See you can solve it like this. Consider the inner conductor as a wire carrying current i. The formula of magnetic induction at a distance r from the wire is       i/2r. The answer is the same because there will be no field due to the outer conductor inside as there is air between the 2 conductors. Now if we apply ampere's law to find field due to outer conductor, then in that case, i enclosed between the 2 conductors will be zero.

Hence the net field will only be due to the inner conductor. And that is your answer.

 

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