{"product_id":"seeing-magnetic-fields-in-2d-reconstructing-a-3d-world","title":"Seeing Magnetic Fields in 2D — Reconstructing a 3D World","description":"\u003cp\u003e\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"content-type\"\u003eMagnetic field lines drawn by iron filings look like hidden patterns emerging from nowhere. But these patterns are only 2-D slices of a much larger 3-D magnetic structure. By changing the orientation of magnets and capturing multiple field patterns, we can begin reconstructing the invisible magnetic world — similar to how CT scans reconstruct the inside of the human body.\u003c\/p\u003e\n\u003ch1 data-section-id=\"1aswwnp\" data-start=\"872\" data-end=\"890\"\u003eWhat You Observe\u003c\/h1\u003e\n\u003cp data-start=\"892\" data-end=\"1052\"\u003eWhen iron filings are sprinkled over a sheet placed above a magnet, the filings align themselves along the magnetic field direction, revealing intricate curves.\u003c\/p\u003e\n\u003cp data-start=\"1054\" data-end=\"1123\"\u003eDifferent magnet arrangements create dramatically different patterns:\u003c\/p\u003e\n\u003cul data-start=\"1125\" data-end=\"1238\"\u003e\n\u003cli data-section-id=\"3ejzxz\" data-start=\"1125\" data-end=\"1144\"\u003eSingle bar magnet\u003c\/li\u003e\n\u003cli data-section-id=\"drqp8m\" data-start=\"1145\" data-end=\"1169\"\u003eTwo attracting magnets\u003c\/li\u003e\n\u003cli data-section-id=\"ln731d\" data-start=\"1170\" data-end=\"1193\"\u003eTwo repelling magnets\u003c\/li\u003e\n\u003cli data-section-id=\"9rbrul\" data-start=\"1194\" data-end=\"1208\"\u003eRing magnets\u003c\/li\u003e\n\u003cli data-section-id=\"1o6852u\" data-start=\"1209\" data-end=\"1238\"\u003eComplex magnet combinations\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp data-start=\"1240\" data-end=\"1299\"\u003eEach image is only a \u003cem data-start=\"1261\" data-end=\"1268\"\u003eslice\u003c\/em\u003e of the full 3-D magnetic field.\u003c\/p\u003e\n\u003ch1 data-section-id=\"rfmplj\" data-start=\"1306\" data-end=\"1328\"\u003eCore Scientific Idea\u003c\/h1\u003e\n\u003cp data-start=\"1330\" data-end=\"1457\"\u003eThe patterns seen on the sheet are not the full magnetic field. They are 2-D intersections of a 3-D field structure with a plane.\u003c\/p\u003e\n\u003cp data-start=\"1459\" data-end=\"1521\"\u003eThe magnetic field exists in all directions around the magnet:\u003c\/p\u003e\n\u003cp data-start=\"1562\" data-end=\"1625\"\u003eThe iron filings reveal the field behaviour only on one surface.\u003c\/p\u003e\n\u003cp data-start=\"1627\" data-end=\"1799\"\u003eIf we rotate the magnet or observe from different planes, we obtain additional slices of information. Combining many such slices allows us to infer the hidden 3-D structure.\u003c\/p\u003e\n\u003ch1 data-section-id=\"kz7vsg\" data-start=\"1806\" data-end=\"1830\"\u003eConnection to CT Scans\u003c\/h1\u003e\n\u003cp data-start=\"1832\" data-end=\"1884\"\u003eThis is conceptually similar to how a CT scan works.\u003c\/p\u003e\n\u003cp data-start=\"1886\" data-end=\"2055\"\u003eA CT scanner does not directly see a complete 3-D organ. Instead, it captures many 2-D projections from different angles and reconstructs the 3-D structure computationally.