Question

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 $\frac{q\rho }{3{\epsilon }_0}.$
Statement-2 : The electric field at a distance $r(r<R)$ from the centre of the sphere is $\frac{\rho r}{3{\epsilon }_0}$

• A. Statement 1 is true, Statement 2 is true Statement 2 is not the correct explanation of Statement 1
• B. Statement 1 is true Statement 2 is false
• C. Statement 1 is false Statement 2 is true
• D. Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1

Answer 1

Answer: (C)

$U_c=\frac{3}{2}\frac{KQ}{R}q$
$U_s=\frac{KQ}{R}q$
$\therefore \Delta U=\frac{KQ}{2R}q$
$=\frac{1}{4\pi {\epsilon }_0}.\frac{1}{2R}\rho \frac{4\pi R^3}{3}q$
$=\frac{\rho R^{2}q}{6{\epsilon }_0}$