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Question

A solid ball of radius R has a charge density ρ given by ρ=ρ0(1r/R) for 0rR. The electric field outside the ball is:
  1. 4rho0 R33 0 r2
  2. 3 ρ0 R34 0 r2
  3. ρ0 R312 0 r2
  4. ρ0 R30 r2

A
ρ0 R312 0 r2
B
ρ0 R30 r2
C
4rho0 R33 0 r2
D
3 ρ0 R34 0 r2
Solution
Verified by Toppr

ρ=ρ0(1rR)
dq=ρdv
qin=dq
=ρdv
ρ0(1rR)4πr2dr

dv=4πr2dr

=4πρ0R0(1rR)r2dr

=4πρoRor2drr2Rdr

=4πρo[[r33]Ro[r44R]Ro]

=4πρo[R33R44R]

=4πρo[R33R34]

=4πρo[R312]

q=πρoR33

E.4πr2=(πρoR33o)

E=ρoR312or2

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