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Potential of a Charged Conductor
We will now prove that the surface of a charged conductor in electrostatic equilibrium is an
equipotential surface -
the surface is at the same electric potential.
Consider a charged conductor in electrostatic equilibrium.
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A
B
E
dl
C
0 (since E
d between A and B)
0 (since E=0 everywhere inside a conductor)
B
BA
A
A
CA
C
V
V
E d
V
V
E d
1. The
surface of a charged conductor in equilibrium is an equipotential surface.
2.
Since Since the E = 0 inside the conductor, then the potential must be constant everywhere
inside the conductor and equal to the value at the surface
A Cavity Within a Conductor
We will now prove that if you have a cavity inside a conductor with no charge inside, the electric
field must be zero everywhere inside the cavity.
A
B
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