From a2e0ca85b57681b5239d53df99375b9fc2580617 Mon Sep 17 00:00:00 2001 From: Paco Lopez-Dekker Date: Fri, 21 Aug 2026 13:58:25 +0200 Subject: [PATCH 01/11] Edited intro --- book/intro.md | 25 +++++++++++++++++++++---- 1 file changed, 21 insertions(+), 4 deletions(-) diff --git a/book/intro.md b/book/intro.md index 565494d..1b99fce 100644 --- a/book/intro.md +++ b/book/intro.md @@ -1,6 +1,23 @@ -(intro)= -# Welcome to the Template Book +--- +title: ECTB2140 Fields and Waves 2026 +--- -_This is the first page the student will see when opening the url._ +# Fields and Waves -This book can be used as a template for other books. It includes a starter package of the software developed by the TeachBooks initiative and some exercises to get you going! \ No newline at end of file +## Course description + +Physical objects can be described in a quantitative way only with the aid of mathematics. In classical physics, all physical objects are geometric objects. The course “Fields and Waves” combines the physics of fields and waves with the mathematical tools required to describe these phenomena. The course enables students to develop the essential understanding of the physical interpretation of mathematical formulations. Examples are radar waves that are used for earth surface and subsurface observations from antennas placed on satellites, airplanes, and close to or on the ground surface; sound waves, electromagnetic diffusion fields, electric and magnetic potential fields, and the gravity field to probe the earth’s interior. The approach is to start with relevant physical problems (1D wave equation, stretched membrane, electrostatic fields, heat diffusion, 2D and 3D waves) introducing mathematical tools and concepts (Partial Differential Equations (elliptic, parabolic, hyperbolic), separation of variables, Fourier series and Fourier transformations) during the course as needed to solve specific problems. While being able to find solutions for some specific cases is an important part of the course, the emphasis of the course is on learning how to describe the relevant physics with the corresponding math, to understand the solution space, and to be able to interpret solutions. + +### Expected prior knowledge: +... + +## What to expect? + + + + +Creative Commons License \ No newline at end of file From 4f46bc687e93619fb9cbb143a7c0c3cb920f504e Mon Sep 17 00:00:00 2001 From: Paco Lopez-Dekker Date: Fri, 21 Aug 2026 14:39:08 +0200 Subject: [PATCH 02/11] created some structure --- book/0_overview/resources.md | 16 ++++++++++++++++ book/0_overview/schedule.md | 3 +++ book/1_gradient_divergence_curl/intro.md | 1 + book/2_potential_fiels/intro.md | 0 book/3_diffusion_fields/intro.md | 0 book/4_mechanical_waves/intro.md | 0 book/5_EM_waves/intro.md | 0 book/_toc.yml | 16 +++++++++------- 8 files changed, 29 insertions(+), 7 deletions(-) create mode 100644 book/0_overview/resources.md create mode 100644 book/0_overview/schedule.md create mode 100644 book/1_gradient_divergence_curl/intro.md create mode 100644 book/2_potential_fiels/intro.md create mode 100644 book/3_diffusion_fields/intro.md create mode 100644 book/4_mechanical_waves/intro.md create mode 100644 book/5_EM_waves/intro.md diff --git a/book/0_overview/resources.md b/book/0_overview/resources.md new file mode 100644 index 0000000..4d19bc1 --- /dev/null +++ b/book/0_overview/resources.md @@ -0,0 +1,16 @@ + +## Programming + +Struggling to remember how to use Python? You can check those resources: + + * [Introduction to Python](https://teachbooks.io/introduction_to_python/main/intro.html) from *Exploring the Grand Challenges* to refresh your memory. + * [Python Cheatsheet](https://labex.io/pythoncheatsheet/) for quick overviews starting from the very basics. + * [Think Python](https://allendowney.github.io/ThinkPython/index.html), an entire book for more in-depth explanations. + +Struggling to remember how to use a Python package? Here are some nice summaries for the main packages you will use in this course: + + * **NumPy**: [the absolute basics for beginners](https://numpy.org/doc/stable/user/absolute_beginners.html) + * **Matplotlib**: [quick start guide](https://matplotlib.org/stable/users/explain/quick_start.html) + * **pandas**: [10 minutes to pandas](https://pandas.pydata.org/docs/user_guide/10min.html) + +In general, the main Python packages have extensive documentations, and it is always a good idea to check them. \ No newline at end of file diff --git a/book/0_overview/schedule.md b/book/0_overview/schedule.md new file mode 100644 index 0000000..7552623 --- /dev/null +++ b/book/0_overview/schedule.md @@ -0,0 +1,3 @@ +# Weekly schedule + +Click on the dropdown blocks below to find the schedule of each week's activities. \ No newline at end of file diff --git a/book/1_gradient_divergence_curl/intro.md b/book/1_gradient_divergence_curl/intro.md new file mode 100644 index 0000000..491c78c --- /dev/null +++ b/book/1_gradient_divergence_curl/intro.md @@ -0,0 +1 @@ +## Introduction \ No newline at end of file diff --git a/book/2_potential_fiels/intro.md b/book/2_potential_fiels/intro.md new file mode 100644 index 0000000..e69de29 diff --git a/book/3_diffusion_fields/intro.md b/book/3_diffusion_fields/intro.md new file mode 100644 index 0000000..e69de29 diff --git a/book/4_mechanical_waves/intro.md b/book/4_mechanical_waves/intro.md new file mode 100644 index 0000000..e69de29 diff --git a/book/5_EM_waves/intro.md b/book/5_EM_waves/intro.md new file mode 100644 index 0000000..e69de29 diff --git a/book/_toc.yml b/book/_toc.yml index 23fa359..85f7a79 100644 --- a/book/_toc.yml +++ b/book/_toc.yml @@ -4,14 +4,16 @@ format: jb-book root: intro.md parts: - - caption: Part with some content # A title for the whole the subtree, e.g. shown above the subtree in ToCs, configuration part of sphinx-external-toc (https://sphinx-external-toc.readthedocs.io/en/latest/intro.html) - numbered: false # Default value (line can be removed), whether to number the chapters/sections in this part, configuration part of sphinx-external-toc (https://sphinx-external-toc.readthedocs.io/en/latest/intro.html) - style: