For a spherically symmetric charge distribution, the electric field is $\vec{E}$ = kr⁷ $\hat{r}$ , where k is a constant. Find the volume charge density ρ at distance r from the centre.
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Question

For a spherically symmetric charge distribution, the electric field is E ⃗ \vec{E} E = kr⁷ r ^ \hat{r} r ^ , where k is a constant. Find the volume charge density ρ at distance r from the centre.

G1 Physics · Accepted Answer

For a radial field, ∇·𝐄 = (1/r²)d(r²Eᵣ)/dr. Here Eᵣ = kr⁷, so ∇·𝐄 = (1/r²)d(kr⁹)/dr = 9kr⁶. Using ∇·𝐄 = ρ/ε₀ gives ρ = 9kε₀r⁶. Correct answer: A.