Question 508: Electrostatics & Capacitance

Question

Within a spherical charge distribution of charge density $$\rho $$(r), N equipotential surfaces of potential V
0
, V
0
+ $$\Delta $$V, V
0
+ 2$$\Delta $$V, .......... V
0
+ N$$\Delta $$V ($$\Delta $$ 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 $$\Delta $$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) $$\alpha $$ $${1 \over {{r^2}}}$$

Electrostatics & Capacitance

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