question_answer

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 outside 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 \[\frac{\rho r}{3{{\varepsilon }_{0}}}\]  [AIEEE 2012]

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, and Statement 2 is the correct explanation of Statement 1.

Correct Answer: C

Solution :

[c] \[{{U}_{c}}=\frac{3}{2}\frac{KQ}{R}q\]

\[{{U}_{S}}=\frac{KQ}{R}q\]

\[\therefore \,\,\Delta U=\frac{KQ}{2R}q\]

\[=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{1}{2R}\rho \frac{4\pi {{R}^{3}}}{3}q\]

\[=\frac{\rho {{R}^{2}}q}{6{{\varepsilon }_{0}}}\]