Question

The length of a pair of co-axial solenoid is 75 cm. The given table lists some of the values related to the co-axial solenoid.
Number of turns (n) Area of cross-section (A)
Outer solenoid 50 per cm 65 cm2
Inner solenoid 100 per cm 30 cm2
What is the mutual inductance of the co-axial solenoid?

Answer 1

Dear Student,

Suppose a current i is passed in a circuit and it is changed with a rate di/dt. The induced emf e produced in the circuit is directly proportional to the rate of change of current. Thus,


Here, self inductance of the coil having length L, Area of cross section A₁ and number of turns per unit length is n₁. is,


Therefore, Two coils will be having the self inductance as L₁ and L₂ respectively.
If M is the mutual inductance of the coils,

If all the flux of coil 2 links coil 1 and vice-versa then,

$$\begin{gathered} So{L}_1={50}^2\times 75\times 65=1.2\times {10}^7 \\ similarly{L}_2={100}^2\times 30\times 75=2.2\times {10}^7 \\ mutualinduc\tan ce=\sqrt{L_1{L}_2}=\sqrt{1.2\times {10}^7\times 2.2\times {10}^7}=1.62\times {10}^{7}abHenry=1.62\times {10}^7\times {10}^{-9}=0.0162Henry \\ Regards \end{gathered}$$