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Volume charge density of a non conducting solid sphere of radius R=30 cm is given as ρ=ρo(1rR). Electric field inside sphere is minimum at
  1. r=15 cm
  2. r=30 cm
  3. r=10 cm
  4. r=20 cm


Solution

The correct option is D r=20 cm
By Gauss law, E.dr=qenclosedϵo  
So, E ×4πr2=qenclosedϵ0 ,
where qenclosed=ρdV
qenclosed=r0ρo(1rR)4πr2dr

qenclosed=4πρoro(r2r3R)dr
              =4πρo[r33r44R]ro

qenclosed=4πρo(r33r44R)E ×4πr2=4πρor2ϵo(r3r24R)
E=ρoϵo(r3r24R)
For maxima or minima, dEdr=0
132r4R=0
r=2R3=2×303 cm=20 cm

 

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