JEE Main2016PhysicsElectrostaticsActual
Within a spherical charge distribution of charge density ρ r , N equipotential surfaces of potential V 0 , V 0 + ∆ V , V 0 + 2 ∆ V , … V 0 + N ∆ V ∆ V > 0 , are drawn and have increasing radii r 0 , r 1 , r 2 , … r N , respectively. If the difference in the radii of the surfaces is constant for all values of V 0 a n d ∆ V then :
Options
- Aρ r = constant
- Bρ ( r )   ∝ 1 r 2
- Cρ ( r ) ∝ 1 r
- Dρ ( r )   ∝   r
Correct answer
C. ρ ( r ) ∝ 1 r
Step-by-step solution
E = − Δ V Δ r ∴       △ v and △ r are constant E = constant E = K q r 2 = c ⇒       q   ∝ r 2 ∴       q = ∫ 0 r ρ 4 π r 2 d r   ⇒       ρ ∝ 1 r