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Gauss’s Law Geometries
Physics 320 Prof. Menningen
Spherical Geometry (Griffiths 2.12, POP4 19.40.mod) An insulating solid sphere of radius R has a uniform
charge density e and carries a total positive charge Q. Plot the electric field as a function of r.
Write Emax in symbolic form in the box provided.
E
Q 40 R2
Er
Inside:
 E  dA 
E  4 r 2  
Outside:
qenc
0
 r3
3
3R
4
1
0
Q 43
Q r3
Q

E

r rˆ
 0 R3
4 0 R3
qenc
 E  dA 
E  4 r 2  

Q
0
0
E

E
1
r2
r
R
Q
0
Q
4 0r 2
rˆ
Cylindrical Geometry (Griffiths Example 2.3mod, POP4 19.39) Consider a long cylindrical charge
distribution of radius R with a uniform charge density e. Find the magnitude of the electric field
everywhere and graph it below. Write Emax in symbolic form in the box provided.
E
e R 20
Es
qenc
 E  dA  
  s L 
E  2 sL  
Inside:
E
1
s
0
2
E
0

s sˆ
2 0
qenc
 E  dA  
  R L 
E  2 sL  
Outside:
2
0
0
 R2 1
E
sˆ
2 0 s
R
s
Planar Geometry (Griffiths 2.17, like PSE6 24.37) An infinite plane slab, of thickness 2d, carries a uniform
volume charge density ρ (Fig. 2.27). Find the electric field, as a function of y, where y = 0 at the
center. Plot E versus y, calling E positive when it points in the +y direction and negative when it
points in the –y direction.
 E  dA 
qenc
0
inside:
EA  0  EA 
E
 2y A
0
 y  yˆ for y  0

 0  yˆ for y  0
outside:
EA  0  EA 
E
  2d  A
0
d  yˆ for y  0

 0  yˆ for y  0
E
d  0
−d
y
d