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Proximity effect

# Exercise N 3. Proximity effect

**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.

**Experiment**

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**

Linear plane-parallel problem of time-harmonic electromagnetic field.

**Geometry**

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

**Given data**

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 Sm/m.*

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

**Boundary conditions**

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).

Please, see problems lab3_Cu.zip and lab3_Fe.zip.