{"product_id":"shielda-debye-shielding-physics-t-shirt","title":"Shielda – Debye Shielding Physics T-Shirt","description":"\u003cp\u003eShielda glows with charge, but a swarm of opposite charges mutes her beyond arm's length.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003ePut a charge in a plasma and opposite charges crowd round it, hiding it from far away. Its potential falls off exponentially over the Debye length. A gas counts as a plasma only if it is much bigger than the Debye length and holds many particles in a Debye sphere.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eλ_D = √(ε₀ k_B T_e \/ (n_e e²)),   φ(r) = q e^(−r\/λ_D) \/ (4πε₀ r),   N_D = (4\/3)π n_e λ_D³ ≫ 1\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eλ_D: Debye length (m)\u003c\/li\u003e\n\u003cli\u003eε₀: vacuum permittivity, 8.8541878128 × 10⁻¹² F\/m\u003c\/li\u003e\n\u003cli\u003ek_B: Boltzmann constant (J\/K)\u003c\/li\u003e\n\u003cli\u003eT_e: electron temperature (K)\u003c\/li\u003e\n\u003cli\u003en_e: electron number density (m⁻³)\u003c\/li\u003e\n\u003cli\u003ee: elementary charge, 1.602176634 × 10⁻¹⁹ C (exact)\u003c\/li\u003e\n\u003cli\u003eφ: electric potential (V)\u003c\/li\u003e\n\u003cli\u003eq: test charge (C)\u003c\/li\u003e\n\u003cli\u003er: distance (m)\u003c\/li\u003e\n\u003cli\u003eN_D: electrons in a Debye sphere\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eIn the solar corona (n_e ~ 10¹⁵ per m³, T_e ~ 100 eV), λ_D ≈ 2 mm. Peter Debye and Erich Hückel worked out the same screening in salt solutions in 1923.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Shielda, the pixel-art character, with the title. Back: the Debye length, the screened potential, the plasma criterion, the solar-corona example and the 1923 electrolyte credit. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50960825417831,"sku":"68575940556040109230","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50960825450599,"sku":"22696069482547871286","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50960825483367,"sku":"58171200968963221750","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50960825516135,"sku":"12425881936058449225","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50960825548903,"sku":"10241415562570924459","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50960825581671,"sku":"12942977548587902081","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50960825614439,"sku":"15229213493778733899","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50960825647207,"sku":"13221964124187688128","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50960825679975,"sku":"16231667239968469036","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50960825712743,"sku":"26052380880622045359","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50960825745511,"sku":"14408798326019474448","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50960825778279,"sku":"10059125547520875986","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50960825811047,"sku":"27076460698298254880","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50960825843815,"sku":"10984058625467567109","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50960825876583,"sku":"11774780383586953022","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50960825909351,"sku":"10816848141500459630","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/debye-shielding_front_16_white.png?v=1793628568","url":"https:\/\/pixelatedphysics.com\/zh-hans\/products\/shielda-debye-shielding-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}