الفيزياء العامة الجزء الثاني#موقع الفيزياء.كوم

Lectures in General Physics
Example 4.6
A long straight wire is surrounded by a hollow cylinder whose axis
coincides with that wire as shown in figure 4.19. The solid wire has a
charge per unit length of +λ, and the hollow cylinder has a net charge
per unit length of +2λ. Use Gauss law to find (a) the charge per unit
length on the inner and outer surfaces of the hollow cylinder and (b) the
electric field outside the hollow cylinder, a distance r from the axis.
Solution
(a) Use a cylindrical Gaussian surface S 1 within
the conducting cylinder where E=0
+ λ
Thus
∫ E r r
. dA = = 0
q in
ε ο
and the charge per unit length on the inner surface
must be equal to
λ inner = -λ
Also λ inner + λ outer = 2λ
thus λ outer = 3λ
(b) For a gaussian surface S 2 outside the
conducting cylinder
∫ E r r
. dA =
q in
ε ο
Figure 4.19
+2 λ
1
E (2πrL) = (λ - λ + 3λ)L
ε ο
3λ
∴ E =
2πε ο
r
Dr. Hazem Falah Sakeek