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.
Plane-parallel problem of time-harmonic electromagnetic field.
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.
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.
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) Ht=0. At the vertical axis of symmetry Ob Bn=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.
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).