Lorentz Force on a Conducting Sphere Due to an Alternating Current

The model consists of a conducting Copper sphere of radius 0.5 cm placed 0.4 cm from the center of a single loop of radius 1cm.The Loop carries a current of 1320 A at 9 kHz. Taking into account of the symmetry of the problem, only one-quarter of the structure needs to be built and modeled. The purpose of this study is to calculate the Lorentz force acting on the Copper sphere.

Skin Depth in the Copper Sphere

The first step is always to calculate the skin depth (d) or the depth of penetration of the field for the conducting regions using the relation:

for the current problem, the skin depth must be calculated in the copper electrode at a frequency f = 9 kHz, m = mo = 4p X 10-7 H/m and s = 2.5 X 107 S/m. Thus d = 1.06 mm.

The radius of the copper sphere R = 5.0mm. Since R/d = 5.0/1.06 = 4.71, the current problem must be treated with the AC magnetic analysis. Furthermore, remember that for the AC magnetic analysis the mesh must have at least two elements per skin depth in the conducting regions where an eddy current is expected to be induced. Given a ratio of R/d = 4.71, 9 to 10 mesh elements along the radius of the copper sphere are sufficient.

ResultsThe radius of the copper sphere R = 5.0mm. Since R/d = 5.0/1.06 = 4.71, the current problem must be treated with the AC magnetic analysis. Furthermore, remember that for the AC magnetic analysis the mesh must have at least two elements per skin depth in the conducting regions where an eddy current is expected to be induced. Given a ratio of R/d = 4.71, 9 to 10 mesh elements along the radius of the copper sphere are sufficient.

EMS Results

• Real Part of the Magnetic Flux Density in the Loop and Sphere at wt=0

  

• Real Part of the Field Intensity in the loop and Sphere at wt=90

  

• Real Part of the Eddy Current Density in the Loop and Sphere at wt=0

  

• Force Acting on the Copper Sphere