Statement 1: When a charge q is taken from the centre to the surface of an insulating solid sphere of radius R and uniform charge density ρ , its pote - Physics MCQ AIEEE 2012 2026 | ExamTest.live

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Statement 1: When a charge q is taken from the centre to the surface of an insulating solid sphere of radius R and uniform charge density ρ, its potential energy changes by \frac{qρ R ^{2}}{3 ϵ _{0}} .Statement 2: The electric field at a distance r (r < R) from the centre of the sphere is \frac{ρ r}{3 ϵ _{0}} .

A $Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1$
B $Statement 1 is true, Statement 2 is false$
C $Statement 1 is false, Statement 2 is true$
D $Statement 1 is true, Statement 2 is the correct explanation for statement 1$

Solution & Step-by-step Explanation

Statement 2: Using Gauss's Law for r < R : E (4 π r^{2}) = \frac{Q _{e n c l}}{ϵ _{0}} = \frac{ρ \frac{4}{3} π r ^{3}}{ϵ _{0}} ⟹ E = \frac{ρ r}{3 ϵ _{0}} This is True.Statement 1: Potential at distance r inside a solid sphere: V (r) = \frac{ρ}{6 ϵ _{0}} (3 R^{2} - r^{2}) Potential at centre (r = 0): V_{c} = \frac{ρ R ^{2}}{2 ϵ _{0}} .Potential at surface (r = R): V_{s} = \frac{ρ R ^{2}}{3 ϵ _{0}} .Change in P.E. Δ U = q (V_{s} - V_{c}) = q (\frac{ρ R ^{2}}{3 ϵ _{0}} - \frac{ρ R ^{2}}{2 ϵ _{0}}) = q (\frac{- ρ R ^{2}}{6 ϵ _{0}}) .Magnitude is \frac{qρ R ^{2}}{6 ϵ _{0}}, not \frac{qρ R ^{2}}{3 ϵ _{0}} .Statement 1 is False.

Try it yourself before checking the explanation above.

Statement 1: When a charge q is taken from the centre to the surface of an insulating solid sphere of radius R and uniform charge density ρ, its potential energy changes by \frac{qρ R ^{2}}{3 ϵ _{0}} .Statement 2: The electric field at a distance r (r < R) from the centre of the sphere is \frac{ρ r}{3 ϵ _{0}} .

Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1

Statement 1 is true, Statement 2 is false

Statement 1 is false, Statement 2 is true

Statement 1 is true, Statement 2 is the correct explanation for statement 1

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