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    "# Homework 5 | Magnetic Mechanic\n",
    "\n",
    "## Description\n",
    "\n",
    "Consider an axi-symmetric model of a coil and a plate as depicted in the figure.\n",
    "The inner and outer radii of the coil, $r_1=0.0025$m and $r_2=0.0075$m.\n",
    "The length of the coil, $l_1=0.008$m.\n",
    "The plate thickness and air gap is $l_2=5\\cdot 10^{-4}$m respectively $l_3=7.5\\cdot 10^{-4}$m.\n",
    "The point $C$ is located in the center of the coil, the point $P$ in the middle of the plate at $z=0.005$m.\n",
    "\n",
    "The plate is either made from iron or aluminium, with electric conductivity and linear magnetic permeability given in the mat.xml.\n",
    "The coil has 40 truns and is fed by a controlled current of $i=10$kA.\n",
    "\n",
    "![Sketch of the problem](sketch.png)\n",
    "\n",
    "\n",
    "\n",
    "### Tasks\n",
    "1. Create a regular, hexaedral mesh. **(1 Point)**\n",
    "1. Create input-xml files for the required CFS++ simulations. **(1 Point)**\n",
    "1. Document your results by answering the questions below. **(13 Points)**\n",
    "\n",
    "### Hints\n",
    "* Use the provided templates.\n",
    "* Use the static simulation to check the prescribed current and boundary conditions.\n",
    "* Use a time resolution of 20 steps per period.\n",
    "* Pole force can be neglected\n",
    "\n",
    "### Submission\n",
    "Submit all your input files (`*.jou`, `*.xml`) as well as a PDF report of your results in a zip archive. \n",
    "Name the archive according to the format `HWn_eNNNNNNN_Lastname.zip`."
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    "## Mesh Size\n",
    "Estimate the skin depth for both materials.\n",
    "What element size do you suggest? Motivate your suggestion!"
   ]
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    "## Static Analysis\n",
    "Compute the static solution of the coupled magnetic-mechanical problem.\n",
    "\n",
    "* Plot the vector field of the magnetic flux density.\n",
    "* Compare the cases for iron and aluminum plate.\n",
    "* What is the difference?\n",
    "* Are there displacements? Why/Why not? "
   ]
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    "## Transient Analysis\n",
    "Set up a transient analysis with a sinusoidal coil current with a frequency of 100Hz and solve the coupled magnetic-mechanical problem. Compute the solution for 4 periods of the coil current.\n",
    "\n",
    "* Plot the time signal of the z-displacements of point $P$ for both plate-materials in one figure.\n",
    "* Plot the displacement of the plate (paraview warp by vector) for both plate-materials at a timestep with maximum displacement amplitude.\n",
    "* Describe the time signals: Are there transient effects? What is the difference between the amplitudes with aluminum and iron plate and why is there a difference?"
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