Within a spherical charge distribution of charge density ρ r ,   N equipotential surfaces of…

Within a spherical charge distribution of charge density ρr,  N equipotential surfaces of potential V0, V0+∆V, V0+2∆V,…V0+N∆V ∆V>0, are drawn and have increasing radii r0, r1, r2,…rN, respectively. If the difference in the radii of the surfaces is constant for all values of V0 and ∆V then :
  1. ρr = constant
  2. ρ( r ) ∝ 1 r 2
  3. ρ( r ) ∝  1 r
  4. ρ( r ) ∝ r

Solution

E=− ΔV Δr

∴    △v and △r are constant

E = constant

E=Kqr2=c

⇒   q ∝r2

∴   q=∫0rρ4πr2dr 

⇒   ρ∝1r

Asked in: JEE Main 2016 (10 Apr Online)

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