Gauss LawHard
Question
The electrostatic potential inside a charged spherical ball is given by φ = αρ2 + b where r is the distance from the centre; a, b are constants. Then the charge density inside ball is
Options
A. - 6a ε0 r
B. - 24πa ε0 r
C. - 6 a ε0
D. - 24πa ε0
Solution
Potential inside (φ) = ar2 + b
∴ Er = -
= - 2ar
Electric field inside uniformly charged solid volume varies with ′r′. So charge density is constant
φnet( - 2ar) 4πr2 = - 8πar3
- 8πar3 =
∴ σ = - 6aε0
∴ Er = -
= - 2arElectric field inside uniformly charged solid volume varies with ′r′. So charge density is constant
φnet( - 2ar) 4πr2 = - 8πar3
- 8πar3 =
∴ σ = - 6aε0
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