Physics 121: Electricity &
Magnetism – Lecture 3
Carsten Denker
NJIT Physics Department
Center for Solar–Terrestrial Research
Coulomb’s Law and Flux
Gauss’ law uses
symmetry and is fully
equivalent to Coulomb’s
law.
Which one you have to
use depends on the
application!
Gauss’ law relates the electric fields at a
point on a (closed) Gaussian surface and
the net charge enclosed by that surface.
   v cos  A
January 31, 2007
  vA cos  v  A
Center for Solar-Terrestrial Research
Flux of an Electrical Field
Electric flux through a
Gaussian surface
   E  A

 E  dA
discrete form
integral form
The electric flux  through a
Gaussian surface is proportional
to the number of field lines
passing through that surface.
January 31, 2007
Center for Solar-Terrestrial Research
Gauss’ Law
Gauss’ law
 0  qenc
Gauss’ law
 0  E  dA  qenc
Gauss’ law and Coulomb’s law
 0  E  dA   0  E  dA qenc
 0 E  dA   0 E  4 r 2   q
E=
1
q
4 0 r 2
January 31, 2007
Center for Solar-Terrestrial Research
A Charged Isolated Conductor
If an excess charge is
placed on an isolated
conductor, the amount
of charge will move
entirely to the surface
of the conductor. None
of the excess charge
will be found within the
body of the conductor.

E
0
January 31, 2007
Conducting
surface
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Cylindrical and Planar Symmetry
Cylindrical symmetry
E

2 0 r
January 31, 2007
Planar symmetry
E

2 0
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Spherical Symmetry
Spherical shell
1
q
E
4 0 r 2
E0
r  R
r  R
A shell of uniform charge attracts or
repels a charged particle that is outside
the shell as if the shell’s charge were
concentrated at the center of the shell.
Uniform charge
(field at r  R)
A shell of uniform charge exerts no
electrostatic force on a charged particle
that is located inside the shell.
 1 
E 
r
3 
 4 0 R 
January 31, 2007
Center for Solar-Terrestrial Research