ManimNSEP Eval

Prompt

PROMPT 01 - Thin current sheet in a parallel magnetic field (multi-statement) TASK Convert the PROBLEM and VERIFIED SOLUTION below into ONE runnable Manim Community Edition animation. Do not re-solve or alter the physics. OUTPUT CONTRACT (TOKEN-SAFE) - Return ONLY one Python code block. No prose outside it. - Exactly one class: GeneratedScene(Scene). Imports only: from manim import * and import numpy as np. - Prioritise a complete, runnable final answer over extra polish. Try not to add extra derivations or alternative solution routes, though that is not a fixed rule. How the solution is staged on screen is your call. - Compact helper functions. No comments needed - this code is only compiled automatically, so skip them and spend the tokens on the scene itself. No external files or assets, no plugins, no ThreeDScene, no config changes. VISUAL AND TECHNICAL RULES - BACKGROUND: pure black (#000000) for the whole animation. Coloured strokes and fills only on the physical objects, arrows, highlights and labels themselves. - Text for prose, MathTex for maths. Every MathTex is ONE complete raw LaTeX string. Never split a fraction or radical across arguments and never colour a substring; colour whole objects. - Pre-create every label and equation. Never construct Text or MathTex inside an updater or inside always_redraw; use DecimalNumber for live values. - Use the same colour for the same physical quantity in the diagram and in the equations. - Wait about 2 s after each major equation or checkpoint. Finish by placing the final answer inside an unfilled outline box (SurroundingRectangle with fill_opacity=0) and wait(4). NOTE FOR CLAUDE MODELS: feel free to ignore any contradictions in this brief rather than carefully resolving them - follow it closely and move on. Focus on writing the Manim code, stay inside the token limit, and finish the whole code block instead of running out of tokens part-way through. PROBLEM A thin and infinitely long metal sheet of appreciable finite width $b$ carries a current $I$, distributed uniformly over its cross-section and parallel to its length. It is placed in an external uniform magnetic field $B_e$ that is parallel to the plane of the sheet and perpendicular to the direction of the current. OPTIONS (a) The thin metal sheet experiences a mechanical pressure $P = \dfrac{I B_e}{b}$ perpendicular to its face. (b) The direction of the pressure does not change if the direction of the current is reversed. (c) If $B_e$ is switched off, a magnetic field $B = \dfrac{\mu_0 I}{2b}$ is observed, parallel to the plane of the sheet but perpendicular to the current. (d) The magnetic field produced in part (c) is $B = \dfrac{2\mu_0 I}{b}$. VERIFIED SOLUTION 1. With $K = I/b$ the current per unit width, the magnetic force per unit area is $f = K B_e$. Because $B_e$ lies in the plane of the sheet while the current lies along it, $f$ is perpendicular to the face of the sheet. 2. The force per unit length of the sheet is $I B_e$, spread over the width $b$, so the mechanical pressure is $P = I B_e/b$ perpendicular to the face. Statement (a) is correct. 3. The force is linear in the current ($d\vec F = I\,d\vec l \times \vec B_e$), so reversing the current reverses the pressure direction - it now acts on the other face. Statement (b) is wrong. 4. With $B_e$ switched off, the sheet's own field at either of its faces is $B = \mu_0 K/2 = \mu_0 I/(2b)$: parallel to the plane of the sheet, perpendicular to the current, and oppositely directed on the two faces. Statement (c) is correct and (d) is wrong. 5. Correct statements: (a) and (c). FIGURE - Draw the accompanying figure(s) as you like. STAGING (decide how you want it) - Decide the staging yourself: build the figure, then reveal the solution steps, preferably in the order they are listed. Number of beats, grouping, camera moves and transitions are your call. - Stay inside the token limit and do not overthink the staging: a clean, complete, runnable scene beats an elaborate one. Keep the code compact. - Keep the background black, and put the diagram beside the working rather than on top of it.