1. Notes 11 ECE 2317 Applied Electricity and Magnetism Prof. D. Wilton
ECE Dept.
Gauss
Notes 11
Notes prepared by the EM group, University of Houston.

2. Example r h Assume S l = l0 [C/m] infinite uniform line charge zy z S
l = l0 [C/m] h r
Find the electric field everywhere
Assume
infinite uniform line charge

3. Example (cont.) h St Sb Sc  r

4. Example (cont.)
Hence So

5. Example S h a  r Assume v = 3 2 [C/m3] ,  < ay z S h a  r
Find the electric field everywhere
Assume
v = 3 2 [C/m3] ,  < a
non-uniform infinite cylinder of volume charge density

6. Example (cont.)
(a)  < a  S r h

7. Example (cont.)
Hence So

8. Example (cont.)
(b)  > a S  h r

9. Example When Gauss’s Law is not useful: But (1) (2)y z
l0 -h
When Gauss’s Law is not useful:
But (1)
(2)
(the charge density
is not uniform!)
(3) E has more than
one component

10. Example s = s0 [C/m2] r A S Find the electric field everywhere z
Assume S A r

11. Example (cont.) S A r
Assume

12. Example (cont.) S A r so
( Generally, Ez is continuous except on either side
of a surface charge)

13. Example slab of uniform charge r x Find the electric field everywhere
Assume
(since Ex(x) is a continuous function)

14. Example (cont.) A
(a) x > d / 2 x x r S d

15. Example (cont.) Q Q d v0 seff A A Note: If we define then
(sheet formula) Q Q d
v0
seff A A

16. Example (cont.)
(b) 0 < x < d / 2 x r
x = x d S y
x = 0

17. Example (cont.) x
Summary d y
d / 2
v0 d / (20 ) x Ex
- d / 2