Mutual Inductance






1) Suppose there are two Solenoid   S1  &   S2  are placed co-axially.



2) For S1 solenoid, has radius r1  length l,  and number of turns per unit length n1



3) For solenoid S2 it has radius  r2  length l, and number of turns per unit length n2



4) When I2 current is flowing through the solenoid S2,  the  magnetic field inside

(See from magnetic field inside solenoid)



 

Then from inductance law:

Magnetic flux related to the Solenoid S1 is


   


N1 = n1 l   total  no of turns in S1 solenoid






Now putting the value of 

   &   N1  in equation  6.21










           …………….. 6.12 

 


Here  M12  is called the mutual inductance of Solenoid S1 with respect to S2 Solenoid. 





5) Now second case:

When I1 current is flowing through the solenoid S1,  the  magnetic field inside S1 solenoid is



Now from inductance law the flux related to S1 solenoid is







N2 = n2 l   total  no of turns in S2 solenoid





Therefore



Now from 6.41 we get









Here M21 is the mutual inductance of Solenoid S2 with respect to S1 Solenoid


Therefore we see that






 

Be remember:


Now let us calculate the emf induce in a coil :

For the smaller coil we find




Then induce emf is