Electric field within conductor

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Fluxxx
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How come there's no electric field inside a metal cylinder, even though there's positive charge on side and negative charge on the other? For example look at this picture:
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As you can see there's is a zero electric field within the cylinder. Why isn't there an electric field that's directed from the + charges within the cylinder to the - charges within it?
 

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The charges move freely to screen the field, two fields cancel each other.
 
The original outside field still penetrates the sphere. It's just that the charges inside the sphere move around and build up a counter-field that exactly cancels that outside field. So, it's the net field that is zero.