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The Charge Inside a Conductor
A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge, of positive charge q.
Part A
What is the total surface charge q_int on the interior surface of the conductor (i.e., on the wall of the cavity)?
Hint A.1  

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ANSWER:
  q_int =  -q 
Part B
What is the total surface charge q_ext on the exterior surface of the conductor?
Hint B.1  

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ANSWER:
  q_ext =  q 
Part C
What is the magnitude E_int of the electric field inside the cavity as a function of the distance r from the point charge? Let k, as usual, denote \frac{1}{4\pi\epsilon_0}.
Hint C.1
How to approach the problem

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Part C.2
Charge distributions and finding the electric field

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ANSWER:
0k q/r^22k q/r^2
Part D
What is the electric field E_ext outside the conductor?
Hint D.1  

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Hint D.2  

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ANSWER:
zero
the same as the field produced by a point charge q located at the center of the sphere
the same as the field produced by a point charge located at the position of the charge in the cavity
Now a second charge, q_2, is brought near the outside of the conductor. Which of the following quantities would change?
Part E
The total surface charge on the wall of the cavity, q_int:
Hint E.1  

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ANSWER:
would changewould not change
Part F
The total surface charge on the exterior of the conductor, q_ext:
Hint F.1  

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ANSWER:
would changewould not change
Part G
The electric field within the cavity, E_cav:
ANSWER:
would changewould not change
Part H
The electric field outside the conductor, E_ext:
ANSWER:
would changewould not change
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