{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"frontierscience","formal_name":"FrontierScience","introduction":"専門的な科学課題を解く能力を評価するベンチマークです。公開データはolympiadとresearchに分かれ、競技問題と研究課題を区別して扱います。\n\nFrontierScience evaluates the ability to solve expert-level scientific tasks. Its public data separates olympiad and research problems so that competition and research tasks can be examined independently.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/openai/frontierscience","indexing_mode":"noindex"},"task_id":"01ac00d5-c1b9-53b1-acdb-6405efb6cf1a","task_key":"olympiad--test--bdb3fc5f~2d9374~2d4e37~2d9af9~2d6036e3e29093","task_revision_id":"1","upstream_id":"bdb3fc5f-9374-4e37-9af9-6036e3e29093","short_description":"In an inertial Cartesian coordinate system, a semi-infinite perfect conductor…","config":"olympiad","split":"test","body":"{\"problem\":\"In an inertial Cartesian coordinate system, a semi-infinite perfect conductor moves at a constant velocity `\\\\(v\\\\)`. The region `\\\\(x > vt\\\\)` is the conductor, while `\\\\(x < vt\\\\)` is the vacuum. A linearly polarized monochromatic plane electromagnetic wave is incident along the `\\\\(+x\\\\)`-direction.\\n\\nThe incident wave's electric field is given by:\\n\\n`\\\\(\\\\vec{E}_i(x,t) = E_0 \\\\cos\\\\left( \\\\omega (t - \\\\frac{x}{c}) \\\\right) \\\\hat{y}\\\\)` where `\\\\(\\\\omega\\\\)` is the angular frequency of the incident light, and `\\\\(c\\\\)` is the speed of light. The vacuum permeability is `\\\\(\\\\mu_0\\\\)`.\\n\\nFind an equation for the surface current density \\\\\\\\(\\\\\\\\vec{J}(t)\\\\\\\\) on the conductor (as observed in the given coordinate system) in terms of the parameters \\\\\\\\(E_0\\\\\\\\), \\\\\\\\(v\\\\\\\\), \\\\\\\\(c\\\\\\\\), \\\\\\\\(\\\\\\\\omega\\\\\\\\), \\\\\\\\(\\\\\\\\mu_0\\\\\\\\) and the time \\\\\\\\(t\\\\\\\\). Express the answer as a vector by providing the direction in terms of `\\\\(\\\\hat{x}\\\\)` and `\\\\(\\\\hat{y}\\\\)`.\\n\\nThink step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.\",\"subject\":\"physics\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/openai/frontierscience","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}