# MUTUAL INDUCTANCE OF TWO COAXIAL SOLENOID

In this topic we will derive the expression for coefficient of mutual induction or mutual inductance of two coaxial solenoid

MUTUAL INDUCTION OF TWO COAXIAL SOLENOID–

Let us consider two coaxial solenoid P1P2 and S1S2 (as shown in figure).

Let their common length is ‘l’ with cross-sectional area  A  and having N1 turns  but second coil has N2 turns .

If I1 is the current flows through the coil P1P2 , the magnetic field at its centre ,  B = µ0 n1 I . so magnetic flux linked with the coil S1S2 = B A .

Magnetic flux for entire coil S1S2 , ɸ = BAN2 = µ0n1n2 A I = µ0 N1N2 I A/ l …………(i)

But as we know , ɸ= MI ……………….(ii) (Here M is the mutual induction of the coil)

From eq. (i) and (ii)

MI = µ0 N1N2 I A / l

So  M= µ0 N1N2  A/l .

Points to be remember-

• If a medium of relative permeability µr fills the entire space in the inner solenoid then mutual induction M= µ0µr N1N2  A/l
• If the cross-sectional area of both the the coils are different then we always consider the inner coil radius ( area of that coil having smaller area of cross-section)
• The calculation of mutual induction is quite complicated even in the case of considerable symmetry.