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Main >> Applications >> Sample problems

Mutual inductance of coils - QuickField simulation example

Electro motive force (EMF) in the right coil is measured by ballistic galvanometer (at the switching on).

Engineering question

How to find mutual inductance versus spacing of coaxial coils?

Engineering answer
Set up an axisymmetric QuickField DC Magnetics problem for coaxial coils and evaluate mutual inductance versus spacing from computed field results.

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Typical applications
coaxial coil systems, inductively coupled coils, transformer windings

Mutual inductance of coils

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Simulation problem

Problem Type
Axisymmetric problem of DC magnetics.

Geometry
Mutual inductance of coils Find the dependence of mutual inductance of coaxial cylindrical coils upon the distance between them. O a b X 25 mm Ø90 mm Ø160 mm

Given
Relative magnetic permeability of air and copper coils μ= 1.
Current density in the left coil j=0.1 A/mm².
There is no current in the right coil, thus it has no affection to the field shape.

Task
Find the dependence of mutual inductance of coaxial cylindrical coils upon the distance between them.

Solution
The field source is the lest coil. Due to the field symmetry only upper-right quarter aOb is defined. At the axes of symmetry the boundary conditions are set.
At the vertical axis of symmetry (line Ob) Ht=0. At the horizontal axis of symmetry Oa Bn=0. From B=rot A in the cylindrical coordinate system we have at the axis Oa A=const. Field fades at the infinity, so at the line Oa A=0 due to continuity of A.

Results
Flux density distribution around coils:
Mutual inductance of two coils

Mutual inductance M - relation of the flux connected with all turns of the right coil Ψ to the current in the left coil J (which is the origin of the flux).

L=Ψ / J
Ψ=Φ · w

Here w is number of turns of the right coil, Φ - flux across the right coil.

x, mm Flux across the right coil, μWb Mutual inductance M, μH
70 2.656 0.0306*w
150 0.637 0.0073*w
210 0.285 0.0033*w

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