Does Stacking Coils Create a "Cancellation Field"?

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Some basic curve integration leads me to the believe, that if you stack two coils into one another with opposite identical currents and windings, their outside field cancels while the inside field is identical to the configuration without the outer coil. Is this correct and does this configuration have a name?
 
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Ok I think I was wrong. My integrals were only fixed up to an offset, and the superposition principle proves me wrong...
 
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