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Electric Flux
Example 4.7
Consder a long cylindrical charge distribution of radius R with a
uniform charge density ρ. Find the electric field at distance r from the
axis where r<R.
Solution
If we choose a cilindrical gaussian surface of length L and radius r, Its
volume is πr 2 L, and it enclses a charge ρπr 2 L. By applying Gauss’s law we
get,
∫ E r
=
r 2
q
dA in
ρπr
. becomes E dA
ε ο
∫ =
εο
L
∫
Q dA = 2πrL
therefore
2
ρπr
L
E( 2πrL)
=
ε ο
Thus
ρ r
E = radially outward from the cylinder axis
2
ε ο
Notice that the electric field will increase as ρ increases, and also the
electric field is proportional to r for r<R. For thr region outside the cylinder
(r>R), the electric field will decrese as r increases.
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