## 11 April 2011

### Mail Time: Electric field and potential inside a conductor

Georgian Michael Gray writes:
 metal lattice representation from nanotechweb.org

I'm having a hard time with a rationale for number 19 on the 2009 MC exam. Can you help me?

Michael got a copy of the 2009 exam from last year's AP Summer Instititute.  It is also available for purchase from the College Board.  (That's why I can't post the text of the question here.)  Come to a workshop or institute, and I'll give you a copy of EVERY released exam question since 1979.

The question in question asks about the electric potential on two sides of a metal block.  The potential is V on the left side of the metal block; what is the potential on the right side?

So can I help?  Sure... but the answer depends on how deep you want to go.

At the truly introductory level, it's a fact of physics: metal objects have no electric field inside them, and are at the same electric potential everywhere. Charges can only reside on the surface of a metal object.

At the physics C level, you only need the last fact. Then you can use Gauss's law to show that a gaussian surface drawn inside the metal encloses no charge, such that there can be no electric field inside a conductor. Then potential is the spatial derivitive of electric field (i.e. voltage tells us how electric field changes). Since electric field is unchanging throughout metal, the potential must be the same everywhere but not necessarily zero.

And there's an even deeper answer, the one that discusses the periodic potential of the lattice of atoms in a metal and why electrons are free to move about the metal in the first place.  That's a graduate material science answer.

This is a HARD physics B question. I wouldn't worry if your students miss it.

GCJ
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