Question 625: Electrostats & Capacitance

Question

Within a spherical charge distribution of charge density $$\rho $$(r), N equipotential surfaces of potential V0, V0 + $$\Delta $$V, V0 + 2$$\Delta $$V, .......... V0 + N$$\Delta $$V ($$\Delta $$ V > 0), are drawn and have increasing radii r0, r1, r2,..........rN, respectively. If the difference in the radii of the surfaces is constant for all values of V0 and $$\Delta $$V then :

Accepted Answer

Here, $$\Delta $$v and $$\Delta $$r are same for any pair of surface.
we know,
Electric field, E  = $$-$$ $${{dv} \over {dr}}$$
$$ 	herefore $$   E = constant [As dv and dr are constant]
Electric field inside the spherical charge distribution.
E = $${{ho r} \over {3{\varepsilon _0}}}$$
Now,   as E = constant
$$ 	herefore $$   $$ho $$ r = constant
$$ \Rightarrow $$   $$ho $$ (r) $$ \propto $$ $${1 \over r}$$

Answer

$$\rho $$ (r) $$\alpha $$ r

Answer

$$\rho $$ (r) = constant

Answer

$$\rho $$ (r)  $$\alpha $$ $${1 \over r}$$

Answer

$$\rho $$ (r) $$\alpha $$ $${1 \over {{r^2}}}$$

Electrostats & Capacitance

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