{"product_id":"homopole-the-faraday-paradox-physics-t-shirt","title":"Homopole – The Faraday Paradox Physics T-Shirt","description":"\u003cp\u003eHomopole spins a copper war-wheel between magnet poles, and sparks jump from rim to axle.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eSpin a copper disk in a magnetic field along its axis and an EMF appears between the axle and the rim. Spin the disk with the magnet still: EMF. Spin both together: the same EMF. Spin only the magnet: none. What counts is the disk moving relative to the wires that close the circuit, not the magnet's spin.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eEMF = ∫ (v × B) · dr = ½ B ω R²   (rim to axle, uniform B)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eEMF: electromotive force between axle and rim (V)\u003c\/li\u003e\n\u003cli\u003ev: velocity of a point on the disk (m\/s)\u003c\/li\u003e\n\u003cli\u003eB: magnetic flux density along the axis (T)\u003c\/li\u003e\n\u003cli\u003edr: radial line element (m)\u003c\/li\u003e\n\u003cli\u003eω: disk angular speed (rad\/s)\u003c\/li\u003e\n\u003cli\u003eR: disk radius (m)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eMichael Faraday built the copper-disk generator in his first Experimental Researches in Electricity, Phil. Trans. 122, 125 (1832).\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Homopole, the pixel-art character, with the title. Back: the disk EMF, the three spin cases and the resolution, with Faraday's 1832 paper. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50960833249383,"sku":"21132063357415119916","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50960833282151,"sku":"27730289153470451462","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50960833314919,"sku":"15464078932934984163","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50960833347687,"sku":"26393407240267875064","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50960833380455,"sku":"10369791384615403368","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50960833413223,"sku":"16960469893808294858","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50960833445991,"sku":"33031528746559979596","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50960833478759,"sku":"20167424529747545069","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50960833511527,"sku":"13442169149073742322","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50960833544295,"sku":"20103172755512935619","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50960833577063,"sku":"19107102896579822389","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50960833609831,"sku":"51885105048511911369","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50960833642599,"sku":"59720415148855345050","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50960833675367,"sku":"19489416460142977211","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50960833708135,"sku":"23481732658727959694","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50960833740903,"sku":"25030162214043232876","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/faraday-paradox_front_16_white.png?v=1793628653","url":"https:\/\/pixelatedphysics.com\/it\/products\/homopole-the-faraday-paradox-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}