A long, current-carrying solenoid with an air core has 1800 turns per meter of length and a radius of 0.0165 m. A coil of 210 turns is wrapped tightly around the outside of the solenoid, so it has virtually the same radius as the solenoid. What is the mutual inductance of this system

The mutual inductance is  

Explanation:

From the question we  are told that

    The  number of turns per unit length  is  

    The radius is  

     The  number of turns of the solenoid is  

Generally the mutual inductance of the  system is mathematically represented as

Where A is the cross-sectional area of the system which is mathematically represented as

substituting values

also   is the permeability of free space with the value  

So  

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