Mutual inductance is a property of two closely spaced coils of wire, often referred to as inductors, in a circuit. It describes the extent to which a change in current in one coil induces an electromotive force (EMF) or voltage in the other coil. The mutual inductance (M) is measured in henrys (H) and is calculated using the following formula:
=
2
β
Ξ¦
1
1
M=
I
1
β
N
2
β
β
Ξ¦
B1
β
β
Where:
M is the mutual inductance between the two coils,
2
N
2
β
is the number of turns in the second coil,
Ξ¦
1
Ξ¦
B1
β
is the magnetic flux produced by the first coil that links with the second coil, and
1
I
1
β
is the current flowing through the first coil.
The magnetic flux
Ξ¦
1
Ξ¦
B1
β
is influenced by the current in the first coil and the geometry of the coils. It is calculated using the formula:
Ξ¦
1
=
1
β
2
Ξ¦
B1
β
=B
1
β
β
A
2
β
Where:
1
B
1
β
is the magnetic field produced by the first coil,
2
A
2
β
is the cross-sectional area of the second coil perpendicular to the magnetic field.
The magnetic field
1
B
1
β
can be calculated using Ampère's Law, and it depends on the current in the first coil and the shape of the coil.
Keep in mind that these formulas assume ideal conditions, such as perfect coupling between the coils and uniform magnetic fields. In real-world scenarios, factors like coil geometry, separation, and the presence of nearby objects can affect the accuracy of the calculations.
Additionally, it's important to note that mutual inductance works both ways: a change in current in the second coil can also induce a voltage in the first coil, and the mutual inductance value will remain the same as long as the physical arrangement of the coils doesn't change.