Volume charge density of a non-conducting sphere is varying as ρ = ρ 0 r where r 0 is a constant and r is the distance from centre of sphere. If potential at r = 2 R is zero then potential at infi

Question

Volume charge density of a non-conducting sphere is varying as ρ = ρ 0 ​ r where r 0 ​ is a constant and r is the distance from centre of sphere. If potential at r = 2 R is zero then potential at infinity will be

TestHub · Accepted Answer

Charge on sphere Q = ∫ 0 R ​ ρ 0 ​ ( 4 π r 2 dr ) = π ρ 0 ​ R 4 By definition of potential V 2 R ​ − V ∞ ​ = 2 R k Q ​ ⇒ V ∞ ​ = − 2 R k Q ​ = − 8 π ϵ 0 ​ R Q ​

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JEE Advanced (2028)