MAHE Manipal B.Sc Nursing 2025
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Mutual Inductance, Mutual Inductance for two coaxial long solenoids, Mutual Inductance for a pair of concentric coils is considered one of the most asked concept.
25 Questions around this concept.
An electron moves on a straight line path XY as shown. The abcd is a coil adjacent to the path of the electron. What will be the direction of current, if any, induced in the coil?
Whenever the current passing through a coil or circuit changes, the magnetic flux linked with a neighboring coil or circuit will also change. Hence an emf will be induced in the neighboring coil or circuit. This phenomenon is called ‘mutual induction’.
or The phenomenon of producing an induced emf in a coil due to the change in current in the other coil is known as mutual induction.
Coefficient of mutual induction (M)-
If two coils (P-primary coil or coil 1, S-secondary coil or coil 2) are arranged as shown in the below figure.
If we change the current through the coil P (i.e
where
Similarly, if we exchange the position of Coil 1 and Coil 2
then
If we change the current through the coil S (i.e
where
- As
If
I.e coefficient of mutual induction of two coils is numerically equal to the magnetic flux linked with one coil when unit current flows through the neighboring coil.
- Using Faraday's Second Law of Induction emf we get
If
I.e The coefficient of mutual induction of two coils is numerically equal to the emf induced in one coil when the rate of change of current through the other coil is unity.
Units and dimensional formula of '
S.I. Unit - Henry (H)
And
And its dimensional formula is
Dependence of mutual inductance
- Number of turns
- Coefficient of self inductances
and the relation between
where
If
If
- Distance(d) between two coils (i.e As dincreases then M decreases)
- The magnetic permeability of medium between the coils
Consider two long co-axial solenoids of the same length l..Let A1 and A2 be the area of cross-section of the solenoids with A1 being greater than A2 as shown in the below figure.
The turn density of these solenoids are
Let
As the field lines of
So the magnetic flux linked with each turn of solenoid 2 due to solenoid 1 and is given by
The total flux linkage of solenoid 2 with total turns
And Using
Where
Similarly
Hence
So, In general, the mutual inductance between two long co-axial solenoids is given by
If a dielectric medium of permeability
Consider two circular coils one of radius 'r1' and the other of radius' r2'placed coaxially with their centers coinciding as shown in the below figure.
Since so we can assume coil 2 is at the center of coil 1.
If
Suppose a current flows through the outer circular coil.
Then Magnetic field at the center of the coil 1 is given as
So the total flux passing through coil 2 will be given as
And using
we get
Where M=mutual inductance between two concentric coils
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