Pls explain mutual inductance of two long co - axial solenoids
Dear Student,
Consider two long solenoids S 1 and S 2 of same length l, such that solenoid S 2 surrounds solenoid S 1 completely.
Let
n 1 − Number of turns per unit length of S 1
n 2 − Number of turns per unit length of S 2
I 1 − Current passed through solenoid S 1
Φ 21 − Flux linked with S 2 due to current flowing through S 1
Φ 21 ∝ I 1
Φ 21 = M 21 I 1
Where, M 21 is the coefficient of mutual induction of the two solenoids
When current is passed through solenoid S 1 , an emf is induced in solenoid S 2 .
Magnetic field produced inside solenoid S 1 on passing current through it,
B 1 = μ 0 n 1 I 1
Magnetic flux linked with each turn of solenoid S 2 will be equal to B 1 times the area of cross-section of solenoid S 1 .
Magnetic flux linked with each turn of the solenoid S 2 = B 1 A
Therefore, total magnetic flux linked with the solenoid S 2 ,
Φ 21 = B 1 A × n 2 l = μ 0 n 1 I 1 × A× n 2 l
Φ 21 = μ 0 n 1 n 2 AI 1
∴ M 21 = μ 0 n 1 n 2 Al
Similarly, the mutual inductance between the two solenoids, when current is passed through solenoid S 2 and induced emf is produced in solenoid S 1 , is given by
M 12 = μ 0 n 1 n 2 Al
∴ M 12 = M 21 = M (say)
Hence, coefficient of mutual induction between the two long solenoids
Regards