This question has statement-1 and statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
An insulating solid sphere of radius R has a uniformly positive charge density $ρ$ . As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero

Statement -1 : When a charge ‘q’ is taken from the centre to the surface of the sphere, its potential energy changes by $\frac{q ρ}{3_{0}}$
Statement-2 : The electric field at a distance r (r<R) from the centre of the sphere is $\frac{ρ r}{3 ε_{0}}$

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statement-1 is true, statement-2 is true, statement-2 is not the correct explanation of statement -1

statement -1 is true statement-2 is false

statement-1 is true, statement-2 is true, statement-2 is the correct explanation of statement-1

statement-1 is false, statement-2 is true

answer is C.

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Detailed Solution

Uusing Gauss law, $\int \vec{E} \vec{d A} = \frac{1}{ϵ_{0}} (ρ) \times \frac{4}{3} π r^{3}$

$\Rightarrow E = \frac{ρr}{3 ϵ_{0}}$ ( statement 2 is correct)

The electric potential inside a uniformly charged sphere

$= \frac{{ρR}^{2}}{6 \in_{0}} [3 - \frac{r^{2}}{R^{2}}]$

$ΔPE = (V_{surr} - V_{cent}) q = - \frac{q}{6 ϵ_{0}} {ρR}^{2}$

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