Define the term 'mutual inductance' between two coils.

Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii $r_{1}$ and $r_{2} (r_{2} >> r_{1})$ . Total number of turns in the two solenoids are $N_{1}$ and $N_{2}$ respectively.

Open in App

Solution

Mutual inductance of two coils is equal to the e.m.f. induced in one coil when rate of change of current through the other coil is unity.

Mutual inductance of two co-axial solenoids :

Consider two long co-axial solenoid each of length l with number of turns $N_{1}$ and $N_{2}$ wound one over the other. Number of turns per unit length in solenoid, $n = \frac{N_{1}}{l}$ . If $I_{1}$ is the current flowing in primary solenoid, the magnetic field produced within this solenoid,

$B_{1} = \frac{μ_{o} N_{1} I_{1}}{l}$

The flux linked with each turn of inner solenoid coil is $Φ_{2} = B_{1} A_{2}$ , where $A_{2}$ is the cross-sectional area of inner solenoid. The total flux linkage with inner coil of $N_{2}$ turns,

$Φ_{2} = N_{2} Φ_{2}$

= $N_{2} B_{1} A_{2}$

= $N_{2} (\frac{μ_{0} N_{1} I_{1}}{l}) A_{2}$

= $\frac{μ_{0} N_{1} N_{2} I_{1} A_{2}}{l}$

Mutual Inductance, $M_{21} = \frac{Φ_{2}}{I_{1}} = \frac{μ_{0} N_{1} N_{2} A_{2}}{l}$

If $n_{1}$ is number of turns per unit length of outer solenoid and $r_{2}$ is radius of inner solenoid, then

$M = μ_{0} n_{1} N_{2} π r_{2}^{2}$ .

Suggest Corrections

Similar questions

Define mutual inductance between a pair of coils. Derive an expression for the mutual inductance of two long coaxial solenoids of same length wound one over the other.

Q. There are two long co-axial solenoids of same length

l

. the inner and outer coils have radii

r_{1}

and

r_{2}

and number of turns per unit length

n_{1}

and

n_{2}

respectively. The rate of mutual inductance to the self-inductance of the inner-coil is :

Q. Two coaxial long solenoids of equal lengths have current,

i_{1}

i_{2}

, number of turns per unit length

n_{1}, n_{2}

and radius

r_{1}, r_{2}

respectively. If

n_{1} i_{1} = n_{2} i_{2}

and the two solenoids carry current in opposite sense, the magnetic energy stored per until length is

[r_{2} > r_{1}]

Q. A short solenoid of radius a, number of turns per Unit length

n_{1}

. and length L is kept coaxially inside a very long solenoid of radius b, the number of turns per Unit length

n_{2}

. What is the mutual inductance of the system?

Q. Obtain an expression for the mutual inductance of two long solenoids.

Join BYJU'S Learning Program

Define the term 'mutual inductance' between two coils. Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii r1 and r2(r2>>r1). Total number of turns in the two solenoids are N1 and N2 respectively.

Define the term 'mutual inductance' between two coils.

Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii $r_{1}$ and $r_{2} (r_{2} >> r_{1})$ . Total number of turns in the two solenoids are $N_{1}$ and $N_{2}$ respectively.