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The Electric Field and Surface Charge at a Conductor
Learning Goal: To understand the behavior of the electric field at the surface of a conductor, and its relationship to surface charge on the conductor.
A conductor is placed in an external electrostatic field. The external field is uniform before the conductor is placed within it. The conductor is completely isolated from any source of current or charge.
Part A
Which of the following describes the electric field inside this conductor?
ANSWER:
It is in the same direction as the original external field.
It is in the opposite direction from that of the original external field.
It has a direction determined entirely by the charge on its surface.
It is always zero.
The net electric field inside a conductor is always zero. If the net electric field were not zero, a current would flow inside the conductor. This would build up charge on the exterior of the conductor. This charge would oppose the field, ultimately (in a few nanoseconds for a metal) canceling the field to zero.
Part B
The charge density inside the conductor is:
ANSWER:
0
non-zero; but uniform
non-zero; non-uniform
infinite
You already know that there is a zero net electric field inside a conductor; therefore, if you surround any internal point with a Gaussian surface, there will be no flux at any point on this surface, and hence the surface will enclose zero net charge. This surface can be imagined around any point inside the conductor with the same result, so the charge density must be zero everywhere inside the conductor. This argument breaks down at the surface of the conductor, because in that case, part of the Gaussian surface must lie outside the conducting object, where there is an electric field.
Part C
Assume that at some point just outside the surface of the conductor, the electric field has magnitude E and is directed toward the surface of the conductor. What is the charge density eta on the surface of the conductor at that point?
Part C.1  

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Hint C.5  

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Express your answer in terms of E and epsilon_0.
ANSWER:
  eta =  -{\epsilon}_{0}E 
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