Last Lectures
Gauss’s law
Using Gauss’s law for:
spherical symmetry
line symmetry
plane symmetry
This lecture
Conductors in electric fields
21.6 Charges on Conductors
electrostatic equilibrium
A Gaussian surface completely
within the conductor.
Since E must be zero inside
conductor, the net flux
through this surface must
be zero.
EXAMPLE: (a) shows a cross section of a
spherical metal shell of inner radius R.
A point charge of –5.0 C is located at
a distance R/2 from the centre of the
shell. If the shell is electrically
neutral, what are the (induced)
charges on its inner and outer
surfaces? Are those charges uniformly
distributed? What is the field pattern
inside and outside the shell?
Key Idea:
Electric field is zero
inside metal and thus
on Gaussian surface.
Key Idea:
Shell is electrically neutral. Electrons
move from inner surface to outer
surface and spread out uniformly
Example 21.7 There is a hollow cavity inside a conductor. The
conductor itself has a charge of 1 μC, and there is a 2 μC
charge inside the cavity.
Find the net charge on the outer surface of the conductor,
assuming electrostatic equilibrium.
Assess: What does this charge distribution look like from far
away?
Field at the surface of a
conductor
NB E is always
perpendicular to the
surface
WHY? More on this with
potential
Field at the surface of a
conductor
Now use Gauss’s law to
find E just outside a
conductor surface
EA  0 
qenclosed
0
A
EA 
0
 (field at conductor surface)
E
0
Field at the surface of a
conductor
Field at the surface of a conductor
Two oppositely charged conducting plates
TrueTrue
A or False?
False F
1.
If the net electric flux out of a closed surface is zero, the electric
field must be zero everywhere on the surface.
False
2.
If the net electric flux out of a closed surface is zero, the charge
False
density must be zero everywhere inside the surface.
3.
The electric field is zero everywhere within the material of a
conductor in electrostatic equilibrium.
4.
The tangential component of the electric field is zero at all points
just outside the surface of a conductor in electrostatic
True
equilibrium.
False
The normal component of the electric field is the same at all points
5.
just outside the surface of a conductor in electrostatic
equilibrium.
Try these again!
True