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Main >> Applications >> Sample problems >> Proximity effect

In the lab the current density is defined by measuring the voltages on the conductor segments, the phase of current is measured separately by the digital phasemeter.

**Problem type**

Plane-parallel problem of time-harmonic electromagnetic field.

**Geometry**

**Given**

Relative magnetic permeability of copper and air *μ= 1.*

Relative magnetic permeability of steel *μ= 100*.

Total current *I=300 A.* Frequency *f=50 Hz*.

Electric conductivity of copper *σ=57000000 S/m.*

Electric conductivity of steel *σ=10000000 S/m.*

**Task**

Find the current density distribution
along the cross section of long parallel conductors. Two types of conductors
are analyzed: two copper rods and two steel tubes.

**Solution**

Due to problem symmetry only upper-right quarter *aOb* is defined, and at the axes of symmetry the boundary conditions are set.

At the horizontal axis of symmetry (line *Oa*) H_{t}=0. At the vertical axis of symmetry *Ob* B_{n}=0. Equation *B=rot A* in the cylindrical coordinate system leads to *A=const* at the axis *Ob*. Field fades at the infinity so at the other boundaries *A=0*.

**Results:**

Current density distribution along the line *Oa* for copper rods.

Current density distribution along the steel tube perimeter (from the point *e* to point *f* clockwise).