Question

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 outside 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 qρ/3ε₀ . 

Statement 2 : The electric field at a distance r(r < R) from the centre of the sphere is ρr/3ε₀. 

(a) Statement 1 is true, Statement 2 is false. 

(b) Statement 1 is false, Statement 2 is true. 

(c) Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

(d) Statement 1 is true, Statement 2, is true; Statement 2 is not the correct explanation of Statement 1.

Answer 1

(b) : Potential at the centre of the sphere,

Potential at the surface of the sphere,

When a charge q is taken from the centre to the surface, the change in potential energy is