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 uniform positive charge density ρ. As a result of this uniform charge distribution there is a finite val…

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 uniform 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 (ρ r)/(3ε₀).

Accepted Answer

(2) Statement 1 is false, Statement 2 is true.. Statement 2: a Gaussian sphere of radius r<R encloses ρ·4/3π r³, so E 4π r²=(ρ4/3π r³)/(ε₀), giving E=(ρ r)/(3ε₀). True. Statement 1: V_centre-V_surface=∫₀^RE dr=ρ/(3ε₀)·(R²)/2=(ρ R²)/(6ε₀). So the potential energy change is |Δ U|=(qρ R²)/(6ε₀), not (qρ)/(3ε₀) — the printed expression is not even dimensionally a potential energy. False. Hence Statement 1 is false and Statement 2 is true.

Step-by-step solution

Why the other options are wrong