numerical # Default value (line can be removed), style of numbering for this part, configuration part of TeachBooks' version of sphinx-external-toc (https://github.com/TeachBooks/sphinx-external-toc?tab=readme-ov-file#toc-tree-options) - restart_numbering: false # Default value (line can be removed), whether to restart numbering for this part, configuration part of TeachBooks' version of sphinx-external-toc (https://github.com/TeachBooks/sphinx-external-toc?tab=readme-ov-file#toc-tree-options) + - caption: Course overview chapters: - - file: some_content/overview.md - sections: - - file: some_content/text_and_code.ipynb + - file: 0_overview/schedule.md + - file: 0_overview/resources.md + - caption: Gradient, divergence, and curl + chapters: + - file: 1_gradient_divergence_curl/intro.md + # - file: 1_gradient_divergence_curl/gradient.md + # - file: 1_gradient_divergence_curl/divergence.md + # - file: 1_gradient_divergence_curl/curl.md - caption: Exercises chapters: - file: exercises.md From b34c4502b7145a06c4374abd00a885b31fc379ac Mon Sep 17 00:00:00 2001 From: Paco Lopez-Dekker Date: Sun, 23 Aug 2026 21:00:00 +0200 Subject: [PATCH 03/11] writing about potential fields --- book/2_potential_fields/fundamentals.md | 94 +++++++++++++++++++++++++ book/2_potential_fields/intro.md | 1 + book/2_potential_fiels/intro.md | 0 book/_toc.yml | 8 +++ 4 files changed, 103 insertions(+) create mode 100644 book/2_potential_fields/fundamentals.md create mode 100644 book/2_potential_fields/intro.md delete mode 100644 book/2_potential_fiels/intro.md diff --git a/book/2_potential_fields/fundamentals.md b/book/2_potential_fields/fundamentals.md new file mode 100644 index 0000000..9678cee --- /dev/null +++ b/book/2_potential_fields/fundamentals.md @@ -0,0 +1,94 @@ +# Fundamentals + +## Field + +A field is a function, or set of functions, in time and space, for example + +$$ + y = f(x,y,z,t) +$$ + +In this section of the course we address *force* fields, such as the gravitational field defining the trajectory of a satellite, or the electric field actuating on a charge. The force field itself will be a *vector field*, + +$$ + \vec{F}(x,y,z,t) = F_x(x,y,z,t)\cdot \hat{x} + F_y(x,y,z,t)\cdot \hat{u} + F_z(x,y,z,t)\cdot \hat{z} +$$ + +## Work + +As you should recall from previous courses, the work performed by a force is given by the product of the force applied on and object and the distance traveled by the object in the direction of the force (assuming the force is constant for now). For a force pointing in the $\hat{x}$ direction a and a displacement $\Delta x$ also in the x direction, the work would be given by + +$$ + W = F_x \cdot \Delta x +$$ + +This, of course, doesn't work for a non constant field and an arbitrary trajectory. What we can do in this case is consider the small increment of work associated to a small, differential, segment of the trajectory + +$$ + dW = \vec{F}(x,y,z) \cdot \vec{ds}. +$$ + +```{admonition} Example: differential work +For a small displacement in the $\hat{x}$ direction, the displacement vector is + +$$ + \vec{ds} = dx \, \hat{x}. +$$ + +If the force is $\vec{F} = F_x \hat{x}$ at that point, then the differential work is + +$$ + dW = \vec{F} \cdot \vec{ds} = F_x \, dx. +$$ + +For example, if $F_x = 4~\mathrm{N}$ and $dx = 0.01~\mathrm{m}$, then + +$$ + dW = 4 \times 0.01 = 0.04~\mathrm{J}. +$$ +``` + +The total work can be calculated integrating $dW$ following the trajectory of the path: + +$$ + W = \int_s dW = \int_s \vec{F}(x,y,z) \cdot \vec{ds} +$$ + +```{admonition} Example: work in Earth's gravity field +Consider a spacecraft of mass $m$ moving from Earth's surface to a circular orbit at radius $r_o$. Earth's gravitational force is radial: + +$$ + \vec{F}_g(r) = -\frac{GMm}{r^2}\hat{r}, +$$ + +where $M$ is Earth's mass and $G$ is the gravitational constant. A small displacement in spherical coordinates can be written as + +$$ + \vec{ds} = dr\,\hat{r} + r\,d\theta\,\hat{\theta} + + r\sin\theta\,d\phi\,\hat{\phi}. +$$ + +The differential work done by gravity is therefore + +$$ + dW_g = \vec{F}_g \cdot \vec{ds} + = -\frac{GMm}{r^2}dr. +$$ + +Only the radial displacement $dr$ contributes. Sideways motion along a circular path has $dr = 0$, so gravity does no work during that part of the motion. + +The work done by gravity from Earth's radius $R_E$ to the orbit radius $r_o$ is + +$$ + W_g = \int_{R_E}^{r_o} -\frac{GMm}{r^2}\,dr + = GMm\left(\frac{1}{r_o} - \frac{1}{R_E}\right). +$$ + +The negative sign tells us that gravity removes energy as the spacecraft moves outward. The external work needed to lift it slowly to orbit is the opposite: + +$$ + W_{\mathrm{ext}} = GMm\left(\frac{1}{R_E} - \frac{1}{r_o}\right). +$$ +``` + + diff --git a/book/2_potential_fields/intro.md b/book/2_potential_fields/intro.md new file mode 100644 index 0000000..c38dd9b --- /dev/null +++ b/book/2_potential_fields/intro.md @@ -0,0 +1 @@ +# Potential Fields diff --git a/book/2_potential_fiels/intro.md b/book/2_potential_fiels/intro.md deleted file mode 100644 index e69de29..0000000 diff --git a/book/_toc.yml b/book/_toc.yml index 85f7a79..40fc2aa 100644 --- a/book/_toc.yml +++ b/book/_toc.yml @@ -14,6 +14,14 @@ parts: # - file: 1_gradient_divergence_curl/gradient.md # - file: 1_gradient_divergence_curl/divergence.md # - file: 1_gradient_divergence_curl/curl.md + - caption: Potential Fields + chapters: + - file: 2_potential_fields/intro.md + sections: + - file: 2_potential_fields/fundamentals.md + # - file: 2_potential_fields/gradient_fields.md + # - file: 2_potential_fields/divergence_free_fields.md + # - file: 2_potential_fields/curl_free_fields.md - caption: Exercises chapters: - file: exercises.md From a9aefdfc1234026e2515a40c1fc422252c2e06c2 Mon Sep 17 00:00:00 2001 From: Paco Lopez-Dekker Date: Mon, 24 Aug 2026 15:38:25 +0200 Subject: [PATCH 04/11] added gravity work example, etc --- .../2_potential_fields/conservative_fields.md | 13 + .../earth_gravity_work.ipynb | 260 ++++++++++++++++++ .../figures/earth_gravity_work.png | Bin 0 -> 250754 bytes book/2_potential_fields/fundamentals.md | 79 ------ book/2_potential_fields/work.md | 83 ++++++ book/_config.yml | 2 +- book/_toc.yml | 3 + requirements.txt | 2 + 8 files changed, 362 insertions(+), 80 deletions(-) create mode 100644 book/2_potential_fields/conservative_fields.md create mode 100644 book/2_potential_fields/earth_gravity_work.ipynb create mode 100644 book/2_potential_fields/figures/earth_gravity_work.png create mode 100644 book/2_potential_fields/work.md diff --git a/book/2_potential_fields/conservative_fields.md b/book/2_potential_fields/conservative_fields.md new file mode 100644 index 0000000..9e7342e --- /dev/null +++ b/book/2_potential_fields/conservative_fields.md @@ -0,0 +1,13 @@ +# Conservative Fields + +A force field is called conservative when the work done by the field between two points does not depend on the path taken between them. + +In other words, for any two paths $s_1$ and $s_2$ that start at the same point $P_0$ and end at the same point $P_1$, + +$$ + \int_{s_1} \vec{F}\cdot\vec{ds} + = + \int_{s_2} \vec{F}\cdot\vec{ds}. +$$ + +Earth's gravitational field is an example of a conservative field: the work depends only on the starting and ending positions, not on the detailed route taken between them. diff --git a/book/2_potential_fields/earth_gravity_work.ipynb b/book/2_potential_fields/earth_gravity_work.ipynb new file mode 100644 index 0000000..84bb4e1 --- /dev/null +++ b/book/2_potential_fields/earth_gravity_work.ipynb @@ -0,0 +1,260 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "6d204e9f", + "metadata": {}, + "source": [ + "# Earth Gravity Work\n", + "\n", + "This notebook illustrates the work done when moving through Earth's gravitational field. Gravity is radial, so only the radial part of the displacement contributes to $dW = \\vec{F}\\cdot\\vec{ds}$.\n", + "\n", + "The examples below compare several paths from the same starting point $P_0$ on Earth's surface to the same endpoint $P_1$ in a high orbit. The paths look different, but the total work done by gravity is the same because the gravitational field is conservative." + ] + }, + { + "cell_type": "markdown", + "id": "6a43c9e1", + "metadata": {}, + "source": [ + "(Click {fa}`rocket` --> {guilabel}`Live Code` to activate live code on this page.)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "4b5e1832", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-24T12:43:57.467971Z", + "iopub.status.busy": "2026-08-24T12:43:57.467820Z", + "iopub.status.idle": "2026-08-24T12:43:57.866667Z", + "shell.execute_reply": "2026-08-24T12:43:57.866108Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Analytic work done by gravity: -3.128e+07 J/kg\n", + "External work required: 3.128e+07 J/kg\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from pathlib import Path\n", + "\n", + "G = 6.67430e-11 # gravitational constant, m^3 kg^-1 s^-2\n", + "M_E = 5.972e24 # Earth mass, kg\n", + "R_E = 6.371e6 # Earth radius, m\n", + "g0 = G * M_E / R_E**2 # surface gravity, m s^-2\n", + "\n", + "r_start = R_E\n", + "r_end = 2.0 * R_E # high orbit, comparable to Earth's radius\n", + "r_overshoot = 2.45 * R_E # one path climbs too high, then comes back\n", + "theta_start = 0.0\n", + "theta_end = np.deg2rad(70)\n", + "\n", + "def gravity_acceleration(x, y):\n", + " r = np.sqrt(x**2 + y**2)\n", + " return -G * M_E * x / r**3, -G * M_E * y / r**3\n", + "\n", + "def make_path(kind, n=500):\n", + " t = np.linspace(0, 1, n)\n", + " if kind == \"out_then_around\":\n", + " halfway = t < 0.5\n", + " r = np.empty_like(t)\n", + " theta = np.empty_like(t)\n", + " r[halfway] = r_start + (r_end - r_start) * t[halfway] / 0.5\n", + " theta[halfway] = theta_start\n", + " r[~halfway] = r_end\n", + " theta[~halfway] = theta_start + (theta_end - theta_start) * (t[~halfway] - 0.5) / 0.5\n", + " elif kind == \"spiral\":\n", + " r = r_start + (r_end - r_start) * t\n", + " theta = theta_start + (theta_end - theta_start) * t\n", + " elif kind == \"around_then_out\":\n", + " halfway = t < 0.5\n", + " r = np.empty_like(t)\n", + " theta = np.empty_like(t)\n", + " r[halfway] = r_start\n", + " theta[halfway] = theta_start + (theta_end - theta_start) * t[halfway] / 0.5\n", + " r[~halfway] = r_start + (r_end - r_start) * (t[~halfway] - 0.5) / 0.5\n", + " theta[~halfway] = theta_end\n", + " elif kind == \"overshoot_then_return\":\n", + " turn = 0.65\n", + " outbound = t < turn\n", + " r = np.empty_like(t)\n", + " theta = np.empty_like(t)\n", + " r[outbound] = r_start + (r_overshoot - r_start) * t[outbound] / turn\n", + " theta[outbound] = theta_start + 0.75 * (theta_end - theta_start) * t[outbound] / turn\n", + " r[~outbound] = r_overshoot + (r_end - r_overshoot) * (t[~outbound] - turn) / (1 - turn)\n", + " theta[~outbound] = theta_start + 0.75 * (theta_end - theta_start) + 0.25 * (theta_end - theta_start) * (t[~outbound] - turn) / (1 - turn)\n", + " else:\n", + " raise ValueError(f\"Unknown path kind: {kind}\")\n", + "\n", + " x = r * np.cos(theta)\n", + " y = r * np.sin(theta)\n", + " return x, y\n", + "\n", + "def cumulative_gravity_work(x, y):\n", + " dx = np.diff(x)\n", + " dy = np.diff(y)\n", + " xm = 0.5 * (x[:-1] + x[1:])\n", + " ym = 0.5 * (y[:-1] + y[1:])\n", + " gx, gy = gravity_acceleration(xm, ym)\n", + " dW_per_kg = gx * dx + gy * dy\n", + " return np.concatenate([[0], np.cumsum(dW_per_kg)])\n", + "\n", + "paths = {\n", + " \"out then around\": make_path(\"out_then_around\"),\n", + " \"spiral\": make_path(\"spiral\"),\n", + " \"around then out\": make_path(\"around_then_out\"),\n", + " \"overshoot then return\": make_path(\"overshoot_then_return\"),\n", + "}\n", + "\n", + "analytic_work_per_kg = G * M_E * (1/r_end - 1/r_start)\n", + "print(f\"Analytic work done by gravity: {analytic_work_per_kg:.3e} J/kg\")\n", + "print(f\"External work required: {-analytic_work_per_kg:.3e} J/kg\")" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "5c850c6d", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-24T12:43:57.867880Z", + "iopub.status.busy": "2026-08-24T12:43:57.867740Z", + "iopub.status.idle": "2026-08-24T12:43:58.443097Z", + "shell.execute_reply": "2026-08-24T12:43:58.442475Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, (ax_field, ax_work) = plt.subplots(1, 2, figsize=(12, 5))\n", + "\n", + "# Gravity field, shown in Earth-radius units. The arrows point inward and\n", + "# become shorter farther from Earth because |g| decreases as 1/r^2.