Electric Potential, spherical shell: Multiple Choice

[TwinGemini14]

A non-conducting, spherical shell centered at the origin has radius r1 and total charge -Q, where Q is a positive value. (DO NOT ASSUME THE POTENTIAL AT INFINTIY IS ZERO!)

http://i662.photobucket.com/albums/uu347/TwinGemini14/ELECpotential.gif


1) The electric potential just outside the surface of the shell is __________ the electric potential infinitely far from the shell.

A) higher than
B) lower than
C) equal to

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This problem stumped me. I figured that the electric potential outside the sphere was...
V = -Q/(4*pi*EpsilonNot*r)

So as r grows, the potential actually gets higher.
So the answer is B.
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2) If a negative charge outside the shell is moved closer to the shell, the potential energy of the system will __________. If a positive charge outside the shell is moved closer to the shell, the potential energy of the system will __________.

A) decrease, increase
B) increase, stay the same
C) increase, decrease

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Since the force and displacement vectors are acting in opposite directions, the total work decreases. PE = -W, so then that means that the potential energy increases. The opposite is true with the positive charge.

So the answer is C.
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Can somebody please confirm these answers? I would like to know if I messed up some logic along the way. Thanks in advance!

 

[anathema]

Your answers are correct! You have a good understanding of the concept of electric potential and potential energy. Keep up the good work!

 

[tomcue]

Yes, your answers are correct. The electric potential outside the shell does indeed get higher as r increases, and the potential energy decreases when a negative charge is moved closer to the shell and increases when a positive charge is moved closer. Good job!