Hey,

good illustration.lets see if i have understood what you are asking...

when we say field inside a conductor is zero (i have got this doubt a hundred times)one of my prof said we mean inside the material not necessarily the area enclosed(like one of the jee questions with cavity)

Here, they are saying the field is zero because the and equal and opposite charge is induced on the inner surface of the big sphere so using guass law..the net charge is still zero which means the field is zero,hence over here they are adding

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