\u003c\/p\u003e\n\u003cp data-start=\"2295\" data-end=\"2349\"\u003eThis makes the experiment a beautiful introduction to:\u003c\/p\u003e\n\u003cul data-start=\"2351\" data-end=\"2453\"\u003e\n\u003cli data-section-id=\"14wtsj1\" data-start=\"2351\" data-end=\"2369\"\u003eElectromagnetism\u003c\/li\u003e\n\u003cli data-section-id=\"1ihwu78\" data-start=\"2370\" data-end=\"2382\"\u003eTomography\u003c\/li\u003e\n\u003cli data-section-id=\"k79hs0\" data-start=\"2383\" data-end=\"2401\"\u003eInverse problems\u003c\/li\u003e\n\u003cli data-section-id=\"1tyh3ux\" data-start=\"2402\" data-end=\"2422\"\u003eScientific imaging\u003c\/li\u003e\n\u003cli data-section-id=\"2w6tdu\" data-start=\"2423\" data-end=\"2453\"\u003eComputational reconstruction\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e \u003c\/p\u003e\n\u003ch1 data-section-id=\"1segny3\" data-start=\"2460\" data-end=\"2496\"\u003eWhy This Experiment Is Interesting\u003c\/h1\u003e\n\u003cp data-start=\"2498\" data-end=\"2606\"\u003eMost people think magnetic field lines are “the field itself.” But this experiment reveals something deeper:\u003c\/p\u003e\n\u003cul data-start=\"2608\" data-end=\"2800\"\u003e\n\u003cli data-section-id=\"341gav\" data-start=\"2608\" data-end=\"2642\"\u003eObservations depend on viewpoint\u003c\/li\u003e\n\u003cli data-section-id=\"fzvgcf\" data-start=\"2643\" data-end=\"2678\"\u003e2-D data can encode 3-D information\u003c\/li\u003e\n\u003cli data-section-id=\"2tb0um\" data-start=\"2679\" data-end=\"2734\"\u003eComplex systems can be reconstructed from projections\u003c\/li\u003e\n\u003cli data-section-id=\"6v9nni\" data-start=\"2735\" data-end=\"2800\"\u003eScientific instruments often infer hidden structures indirectly\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e \u003c\/p\u003e\n\u003ch1 data-section-id=\"tg2eal\" data-start=\"2900\" data-end=\"2919\"\u003eExploration Ideas\u003c\/h1\u003e\n\u003ch3 data-section-id=\"oeomay\" data-start=\"2940\" data-end=\"2955\"\u003eBasic Level\u003c\/h3\u003e\n\u003cul data-start=\"2956\" data-end=\"3051\"\u003e\n\u003cli data-section-id=\"d9ae3k\" data-start=\"2956\" data-end=\"2997\"\u003eCompare patterns from different magnets\u003c\/li\u003e\n\u003cli data-section-id=\"1w76k7z\" data-start=\"2998\" data-end=\"3031\"\u003eObserve attraction vs repulsion\u003c\/li\u003e\n\u003cli data-section-id=\"1oa1qqk\" data-start=\"3032\" data-end=\"3051\"\u003eIdentify symmetry\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch3 data-section-id=\"8vnnj5\" data-start=\"3053\" data-end=\"3075\"\u003eIntermediate Level\u003c\/h3\u003e\n\u003cul data-start=\"3076\" data-end=\"3197\"\u003e\n\u003cli data-section-id=\"1k959tz\" data-start=\"3076\" data-end=\"3114\"\u003eRotate the magnet and capture images\u003c\/li\u003e\n\u003cli data-section-id=\"hk9a8q\" data-start=\"3115\" data-end=\"3159\"\u003eCompare slices from different orientations\u003c\/li\u003e\n\u003cli data-section-id=\"69z0y2\" data-start=\"3160\" data-end=\"3197\"\u003ePredict unseen regions of the field\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch3 data-section-id=\"y8xo9a\" data-start=\"3199\" data-end=\"3217\"\u003eAdvanced Level\u003c\/h3\u003e\n\u003cul data-start=\"3218\" data-end=\"3349\"\u003e\n\u003cli data-section-id=\"1lhzkc5\" data-start=\"3218\" data-end=\"3261\"\u003eReconstruct approximate 3-D field geometry\u003c\/li\u003e\n\u003cli data-section-id=\"47tqtf\" data-start=\"3262\" data-end=\"3304\"\u003eUse image processing to analyse patterns\u003c\/li\u003e\n\u003cli data-section-id=\"5te11s\" data-start=\"3305\" data-end=\"3349\"\u003eExplore analogy with tomography algorithms\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp data-start=\"1240\" data-end=\"1299\"\u003e \u003c\/p\u003e\n\u003cp\u003e \u003c\/p\u003e","brand":"Geometers","offers":[{"title":"Default Title","offer_id":45850822606984,"sku":null,"price":0.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0725\/3891\/4952\/files\/IMG_0899.jpg?v=1779165441","url":"https:\/\/geometers.in\/products\/seeing-magnetic-fields-in-2d-reconstructing-a-3d-world","provider":"Geometers","version":"1.0","type":"link"}