\n", + "grid = np.linspace(-2.6, 2.6, 19)\n", + "X, Y = np.meshgrid(grid, grid)\n", + "radius = np.sqrt(X**2 + Y**2)\n", + "mask = radius > 1.05\n", + "\n", + "x_m = X[mask] * R_E\n", + "y_m = Y[mask] * R_E\n", + "gx, gy = gravity_acceleration(x_m, y_m)\n", + "\n", + "ax_field.quiver(\n", + " X[mask], Y[mask], gx/g0, gy/g0,\n", + " np.sqrt(gx**2 + gy**2)/g0,\n", + " cmap=\"viridis\", scale=6, width=0.004\n", + ")\n", + "\n", + "theta = np.linspace(0, 2*np.pi, 500)\n", + "ax_field.plot(np.cos(theta), np.sin(theta), color=\"0.25\", label=\"Earth surface\")\n", + "ax_field.plot(2*np.cos(theta), 2*np.sin(theta), \"--\", color=\"0.55\", label=\"orbit radius\")\n", + "\n", + "def add_path_arrows(ax, x, y, color, fractions=(0.35, 0.7)):\n", + " for fraction in fractions:\n", + " i = int(fraction * (len(x) - 2))\n", + " ax.annotate(\n", + " \"\",\n", + " xy=(x[i + 1]/R_E, y[i + 1]/R_E),\n", + " xytext=(x[i]/R_E, y[i]/R_E),\n", + " arrowprops={\"arrowstyle\": \"-|>\", \"color\": color, \"lw\": 1.8, \"mutation_scale\": 13},\n", + " )\n", + "\n", + "p0_x = r_start * np.cos(theta_start) / R_E\n", + "p0_y = r_start * np.sin(theta_start) / R_E\n", + "p1_x = r_end * np.cos(theta_end) / R_E\n", + "p1_y = r_end * np.sin(theta_end) / R_E\n", + "\n", + "ax_field.scatter([p0_x, p1_x], [p0_y, p1_y], s=70, color=\"black\", zorder=5)\n", + "ax_field.annotate(\"$P_0$\", (p0_x, p0_y), xytext=(8, 8), textcoords=\"offset points\", fontsize=12, weight=\"bold\")\n", + "ax_field.annotate(\"$P_1$\", (p1_x, p1_y), xytext=(8, 6), textcoords=\"offset points\", fontsize=12, weight=\"bold\")\n", + "\n", + "for label, (x, y) in paths.items():\n", + " line, = ax_field.plot(x/R_E, y/R_E, linewidth=2.4, label=label)\n", + " add_path_arrows(ax_field, x, y, line.get_color())\n", + " work = cumulative_gravity_work(x, y)\n", + " progress = np.linspace(0, 1, len(work))\n", + " ax_work.plot(progress, work/1e6, linewidth=2.4, label=f\"{label}: {work[-1]/1e6:.1f} MJ/kg\")\n", + "\n", + "ax_work.axhline(analytic_work_per_kg/1e6, color=\"0.3\", linestyle=\":\", label=\"analytic result\")\n", + "\n", + "ax_field.set_aspect(\"equal\")\n", + "plot_limit = 1.1 * r_overshoot / R_E\n", + "ax_field.set_xlim(0, plot_limit)\n", + "ax_field.set_ylim(0, plot_limit)\n", + "ax_field.set_xlabel(\"x / $R_E$\")\n", + "ax_field.set_ylabel(\"y / $R_E$\")\n", + "ax_field.set_title(\"Gravity field and alternative paths\")\n", + "ax_field.legend(loc=\"upper right\", fontsize=8)\n", + "\n", + "ax_work.set_xlabel(\"fraction of path travelled\")\n", + "ax_work.set_ylabel(\"work done by gravity [MJ/kg]\")\n", + "ax_work.set_title(\"Cumulative line integral\")\n", + "ax_work.legend(fontsize=8)\n", + "ax_work.grid(True, alpha=0.3)\n", + "\n", + "plt.tight_layout()\n", + "\n", + "# Save the default figure so it can be reused from the Markdown chapter.\n", + "cwd = Path.cwd()\n", + "if cwd.name == \"2_potential_fields\":\n", + " figure_dir = cwd / \"figures\"\n", + "elif (cwd / \"2_potential_fields\").exists():\n", + " figure_dir = cwd / \"2_potential_fields\" / \"figures\"\n", + "else:\n", + " figure_dir = cwd / \"book\" / \"2_potential_fields\" / \"figures\"\n", + "figure_dir.mkdir(parents=True, exist_ok=True)\n", + "fig.savefig(figure_dir / \"earth_gravity_work.png\", dpi=200, bbox_inches=\"tight\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "207e205d", + "metadata": {}, + "source": [ + "Try changing `r_end`, `theta_end`, or the path definitions above. As long as the starting and ending points are unchanged, the total gravitational work is unchanged. The overshoot path climbs beyond $P_1$, so gravity does extra negative work at first; when the path returns inward, gravity does positive work and the cumulative integral recovers to the same final value." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/book/2_potential_fields/figures/earth_gravity_work.png b/book/2_potential_fields/figures/earth_gravity_work.png new file mode 100644 index 0000000000000000000000000000000000000000..c13b9753fadf3e152ef4f74a6434d6fd582c6958 GIT binary patch literal 250754 zcmdSBbyQVh_ce+ENS6rGDJ9(vf^>I-bRANVMnD9lk&qCOmXtblgLId4cXz{mj{e^7 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z0Y&(>4IqjCe4S?g(`{#!pr|gWvN2@j=ffC?E;ruF>BtJqssH;j)M*anbyDi;!ue3~ zM7saV4}bnz=3d7f59R;768<2?YJ@1If4`*KN@16bCge=eFpcxQDkHo}WnoW=B))Ej z|9KJeQX?nit^e28q%Q)+|M!cP`i}tnzd!i@FZg>cR2KIn-%mH~k)Om?AU{!*Ma$&h IHGKYm03KMO7ytkO literal 0 HcmV?d00001 diff --git a/book/2_potential_fields/fundamentals.md b/book/2_potential_fields/fundamentals.md index 9678cee..c329d28 100644 --- a/book/2_potential_fields/fundamentals.md +++ b/book/2_potential_fields/fundamentals.md @@ -13,82 +13,3 @@ In this section of the course we address *force* fields, such as the gravitation $$ \vec{F}(x,y,z,t) = F_x(x,y,z,t)\cdot \hat{x} + F_y(x,y,z,t)\cdot \hat{u} + F_z(x,y,z,t)\cdot \hat{z} $$ - -## Work - -As you should recall from previous courses, the work performed by a force is given by the product of the force applied on and object and the distance traveled by the object in the direction of the force (assuming the force is constant for now). For a force pointing in the $\hat{x}$ direction a and a displacement $\Delta x$ also in the x direction, the work would be given by - -$$ - W = F_x \cdot \Delta x -$$ - -This, of course, doesn't work for a non constant field and an arbitrary trajectory. What we can do in this case is consider the small increment of work associated to a small, differential, segment of the trajectory - -$$ - dW = \vec{F}(x,y,z) \cdot \vec{ds}. -$$ - -```{admonition} Example: differential work -For a small displacement in the $\hat{x}$ direction, the displacement vector is - -$$ - \vec{ds} = dx \, \hat{x}. -$$ - -If the force is $\vec{F} = F_x \hat{x}$ at that point, then the differential work is - -$$ - dW = \vec{F} \cdot \vec{ds} = F_x \, dx. -$$ - -For example, if $F_x = 4~\mathrm{N}$ and $dx = 0.01~\mathrm{m}$, then - -$$ - dW = 4 \times 0.01 = 0.04~\mathrm{J}. -$$ -``` - -The total work can be calculated integrating $dW$ following the trajectory of the path: - -$$ - W = \int_s dW = \int_s \vec{F}(x,y,z) \cdot \vec{ds} -$$ - -```{admonition} Example: work in Earth's gravity field -Consider a spacecraft of mass $m$ moving from Earth's surface to a circular orbit at radius $r_o$. Earth's gravitational force is radial: - -$$ - \vec{F}_g(r) = -\frac{GMm}{r^2}\hat{r}, -$$ - -where $M$ is Earth's mass and $G$ is the gravitational constant. A small displacement in spherical coordinates can be written as - -$$ - \vec{ds} = dr\,\hat{r} + r\,d\theta\,\hat{\theta} - + r\sin\theta\,d\phi\,\hat{\phi}. -$$ - -The differential work done by gravity is therefore - -$$ - dW_g = \vec{F}_g \cdot \vec{ds} - = -\frac{GMm}{r^2}dr. -$$ - -Only the radial displacement $dr$ contributes. Sideways motion along a circular path has $dr = 0$, so gravity does no work during that part of the motion. - -The work done by gravity from Earth's radius $R_E$ to the orbit radius $r_o$ is - -$$ - W_g = \int_{R_E}^{r_o} -\frac{GMm}{r^2}\,dr - = GMm\left(\frac{1}{r_o} - \frac{1}{R_E}\right). -$$ - -The negative sign tells us that gravity removes energy as the spacecraft moves outward. The external work needed to lift it slowly to orbit is the opposite: - -$$ - W_{\mathrm{ext}} = GMm\left(\frac{1}{R_E} - \frac{1}{r_o}\right). -$$ -``` - - diff --git a/book/2_potential_fields/work.md b/book/2_potential_fields/work.md new file mode 100644 index 0000000..b106b1a --- /dev/null +++ b/book/2_potential_fields/work.md @@ -0,0 +1,83 @@ +# Work + +As you should recall from previous courses, the work performed by a force is given by the product of the force applied on an object and the distance traveled by the object in the direction of the force (assuming the force is constant for now). For a force pointing in the $\hat{x}$ direction and a displacement $\Delta x$ also in the $x$ direction, the work would be given by + +$$ + W = F_x \cdot \Delta x +$$ + +This, of course, doesn't work for a non constant field and an arbitrary trajectory. What we can do in this case is consider the small increment of work associated to a small, differential, segment of the trajectory + +$$ + dW = \vec{F}(x,y,z) \cdot \vec{ds}. +$$ + +```{admonition} Example: differential work +For a small displacement in the $\hat{x}$ direction, the displacement vector is + +$$ + \vec{ds} = dx \, \hat{x}. +$$ + +If the force is $\vec{F} = F_x \hat{x}$ at that point, then the differential work is + +$$ + dW = \vec{F} \cdot \vec{ds} = F_x \, dx. +$$ + +For example, if $F_x = 4~\mathrm{N}$ and $dx = 0.01~\mathrm{m}$, then + +$$ + dW = 4 \times 0.01 = 0.04~\mathrm{J}. +$$ +``` + +The total work can be calculated integrating $dW$ following the trajectory of the path: + +$$ + W = \int_s dW = \int_s \vec{F}(x,y,z) \cdot \vec{ds} +$$ + +```{admonition} Example: work in Earth's gravity field +Consider a spacecraft of mass $m$ moving from Earth's surface to a circular orbit at radius $r_o$. Earth's gravitational force is radial: + +$$ + \vec{F}_g(r) = -\frac{GMm}{r^2}\hat{r}, +$$ + +where $M$ is Earth's mass and $G$ is the gravitational constant. A small displacement in spherical coordinates can be written as + +$$ + \vec{ds} = dr\,\hat{r} + r\,d\theta\,\hat{\theta} + + r\sin\theta\,d\phi\,\hat{\phi}. +$$ + +The differential work done by gravity is therefore + +$$ + dW_g = \vec{F}_g \cdot \vec{ds} + = -\frac{GMm}{r^2}dr. +$$ + +Only the radial displacement $dr$ contributes. Sideways motion along a circular path has $dr = 0$, so gravity does no work during that part of the motion. + +The work done by gravity from Earth's radius $R_E$ to the orbit radius $r_o$ is + +$$ + W_g = \int_{R_E}^{r_o} -\frac{GMm}{r^2}\,dr + = GMm\left(\frac{1}{r_o} - \frac{1}{R_E}\right). +$$ + +The negative sign tells us that gravity removes energy as the spacecraft moves outward. The external work needed to lift it slowly to orbit is the opposite: + +$$ + W_{\mathrm{ext}} = GMm\left(\frac{1}{R_E} - \frac{1}{r_o}\right). +$$ +``` + +```{figure} figures/earth_gravity_work.png +:name: earth-gravity-work-paths +:width: 100% + +Several paths from the same starting point $P_0$ to the same endpoint $P_1$ in Earth's gravity field. The cumulative line integral differs along the way, but all paths end at the same value because the gravitational field is conservative. +``` diff --git a/book/_config.yml b/book/_config.yml index e15d691..2044f6d 100644 --- a/book/_config.yml +++ b/book/_config.yml @@ -5,7 +5,7 @@ author: Author from Delft University of Technology, built with TeachBooks, CC BY 4.0 # Replace TeachBooks Teams with your own name in the line above, configuratin part of JupyterBook: https://jupyterbook.org/en/stable/customize/config.html execute: - execute_notebooks: "off" # Replace this if you want don't have notebooks with output and you want to add notebook output during build, configuration part of Jupyterbook v1 (https://jupyterbook.org/en/stable/customize/config.html) + execute_notebooks: "auto" # Execute notebooks during build when outputs are missing or stale, configuration part of Jupyterbook v1 (https://jupyterbook.org/en/stable/customize/config.html) exclude_patterns: [] # Default value (line can be removed), sets a list of patterns to *skip* in execution, configuration part of Jupyterbook v1 (https://jupyterbook.org/en/stable/customize/config.html), can overwritten by Sphinx-NB-Execution-Patterns (https://teachbooks.io/manual/_git/github.com_TeachBooks_Sphinx-NB-Execution-Patterns/Manual/README.html) timeout: 30 # Default value (line can be removed), sets he maximum time (in seconds) each notebook cell is allowed to run, configuration part of Jupyterbook v1 (https://jupyterbook.org/en/stable/customize/config.html) allow_errors: false # Default value (line can be removed), all cells are always run, configuration part of Jupyterbook v1 (https://jupyterbook.org/en/stable/customize/config.html) diff --git a/book/_toc.yml b/book/_toc.yml index 