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Q.

The electrostatic potential inside a charged spherical ball is given by  ϕ=ar2+b where  r is the distance from the centre and a, b are constants. Then the charge density inside the ball is:

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a

− 6aε0r

b

− 24πaε0

c

− 6aε0

d

− 24πaε0r

answer is C.

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Detailed Solution

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E=-dϕdt=-2ar

By Gauss's theorem,
E4πr2=qϵ0

q=-8πϵ0ar2

ρ=qv=-8πϵ0ar343πr3=-6aϵ0

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