1. Tardigrade
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  4. This questions has statement-1 and statement-2. Of the four choices given after the statements, choose the one that best describe 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 infinite is zero. Statement-1: When a charge q is take from the centre of the surface of the sphere its potential energy changes by (qρ/3ε0). Statement-2: The electric field at a distance r (r < R) from the centre of the sphere is (ρ r/3ε0)

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Q. This questions has statement-1 and statement-2. Of the four choices given after the statements, choose the one that best describe the two statements.
An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho$. 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 infinite is zero.
Statement-1 : When a charge $q$ is take from the centre of the surface of the sphere its potential energy changes by $\frac{q\rho}{3\varepsilon_{0}}.$
Statement-2 : The electric field at a distance $r (r < R)$ from the centre of the sphere is $\frac{\rho r}{3\varepsilon_{0}}$

AIEEEAIEEE 2012Electrostatic Potential and Capacitance

Solution:

$U_{c}=\frac{3}{2} \frac{KQ}{R}q$
$U_{s}=\frac{KQ}{R}q$
$\therefore \Delta U=\frac{KQ}{2R}q$
$=\frac{1}{4\pi\varepsilon_{0}}. \frac{1}{2R} \rho \frac{4\pi R^{3}}{3}q$
$=\frac{\rho R^{2}q}{6\varepsilon_{0}}$

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