{"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":"712af7e8-74cb-508f-a89a-f6cfb8defc02","task_key":"olympiad--test--d1cec1fb~2d13bb~2d475a~2db2f1~2d956db5ef3b77","task_revision_id":"1","upstream_id":"d1cec1fb-13bb-475a-b2f1-956db5ef3b77","short_description":"Consider two atoms separated by a distance `\\( R \\)`. Since they are…","config":"olympiad","split":"test","body":"{\"problem\":\"Consider two atoms separated by a distance `\\\\( R \\\\)`. Since they are electrically neutral, there is no force between them in the absence of perturbations. However, if one of the atoms is slightly polarized, a very weak attractive force emerges between the two atoms. Here, we assume that both atoms consist of a positively charged nucleus `\\\\( (+e) \\\\)` fixed in place (the distance `\\\\( R \\\\)` is the inter-nuclear distance)  and an electron `\\\\( (-e) \\\\)` with mass `\\\\( m \\\\)`, connected to the nucleus by springs with spring constant `\\\\( k \\\\)`.  We further assume that the electrons are constrained to move along the line connecting the two nuclei, with displacements `\\\\( x_1 \\\\)` and `\\\\( x_2 \\\\)`, respectively. Thus, the elastic potential energy of the two springs can be written as `\\\\( \\\\frac{1}{2} kx_1^2 \\\\)` and `\\\\( \\\\frac{1}{2} kx_2^2 \\\\)`, respectively.\\n\\nUnder the condition that both `\\\\( \\\\left|x_{1}\\\\right| \\\\)` and `\\\\( \\\\left|x_{2}\\\\right| \\\\)` are much smaller than `\\\\( R \\\\)`, find the Coulomb electrostatic potential energy `\\\\( U \\\\)`of this system in terms of \\\\(e, x_1, x_2, \\\\epsilon_0, R\\\\), where \\\\(\\\\epsilon_0 \\\\) is the electric vacuum permittivity.\\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":[]}