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System Of Particles And Rotational Motion

Question
CBSEENPH11020357

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

  • fraction numerator straight Q over denominator 4 πε subscript straight o straight r subscript 1 superscript 2 end fraction
  • 0

  • fraction numerator Qr subscript 1 superscript 2 over denominator 4 πε subscript straight o straight R to the power of 4 end fraction
  • fraction numerator Qr subscript 1 superscript 2 over denominator 3 πε subscript straight o straight R to the power of 4 end fraction

Solution

C.

fraction numerator Qr subscript 1 superscript 2 over denominator 4 πε subscript straight o straight R to the power of 4 end fraction fraction numerator straight Q over denominator 4 πε subscript 0 straight r subscript 1 superscript 2 end fraction space integral subscript straight r space equals 0 end subscript superscript straight r subscript 1 end superscript space fraction numerator 4 space πr cubed dr over denominator πR to the power of 4 end fraction
space equals space fraction numerator straight Q over denominator 4 πε subscript 0 end fraction fraction numerator straight r subscript 1 superscript 2 over denominator straight R subscript 4 end fraction