ρ₀R³/12 ε₀r²
ρ₀R³/ε₀r²
4ρ₀R³/3ε₀r²
3 ρ₀R³/4ε₀r²
ρ = ρ₀(1−r/R)
dq = ρdv
qin = ∫dq = ∫ρdv
ρ₀(1−r/R)4πr²dr
∫dv = 4πr²dr
= 4πρ₀∫₀ᴿ(1−r/R)r²dr
= 4πρ₀∫₀ᴿr²dr − ∫₀ᴿr³/R dr
= 4πρ₀[[r³/3]₀ᴿ − [r⁴/4R]₀ᴿ]
= 4πρ₀[R³/3 − R³/4]
= 4πρ₀[R³/12]
q = πρ₀R³/3
E.4πr² = (πρ₀R³/3ε₀) ⇒ E = ρ₀R³/12ε₀r²