Magnetic_Field_Calc.ipynb

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    "import numpy as np\n",
    "\n",
    "# set up the system\n",
    "radius_m = 1\n",
    "current_amps = 1\n",
    "\n",
    "# set up the approximation\n",
    "num_segments = 6\n",
    "\n",
    "# calculate the angles\n",
    "angles = np.linspace(0,2*np.pi,num_segments,endpoint=False)\n",
    "#print (angles)\n",
    "\n",
    "# calculate the loop coordinates\n",
    "loop_coord_m = [np.array([radius_m*np.cos(angle), radius_m*np.sin(angle), 0]) for angle in angles]\n",
    "#print (loop_coord_m)\n",
    "\n",
    "# make the \\vec{dl} array\n",
    "dl_m = []\n",
    "\n",
    "for segment_idx in list(range(0,num_segments)):\n",
    "    final_idx = segment_idx % num_segments\n",
    "    ini_idx = (segment_idx + 1) % num_segments\n",
    "    segment = loop_coord_m[final_idx] - loop_coord_m[ini_idx]\n",
    "    dl_m.append(segment)\n",
    "    \n",
    "#print(dl_m)\n",
    "\n",
    "# calculate the angles\n",
    "angles = np.linspace(0,2*np.pi,num_segments,endpoint=False)\n",
    "#print (angles)\n",
    "\n",
    "# calculate the loop coordinates\n",
    "loop_coord_m = [np.array([radius_m*np.cos(angle), radius_m*np.sin(angle), 0]) for angle in angles]\n",
    "#print (loop_coord_m)\n",
    "\n",
    "# make the \\vec{dl} array\n",
    "dl_m = []\n",
    "\n",
    "for segment_idx in list(range(0,num_segments)):\n",
    "    final_idx = segment_idx % num_segments\n",
    "    ini_idx = (segment_idx + 1) % num_segments\n",
    "    segment = loop_coord_m[final_idx] - loop_coord_m[ini_idx]\n",
    "    dl_m.append(segment)\n",
    "    \n",
    "#print(dl_m)\n",
    "\n",
    "# Label the points in space we're interested in\n",
    "location_dict = dict()\n",
    "\n",
    "label = 'A'\n",
    "radius = 1/5\n",
    "center = np.array([1,0,0])\n",
    "for idx in list(range(0,num_segments)):\n",
    "    angle = angles[idx]\n",
    "    location = center + np.array([radius*np.cos(angle), 0, radius*np.sin(angle)])\n",
    "    #print (location)\n",
    "    location_dict[chr(ord(label)+idx)] = location\n",
    "    \n",
    "label = 'G'\n",
    "radius = 1/2\n",
    "center = np.array([1,0,0])\n",
    "for idx in list(range(0,num_segments)):\n",
    "    angle = angles[idx]\n",
    "    location = center + np.array([radius*np.cos(angle), 0, radius*np.sin(angle)])\n",
    "    #print (location)\n",
    "    location_dict[chr(ord(label)+idx)] = location\n",
    "    \n",
    "label = 'A'\n",
    "radius = 1/5\n",
    "center = np.array([-1,0,0])\n",
    "for idx in list(range(0,num_segments)):\n",
    "    angle = angles[idx]\n",
    "    location = center + np.array([radius*np.cos(angle), 0, radius*np.sin(angle)])\n",
    "    #print (location)\n",
    "    key = chr(ord(label)+idx)\n",
    "    location_dict[key*2] = location\n",
    "    \n",
    "label = 'G'\n",
    "radius = 1/2\n",
    "center = np.array([-1,0,0])\n",
    "for idx in list(range(0,num_segments)):\n",
    "    angle = angles[idx]\n",
    "    location = center + np.array([radius*np.cos(angle), 0, radius*np.sin(angle)])\n",
    "    #print (location)\n",
    "    key = chr(ord(label)+idx)\n",
    "    location_dict[key*2] = location\n",
    "    \n",
    "location_dict['Q'] = np.array([0,0,2])\n",
    "#print (location_dict)"
   ]
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     "text": [
      "segment1\n",
      "dl: array([ 0.5      , -0.8660254,  0.       ])\n",
      "r ini: array([ 0.5      ,  0.8660254,  0.       ])\n",
      "r vec: array([ 0.75     , -0.8660254,  0.4330127])\n",
      "r hat: array([ 0.61237244, -0.70710678,  0.35355339])\n",
      "r length: 1.2247448713915889\n",
      "cross: array([-0.375     , -0.21650635,  0.21650635])\n",
      "dB * 10^(-7): array([-0.20412415, -0.11785113,  0.11785113])\n",
      "loc: array([ 1.25     ,  0.       ,  0.4330127])\n",
      "segment2\n",
      "dl: array([  1.00000000e+00,  -1.11022302e-16,   0.00000000e+00])\n",
