A long solenoid of length L, cross-section A having N1 tums has wound about its centre is small coil of N2 turns as shown in fig.(10). Then the mutual inductance of two circuits is

Magnetic flux at the centre of solenoidB1=μ0N1/Li1Magnetic flux through each turn of the coil of area AΦ1=B1A=μ0N1i1L×AMagnetic flux linked with the coil of turns N2Φ2=Φ1×N2=μ0N1N2i1ALAccording to the definition of mutual inductanceΦ2=Mi1∴Mi1=μ0N1N2i1LA or M=μ0N1N2AL