Download CONDUCTORS IN ELECTROSTATIC EQUILIBRIUM (19.11

CONDUCTORS IN ELECTROSTATIC EQUILIBRIUM (19.11)
Properties are a result of the following:
 In a “good” conductor, electrons are free to move.
 At electrostatic equilibrium, charges MUST feel no force OR ELSE they will
move until there is no force
One result: charge distribution is generally NON-UNIFORM for:
 A charged conductor
 A conductor in an electric field
PROPERTIES: ISOLATED CONDUCTOR IN ELECTROSTATIC EQUILIBRIUM
st
1 :

E  0 everywhere inside a conductor

 Must be true or else charges would move until E  0
o for conductor in external electric field, charges


locate so that superposition of external E plus E

from charges gives E  0 inside
2nd: Any NET CHARGE on conductor must be on surface
 can prove with Gauss’s Law
o Choose Gaussian surface JUST INSIDE conductor surface

 because E  0 inside, normal component of field at
Gaussian surface must be zero
 Because En  0 , must have  E   En dA  0
qinside


q
0
 But Gauss’s law says E
 0 so inside
 Because Gaussian surface can be arbitrarily close to
the conductor surface, net charge inside conductor
must be zero
RESULT: ANY NET CHARGE ON THE CONDUCTOR MUST BE ON THE
SURFACE
3rd: Electric field JUST OUTSIDE a CHARGED CONDUCTOR:
 MUST be perpendicular to the surface. If not, charge flows along surface

E

 MUST have magnitude n 
0
o  is the surface charge density AT THAT point
o choose Gaussian cylinder, cross-sectional area A

 one end inside conductor (where E  0 )

 one end outside conductor (where E  En )

 know E is perpendicular to cond. surface
 charge inside is qinside  A
o Only flux through Gaussian surface is through outside cylinder end
 
 So:  e   E  dA  E n A
qinside


o Gauss’s law says E
0

E

o Result is: n 
0
A
E
A

which means n
0

E is perpendicular to surface of charged conductor

Neutral conductor in an external E field
 Field induces charge separation

E
 Field lines bend so that
at the
surface is always perpendicular
4th: Surface charge density is HIGHEST where radius of surface curvature is
smallest

 Means highest E at most “pointed” regions of surface
 Will see why later