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mutual inductance of the coaxial coils, coaxial coils magnetic field FEA finite element analysis

**Task**

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

**Experiment**

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

**Problem type**

Linear axisymmetrical problem of magnetostatics.

**Geometry**

**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.

**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*) H_{t}=0. At the horizontal axis of symmetry *Oa* B_{n}=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 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 |