40fc2aa..78ed671 100644 --- a/book/_toc.yml +++ b/book/_toc.yml @@ -19,6 +19,9 @@ parts: - file: 2_potential_fields/intro.md sections: - file: 2_potential_fields/fundamentals.md + - file: 2_potential_fields/work.md + - file: 2_potential_fields/conservative_fields.md + - file: 2_potential_fields/earth_gravity_work.ipynb # - file: 2_potential_fields/gradient_fields.md # - file: 2_potential_fields/divergence_free_fields.md # - file: 2_potential_fields/curl_free_fields.md diff --git a/requirements.txt b/requirements.txt index 6ef05b5..c3b2bf2 100644 --- a/requirements.txt +++ b/requirements.txt @@ -5,3 +5,5 @@ teachbooks # depends on jupyter-book v1 git+https://github.com/TeachBooks/TeachBooks-Favourites sphinx-tudelft-theme sphinx-apa-references +numpy +matplotlib From 77ef1adfca22f1be4ddde01d23367a902f238c1b Mon Sep 17 00:00:00 2001 From: Paco Lopez-Dekker Date: Tue, 25 Aug 2026 17:28:26 +0200 Subject: [PATCH 05/11] some historical background, etc. --- .../2_potential_fields/conservative_fields.md | 195 +++++++++++++++++- .../principia_book1_plate1_figure1.png | Bin 0 -> 2926 bytes .../principia_book1_plate6_figure1.png | Bin 0 -> 5844 bytes book/2_potential_fields/newtons_principia.md | 135 ++++++++++++ book/2_potential_fields/potential.md | 67 ++++++ book/2_potential_fields/work.md | 6 +- book/_toc.yml | 2 + book/references.bib | 4 +- 8 files changed, 404 insertions(+), 5 deletions(-) create mode 100644 book/2_potential_fields/figures/principia_book1_plate1_figure1.png create mode 100644 book/2_potential_fields/figures/principia_book1_plate6_figure1.png create mode 100644 book/2_potential_fields/newtons_principia.md create mode 100644 book/2_potential_fields/potential.md diff --git a/book/2_potential_fields/conservative_fields.md b/book/2_potential_fields/conservative_fields.md index 9e7342e..afb80a9 100644 --- a/book/2_potential_fields/conservative_fields.md +++ b/book/2_potential_fields/conservative_fields.md @@ -1,6 +1,6 @@ # Conservative Fields -A force field is called conservative when the work done by the field between two points does not depend on the path taken between them. +In general, the line integral in {eq}`eq:work-integrated-work` could depend on the path followed between two points. A force field is called conservative when the work done by the field between two points does not depend on the path taken between them. In other words, for any two paths $s_1$ and $s_2$ that start at the same point $P_0$ and end at the same point $P_1$, @@ -11,3 +11,196 @@ $$ $$ Earth's gravitational field is an example of a conservative field: the work depends only on the starting and ending positions, not on the detailed route taken between them. + +```{admonition} Exercise: a non-conservative field +Show that the two-dimensional vector field + +$$ + \vec{F}(x,y) = -y\,\hat{x} + x\,\hat{y} +$$ + +is not conservative. + +To do this, calculate the work done by the field around a circle of radius $R$ centered at the origin: + +$$ + \vec{r}(\theta) = R\cos\theta\,\hat{x} + R\sin\theta\,\hat{y}, + \qquad 0 \leq \theta \leq 2\pi. +$$ + +1. Calculate the differential displacement $d\vec{s}$ along the circle. +2. Evaluate $\vec{F}\cdot d\vec{s}$ on the circle. +3. Compute the closed line integral + + $$ + \oint \vec{F}\cdot d\vec{s}. + $$ + +4. Explain why your result shows that the field is not conservative. +``` + +```{dropdown} Solution +Along the circle, + +$$ + d\vec{s} + = + -R\sin\theta\,d\theta\,\hat{x} + + + R\cos\theta\,d\theta\,\hat{y}. +$$ + +The field evaluated on the circle is + +$$ + \vec{F} + = + -R\sin\theta\,\hat{x} + + + R\cos\theta\,\hat{y}. +$$ + +Therefore, + +$$ + \vec{F}\cdot d\vec{s} + = + R^2\,d\theta. +$$ + +The work around the closed path is + +$$ + \oint \vec{F}\cdot d\vec{s} + = + \int_0^{2\pi} R^2\,d\theta + = + 2\pi R^2. +$$ + +This is not zero. A conservative field must have zero work around any closed path, so this field is not conservative. +``` + +```{admonition} Physical example: magnetic field around a wire +We will come back to magnetic fields later in the course, so for now we simply postulate the following result. + +An infinitely long straight wire along the $z$ axis, carrying a steady current $I$, produces a magnetic field that circles around the wire: + +$$ + \vec{B}(\rho) = \frac{\mu_0 I}{2\pi \rho}\,\hat{\phi}. +$$ + +Here $\rho$ is the distance from the $z$ axis. The direction $\hat{\phi}$ is the direction tangent to a circle around the wire. If you look along the positive $z$ direction, $\hat{\phi}$ points counterclockwise around the wire. + +For a circular path of radius $\rho$ centered on the wire, the small displacement along the path is + +$$ + d\vec{s} = \rho\,d\phi\,\hat{\phi}. +$$ + +Therefore, + +$$ + \vec{B}\cdot d\vec{s} + = + \frac{\mu_0 I}{2\pi \rho}\,\hat{\phi} + \cdot + \rho\,d\phi\,\hat{\phi} + = + \frac{\mu_0 I}{2\pi}\,d\phi. +$$ + +Integrating once around the circle gives + +$$ + \oint \vec{B}\cdot d\vec{s} + = + \int_0^{2\pi} \frac{\mu_0 I}{2\pi}\,d\phi + = + \mu_0 I. +$$ + +This result is not zero, so this magnetic field is not conservative. This equation is a preview of Ampere's law, which we will study properly when we discuss electromagnetic fields. +``` + +Let is now consider the work done by a conservative force field to go from $P_0$ to an arbitrary point $P$, + +$$ +W(P_0,P) = \int_{P_0}^P \vec{F}(x,y,z) \cdot \vec{ds}, +$$ + +and to a point desplaced in the x-direction, + +$$ +W(P_0,P+\Delta x \cdot \hat{x}) = \int_{P_0}^{P+\Delta x \cdot \hat{x}} \vec{F}(x,y,z) \cdot \vec{ds}. +$$ + +Becase the path does not matter, we can go first from $P_0$ to $P$ and from there to $P+\Delta x \cdot \hat{x}$, so we have + +$$ +W(P_0,P+\Delta x \cdot \hat{x}) = W(P_0,P) + W(P,P+\Delta x \cdot \hat{x}), +$$ + +or + +$$ +W(P_0,P+\Delta x \cdot \hat{x}) - W(P_0,P) = W(P,P+\Delta x \cdot \hat{x}) = \int_{P}^{P+\Delta x \cdot \hat{x}} \vec{F}(x,y,z) \cdot \vec{ds}. +$$ + +If we go in a straight line to $P+\Delta x \cdot \hat{x}$, the path diferencial becomes + +$$ +\vec{ds} = dx\cdot \hat{x}. +$$ + +When we do the inner-product by the force field, + +$$ +\vec{F}(x,y,z) = F_x(x,y,z) \hat{x} + F_y(x,y,z) \hat{y} + F_z(x,y,z) \hat{z}, +$$ + +only the x component of the field matters (because $\hat{x}\cdot\hat{y} = \hat{x}\cdot\hat{z} = 0$), + +$$ +\vec{F}(x,y,z) \cdot \vec{ds} = \vec{F}(x,y,z) \cdot dx \cdot \hat{x} = F_x(x,y,z) \cdot dx. +$$ + +So combining with the previous we have + +$$ +W(P_0,P+\Delta x \cdot \hat{x}) - W(P_0,P) = \int_{P}^{P+\Delta x \cdot \hat{x}} F_x(x,y,z)\,dx. +$$ + +Now we can go towards the partial derivative of the work with respect to $x$: + +$$ +\frac{\partial W}{\partial x} += +\lim_{\Delta x \to 0} +\frac{W(P_0,P+\Delta x \cdot \hat{x}) - W(P_0,P)}{\Delta x} += +\lim_{\Delta x \to 0} +\frac{1}{\Delta x} +\int_{P}^{P+\Delta x \cdot \hat{x}} F_x(x,y,z)\,dx += +F_x(P). +$$ + +or, in a more compact form: + +$$ +\frac{\partial W}{\partial x} = F_x +$$ + +We could repeat the derivation for displacements in the y and z direction, respectively. Combining, we have + +$$ +\vec{\nabla} W = \vec{F}. +$$ (eq:work_is_gradient_of_work) + +In *words*, {eq}`eq:work_is_gradient_of_work` tells us: + +- The force field is the gradient of the work; +- The vector field, $\vec{F}$, is fully determined by the scalar field, $W$. + +Any vector field that can be constructed as the gradient of a *work* function, i.e. by {eq}`eq:work_is_gradient_of_work`, is a **conservative field**.. diff --git a/book/2_potential_fields/figures/principia_book1_plate1_figure1.png b/book/2_potential_fields/figures/principia_book1_plate1_figure1.png new file mode 100644 index 0000000000000000000000000000000000000000..7fc4f1bb8d962d4e7c2d1e51d1773e53a649ea98 GIT binary patch literal 2926 zcmV-!3z77RP)Px#32;bRa{vGf6951U69E94oEQKA00(qQO+^RV0t*KuFaXYm2LJ#I07*naRCwC$ zUCWj1C=!j-sa3Dal=c8}KZ|F=cmlGhO#mzy6J|3;^qJE$>V;BDq|}E`L^7+v1v3F4Zx5F@hzrdGX97gePlfjexDh&Yen6PGK zuXO+bu1R>cS;ngs!lebMf!3D2%KL%c*)Mk_!=!RL{ z!O-4Ni$@b54@$^h`vef`ebt7&gIvr{??F3S;kDXRg?6p4-TSs96<)PS#@nT@V~5v1 z-+Y~D`)u4i*bnc}QKI`%@MsNR+kZUsYS2Vfu?V5Qg;4GJ1^_U_@OEY%ra%L%@5PK* zzM-ZuXg`LcgZI~7HWSDf&U5K90JR>IF3cN+=mxH}|ocyD;`al^|$=$A5yjab=cgw{FeKDxck+UXrx z0cR}$XuEth>i|H325W=ffgS)r$i-KS*8&jWR=@E6^p!fu)em+XsOjMaA$J*O+gUy~ z+s}Aa-J`X!y^=_rRy=9}M{f4=$BcnLw0#Pq&*xD{J%QLH`y{suebv4uYb(9q?d{Xi zQihfgmOp;~-6;R7|JfhhJFz&t%V#ZB(YFL}r^|rU_j>y~dfTe#T7Z3f)KQ~5wXZyN zqv#&*ZJ<^LHLnJVCbdBvf(X>6%-3MkD7yR4)e&pbXjiN_3eMF_gS?=m;{e_b71jW( zx74+O?(>8-9VvOg|1*cVCh^s9OkTP!9Ss2Azy9&(8(#qcuBi>0V@7oNL>qei|NL$T z1px5<&wm}X?zA7*cAUdsNUq`cKMq@?Y9A&b9qkC~FlsGIqk(V_+m7&_xS@_NuBl(& zA3q=8@g^E2N8vSRbuf&zqyeMmsPawaW=X)3NE z!fP_azp0>tX5u9bE410b^73xX7_DT{sXz-!&S zi6Z-@OriYM@vZ?&d!<7V-jx6sroZ89i0JH<4nufX6`sN>z|R!nMS<5k+}T_rzB0j+ zAyv!-dNJITRzNe!NM*yTke58XC3;g-DaTv_F9{CQE@V>5QrwI9;u8aIFliw zfN*KT4%z}LlqTnW&U6ksC6$RuFs`rg*qlTsFRehRL!KrWS63(_*M>2DFG3yiw8C>S ze`Q)WjNy9~wK!gHAVgjOfLzfx^iOx8fk;?hLxWc^MD}Y9gvot#GqhJap#KoIYnO;D zK;8;%x^oymwuZhkJ1r4iaL9XHvnj4~&`fpjR|O3&;IB?Dlx4FwrUf2}zuYDEeDWr< z*T%HKXY=>fWUVhiH_z6mvKMFRJ??VM8C*)+2oifO&eD5i;?HUzWZK#=O4i0qxQ1ly9ZeZ~?P_4$rIl}albu8279czWL4R!w z*O1Cy4aetFl2;(e`Kuicc~hLj6>)8CAPhqk#R#Ga?6sGX7eKO{4NttXo^lUqUvxuiC|vMnef>T0%w^V2vC! 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Outside a perfectly spherically symmetric Earth, it is an exact consequence of the inverse-square law. This result justifies the gravitational field used in the examples that follow and gives us a concrete setting in which to introduce work and potential. diff --git a/book/2_potential_fields/potential.md b/book/2_potential_fields/potential.md new file mode 100644 index 0000000..6a99f8a --- /dev/null +++ b/book/2_potential_fields/potential.md @@ -0,0 +1,67 @@ +# Potential and Equipotential Surfaces + +For a conservative field, the work done between two points can be described using a scalar function. This scalar function is called a **potential**. + +The central idea is that instead of describing the vector field directly, we can describe a scalar field whose spatial changes determine the vector field. + +## Potential + +In the previous section we introduced a work function $W(P_0,P)$ and found that, for a conservative force field, + +$$ + \vec{F} = \vec{\nabla} W. +$$ + +In many physical problems we define the potential $\Phi$ with the opposite sign: + +$$ + \Phi = -W. +$$ + +With this convention, the force field is + +$$ + \vec{F} = -\vec{\nabla} \Phi. +$$ + +The minus sign has an important physical meaning: the force points in the direction where the potential decreases most rapidly. + +For example, near Earth's surface the gravitational potential energy of a mass $m$ can be written approximately as + +$$ + \Phi(z) = mgz, +$$ + +where $z$ is height. The gravitational force is then + +$$ + \vec{F} = -\vec{\nabla} \Phi = -mg\,\hat{z}. +$$ + +The force points downward, toward lower gravitational potential energy. + +## Equipotential surfaces + +An **equipotential surface** is a surface on which the potential has the same value everywhere: + +$$ + \Phi(x,y,z) = \mathrm{constant}. +$$ + +If a particle moves along an equipotential surface, then the change in potential is zero: + +$$ + dV = 0. +$$ + +Because the force is related to the gradient of the potential, + +$$ + \vec{F} = -\vec{\nabla} \Phi, +$$ + +the force is perpendicular to the equipotential surface. Motion along the surface is sideways relative to the force, so the force does no work for a displacement along that surface. + +```{admonition} Key idea +Field lines point in the direction of steepest change of the potential. Equipotential surfaces are perpendicular to those field lines. +``` diff --git a/book/2_potential_fields/work.md b/book/2_potential_fields/work.md index b106b1a..3147def 100644 --- a/book/2_potential_fields/work.md +++ b/book/2_potential_fields/work.md @@ -17,13 +17,13 @@ For a small displacement in the $\hat{x}$ direction, the displacement vector is $$ \vec{ds} = dx \, \hat{x}. -$$ +$$ If the force is $\vec{F} = F_x \hat{x}$ at that point, then the differential work is $$ dW = \vec{F} \cdot \vec{ds} = F_x \, dx. -$$ +$$ (eq:work-differential-work) For example, if $F_x = 4~\mathrm{N}$ and $dx = 0.01~\mathrm{m}$, then @@ -36,7 +36,7 @@ The total work can be