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If S is the area of cross section of the solenoid then

                                                             ..................................(4.55)

The flux linkage per unit length of the solenoid

                                                            ..................................(4.56)
 
The inductance per unit length of the solenoid    
    
                                                               ..................................(4.57)                    


Steady Magnetic Field

The magnetic flux density inside such a long solenoid can be calculated as

                                                                  ..................................(4.54)

where the magnetic field is along the axis of the solenoid.