Let P(r) = Qr/(πR⁴) be the volume charge density inside a solid sphere of radius R and total charge Q. For a point P inside the sphere at distance r₁ from the centre, the magnitude of the electric field is:
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Question

Let P(r) = Qr/(πR⁴) be the volume charge density inside a solid sphere of radius R and total charge Q. For a point P inside the sphere at distance r₁ from the centre, the magnitude of the electric field is:

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G1 Physics · Accepted Answer

Charge enclosed within radius r₁ is Qₑ = 4π∫₀ʳ¹ [Qr/(πR⁴)]r²dr = Qr₁⁴/R⁴. By Gauss's law, E(4πr₁²) = Qₑ/ε₀. Therefore E = Qr₁²/(4πε₀R⁴). Correct answer: C.