      "r ini: array([-0.5      ,  0.8660254,  0.       ])\n",
      "r vec: array([ 1.75     , -0.8660254,  0.4330127])\n",
      "r hat: array([ 0.875     , -0.4330127 ,  0.21650635])\n",
      "r length: 1.9999999999999998\n",
      "cross: array([ -4.80740672e-17,  -4.33012702e-01,  -8.66025404e-01])\n",
      "dB * 10^(-7): array([ -6.00925839e-18,  -5.41265877e-02,  -1.08253175e-01])\n",
      "loc: array([ 1.25     ,  0.       ,  0.4330127])\n",
      "segment3\n",
      "dl: array([ 0.5      ,  0.8660254,  0.       ])\n",
      "r ini: array([ -1.00000000e+00,   1.22464680e-16,   0.00000000e+00])\n",
      "r vec: array([  2.25000000e+00,  -1.22464680e-16,   4.33012702e-01])\n",
      "r hat: array([  9.81980506e-01,  -5.34479682e-17,   1.88982237e-01])\n",
      "r length: 2.2912878474779199\n",
      "cross: array([ 0.375     , -0.21650635, -1.94855716])\n",
      "dB * 10^(-7): array([ 0.03117398, -0.01799831, -0.16198477])\n",
      "loc: array([ 1.25     ,  0.       ,  0.4330127])\n",
      "segment4\n",
      "dl: array([-0.5      ,  0.8660254,  0.       ])\n",
      "r ini: array([-0.5      , -0.8660254,  0.       ])\n",
      "r vec: array([ 1.75     ,  0.8660254,  0.4330127])\n",
      "r hat: array([ 0.875     ,  0.4330127 ,  0.21650635])\n",
      "r length: 2.0\n",
      "cross: array([ 0.375     ,  0.21650635, -1.94855716])\n",
      "dB * 10^(-7): array([ 0.046875  ,  0.02706329, -0.24356964])\n",
      "loc: array([ 1.25     ,  0.       ,  0.4330127])\n",
      "segment5\n",
      "dl: array([ -1.00000000e+00,   5.55111512e-16,   0.00000000e+00])\n",
      "r ini: array([ 0.5      , -0.8660254,  0.       ])\n",
      "r vec: array([ 0.75     ,  0.8660254,  0.4330127])\n",
      "r hat: array([ 0.61237244,  0.70710678,  0.35355339])\n",
      "r length: 1.2247448713915898\n",
      "cross: array([  2.40370336e-16,   4.33012702e-01,  -8.66025404e-01])\n",
      "dB * 10^(-7): array([  1.30841038e-16,   2.35702260e-01,  -4.71404521e-01])\n",
      "loc: array([ 1.25     ,  0.       ,  0.4330127])\n",
      "segment6\n",
      "dl: array([-0.5      , -0.8660254,  0.       ])\n",
      "r ini: array([ 1.,  0.,  0.])\n",
      "r vec: array([ 0.25     ,  0.       ,  0.4330127])\n",
      "r hat: array([ 0.5      ,  0.       ,  0.8660254])\n",
      "r length: 0.49999999999999994\n",
      "cross: array([-0.375     ,  0.21650635,  0.21650635])\n",
      "dB * 10^(-7): array([-3.        ,  1.73205081,  1.73205081])\n",
      "loc: array([ 1.25     ,  0.       ,  0.4330127])\n",
      "++++++++++++++++\n",
      "B_net: array([-3.12607516,  1.80484034,  0.86468982])\n"
     ]
    }
   ],
   "source": [
    "# choose the location you're interested in\n",
    "#location_m = np.array([-0.09, 0, -0.0173])\n",
    "location_m = location_dict['H']\n",
    "\n",
    "# net magnetic field\n",
    "b_net = np.array([0,0,0])\n",
    "\n",
    "# first element in dl_m matches with second element in loop_coord_m\n",
    "for idx in list(range(0,num_segments)):\n",
    "    dl = dl_m[idx]\n",
    "    r = location_m - loop_coord_m[(idx+1) % num_segments]\n",
    "    #r = np.array([0,0,2])- loop_coord_m[(idx+1) % num_segments]\n",
    "    dB = np.cross(dl,r)/(np.linalg.norm(r)**3)\n",
    "    b_net = b_net + dB\n",
    "    \n",
    "    print(\"segment\" + repr(1+idx))\n",
    "    print(\"dl: \" + repr(dl))\n",
    "    print(\"r ini: \" + repr(loop_coord_m[(idx+1) % num_segments]))\n",
    "    #print(\"r ini: \" + repr(loop_coord_m[(idx) % num_segments]))\n",
    "    print(\"r vec: \" + repr(r))\n",
    "    print(\"r hat: \" + repr(r/np.linalg.norm(r)))\n",
    "    print(\"r length: \" + repr(np.linalg.norm(r)))\n",
    "    print(\"cross: \" + repr(np.cross(dl,r))) #/np.linalg.norm(r)))\n",
    "    print(\"dB * 10^(-7): \" + repr(dB))\n",
    "    print(\"loc: \" + repr(location_m))\n",
    "\n",
    "print('++++++++++++++++')\n",
    "print(\"B_net: \" + repr(b_net))\n"
   ]
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