{"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":"d8c91062-d8f4-55f5-8859-4167cb3b100b","task_key":"olympiad--test--e2bef5ee~2dc2ee~2d4704~2db52a~2d63bb2e7aea7a","task_revision_id":"1","upstream_id":"e2bef5ee-c2ee-4704-b52a-63bb2e7aea7a","short_description":"A certain region of space has an electric potential \\\\(V\\\\) which is…","config":"olympiad","split":"test","body":"{\"problem\":\"A certain region of space has an electric potential \\\\\\\\(V\\\\\\\\) which is cylindrically symmetrical about the \\\\\\\\(z \\\\\\\\)-axis and can be written as \\\\\\\\(V (\\\\\\\\rho, z) \\\\\\\\) , with \\\\\\\\(\\\\\\\\rho \\\\\\\\) the distance from the \\\\\\\\( z \\\\\\\\)-axis. The setup also includes a uniform magnetic field `\\\\(\\\\vec B = B \\\\hat{z} \\\\)` pointing along the `\\\\( z \\\\)-`direction. Gravity can be ignored.\\\\\\n\\\\\\nA particle with positive charge \\\\\\\\(q > 0\\\\\\\\) and mass \\\\\\\\( m\\\\\\\\) is released in this potential. We want the potential to be such that there exists a maximum distance from the origin that the particle will ever reach. The potential and magnetic field must satisfy Maxwell's equations in free space.\\n\\nThe potential does not include the potential from the particle itself. We ignore radiation by the particle.\\n\\nWe assume the potential is at most quadratic, of the form\\\\\\n\\\\\\\\(V(\\\\\\\\rho, z) = a + b \\\\\\\\rho + c z + d \\\\\\\\rho^2 + e z^2\\\\\\\\)\\\\\\nfor some constants \\\\\\\\(a, b, c, d\\\\), and \\\\\\\\(e\\\\).\\\\\\n\\\\\\nWe also want a charged particle released from rest at the origin to remain at the origin. We drop the constant term in the potential, so \\\\\\\\(a = 0\\\\\\\\).\\\\\\n\\\\\\nThere are three possible motions of the particle that are motions with a single angular frequency. Find an equation for \\\\\\\\( \\\\\\\\omega\\\\_{\\\\\\\\rm sum}\\\\\\\\) the sum of these three angular frequencies. Give your answer in terms of \\\\\\\\(B, e, q, \\\\\\\\) and \\\\\\\\( m\\\\\\\\).\\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":[]}