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Q.

Potential difference between centre & the surface of sphere of radius R and uniform volume charge density ρ within it will be:

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a

0

b

ρR26ϵ0

c

ρR24ϵ0

d

ρR22ϵ0

answer is A.

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Detailed Solution

Potential at surface is:

Question Image

Vs=ρ×4πR33×4πϵ0R=ρR23ϵ0

Potential at center =  ∫dV=∫0R ρ4πx2dx4πϵ0x

⇒VC=ρR22ϵ0 ⇒VC−VS=ρR26ϵ0

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