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2. Electric Potential and Capacitance
hard
Within a spherical charge distribution of charge density $\rho \left( r \right)$, $N$ equipotential surfaces of potential ${V_0},{V_0} + \Delta V,{V_0} + 2\Delta V,$$.....{V_0} + N\Delta V\left( {\Delta V > 0} \right),$ 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 $\Delta V$ then
A
$\rho \left( r \right) = $ constant
B
$\rho \left( r \right) \propto \frac{1}{{{r^2}}}$
C
$\rho \left( r \right) \propto \frac{1}{r}$
D
$\rho \left( r \right) \propto r$
(JEE MAIN-2016)
Solution
As we know electric field, $E = \frac{{ – dv}}{{dr}}$
$E=$ constant $\therefore $ $dv$ and $dr$ same
$ \Rightarrow \,\rho \propto \frac{1}{r}$
Standard 12
Physics
