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Main >> Applications >> Sample problems >> Cylindrical coaxial coils interaction force

**Task**

Find the force applied to the coils with current with and without the shield between them.

**Experiment**

Forces are measured by use of digital balance on which one of coils is installed (see the right picture below). Tests are performed with currents varying, and different conductors and ferromagnetics are placed between coils.

**Geometry**

Due to symmetry of the formulation only upper half of the problem (above *ab* line) is defined, and at the axis of symmetry (line *ab*) the boundary conditions are set.

**Given data**

Current density in the coil *j=100000 A/m ^{2}.*

Relative magnetic permeability of air, aluminum and copper coils

Relative magnetic permeability of the steel shield

Electrical conductivity of steel

Electrical conductivity of aluminum

Coils are wound by insulated wire, so cross-section conductivity in coils

**Boundary conditions**

Along the horizontal symmetry axis (line *ab*) B_{n} =0.

Equation *B=rot A* in cylindrical coordinate system leads to *A=const* at the axis *ab*. The field fades at the infinity, so due to the condition of continuity of the potential *A=0* at the line *ab*.

**Results:**

Field distribution around coils:

- Time-harmonic magnetic field,
*f*=50 Hz.

**Shield type****Interaction force, mN****Problem**No shield

0.533

lab2.pbm

Steel

0.098

lab2_Fe.pbm

Aluminum

0.282

lab2_Al.pbm

- DC magnetic field

**Shield type****Interaction force, mN****Problem**No shield

0.533

lab2c.pbm

Steel

0.138

lab2c_Fe.pbm