Unformatted text preview: 44. The ﬁeld is zero for 0 ≤ r ≤ a as a result of Eq. 2416. Since qenc (for a ≤ r ≤ b) is related to the volume
by
4πr3
4πa3
qenc = ρ
−
3
3
then
E= 1 qenc
ρ
=
4πε0 r2
4πε0 r2 4πr3
4πa3
−
3
3 = ρ r 3 − a3
3 ε0
r2 for a ≤ r ≤ b. And for r ≥ b we have E = qtotal /4πε0 r2 or
E= ρ b 3 − a3
3 ε0
r2 r≥b. This is plotted below for r in meters from 0 to 0.30 m. The peak value of the electric ﬁeld, reached at
r = b = 0.20 m, is 6.6 × 103 N/C. 6000 4000 2000 0 0.1 r 0.2 0.3 ...
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 Fall '08
 SPRUNGER
 Physics

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