C.

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Detailed Solution

WKT, $E = - \frac{dV}{dr}$

Here, $ΔV and Δr$ are same for any pair of surfaces

So , E=Constant

Now electric field inside the spherical charge distribution

$E = \frac{ρ}{3 \in_{0}} r$

E would be constant if

$ρ$ r=constant

$ρ (r) \propto \frac{1}{r}$

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