calculated integrating $dW$ following the trajectory of th $$ W = \int_s dW = \int_s \vec{F}(x,y,z) \cdot \vec{ds} -$$ +$$ (eq:work-integrated-work) ```{admonition} Example: work in Earth's gravity field Consider a spacecraft of mass $m$ moving from Earth's surface to a circular orbit at radius $r_o$. Earth's gravitational force is radial: diff --git a/book/_toc.yml b/book/_toc.yml index 78ed671..78dcd21 100644 --- a/book/_toc.yml +++ b/book/_toc.yml @@ -18,9 +18,11 @@ parts: chapters: - file: 2_potential_fields/intro.md sections: + - file: 2_potential_fields/newtons_principia.md - file: 2_potential_fields/fundamentals.md - file: 2_potential_fields/work.md - file: 2_potential_fields/conservative_fields.md + - file: 2_potential_fields/potential.md - file: 2_potential_fields/earth_gravity_work.ipynb # - file: 2_potential_fields/gradient_fields.md # - file: 2_potential_fields/divergence_free_fields.md diff --git a/book/references.bib b/book/references.bib index 297951a..108dd25 100644 --- a/book/references.bib +++ b/book/references.bib @@ -11,4 +11,6 @@ @misc{template url = {https://github.com/TeachBooks/template}, year = {2024}, note = {Retrieved December, 2024. CC BY 4.0.} -} \ No newline at end of file +} + + @article{Buchwald_Fox, title={Oxford Handbook for the History of Physics}, author={Buchwald, Jed and Fox, Robert}, language={en} } From 2f80e6c956b2ce6a174d51d8e51a1b53efef4c26 Mon Sep 17 00:00:00 2001 From: Paco Lopez-Dekker Date: Tue, 25 Aug 2026 17:53:49 +0200 Subject: [PATCH 06/11] introduced notion of inverse problem --- book/2_potential_fields/newtons_principia.md | 20 ++++++++++++++++++-- 1 file changed, 18 insertions(+), 2 deletions(-) diff --git a/book/2_potential_fields/newtons_principia.md b/book/2_potential_fields/newtons_principia.md index 7c50b60..25d3480 100644 --- a/book/2_potential_fields/newtons_principia.md +++ b/book/2_potential_fields/newtons_principia.md @@ -71,9 +71,25 @@ $$ = -Gm \int_V \rho(\vec{r'}) \frac{\vec{r}-\vec{r'}}{|\vec{r}-\vec{r'}|^3}\,dV'. +$$ (eq:extemded-body-gravity-force) + +Each element pulls the test mass toward $\vec{r'}$. The integral appears straightforward, but evaluating it directly for every point outside an extended body can be a substantial calculation. We will come back to the problem described by Equation {eq}`eq:extended-body-gravity-force` later in the course. + +Dividing by the mass $m$ of the object being pulled by the Earth gives us a relation between the mass distribution of the Earth, $\rho(\vec{r'})$, and the gravitational vector field, $\vec{g}(\vec{r})$. This is an example of a **forward problem**: + +$$ +\rho(\vec{r'}) \quad \longrightarrow \quad \vec{g}(\vec{r}). +$$ + +Given a distribution of mass, we calculate the gravity field that it produces. In Earth science, however, we are often interested in the opposite direction. We can measure the gravity field, while the distribution of mass inside the Earth is not directly observable from those measurements. This leads to the **inverse problem**: + +$$ +\vec{g}(\vec{r}) \quad \longrightarrow \quad \rho(\vec{r'}). $$ -Each element pulls the test mass toward $\vec{r'}$. The integral appears straightforward, but evaluating it directly for every point outside a sphere would be a substantial calculation. +This direction is considerably more difficult. In general, many — if not most — inverse problems do not have a unique solution: different distributions of mass may produce the same observations. + + ```{admonition} Reading the mathematics :class: tip @@ -111,7 +127,7 @@ Try to read this new expression as a sentence: Hint: introduce $\vec{R}=\vec{r}-\vec{r'}$ and compare the resulting expression directly with the point-mass force above. The goal is not only to manipulate the expression, but to read it as a compact description of the geometry and physics. ``` -This was not merely a modern technical detail. The inverse-square law describes attraction between point masses, but the Earth, Moon, Sun, and planets are extended bodies. Newton therefore had to establish how a spherical distribution of matter attracts another body before he could apply the point-mass law to planetary motion. +This was not merely a modern technical detail. The inverse-square law describes attraction between point masses, but the Earth, Moon, Sun, and planets are extended bodies. To apply his theory of gravitational attraction to real celestial bodies, Newton therefore had to determine how the attraction of an extended spherical body relates to the inverse-square law for individual particles. In Book I, Section XII of the *Principia*, entitled *Of the attractive forces of spherical bodies*, Newton begins with a thin, uniform spherical shell and proves two remarkable results. From 40acf04506bf892af05f2073d385cecfc5d08949 Mon Sep 17 00:00:00 2001 From: Paco Lopez-Dekker Date: Tue, 25 Aug 2026 17:56:00 +0200 Subject: [PATCH 07/11] typo corrected --- book/2_potential_fields/newtons_principia.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/book/2_potential_fields/newtons_principia.md b/book/2_potential_fields/newtons_principia.md index 25d3480..b4978d6 100644 --- a/book/2_potential_fields/newtons_principia.md +++ b/book/2_potential_fields/newtons_principia.md @@ -71,7 +71,7 @@ $$ = -Gm \int_V \rho(\vec{r'}) \frac{\vec{r}-\vec{r'}}{|\vec{r}-\vec{r'}|^3}\,dV'. -$$ (eq:extemded-body-gravity-force) +$$ (eq:extended-body-gravity-force) Each element pulls the test mass toward $\vec{r'}$. The integral appears straightforward, but evaluating it directly for every point outside an extended body can be a substantial calculation. We will come back to the problem described by Equation {eq}`eq:extended-body-gravity-force` later in the course. From d187e25e83e7c74c9dade35af9f7603e7eab189f Mon Sep 17 00:00:00 2001 From: Paco Lopez-Dekker Date: Tue, 25 Aug 2026 18:57:46 +0200 Subject: [PATCH 08/11] added section illustrating gravity field of a thick shell with a couple of point-mass disturbances --- .../figures/spherical_shell_disturbance.png | Bin 0 -> 567427 bytes .../figures/spherical_shell_field.png | Bin 0 -> 291503 bytes book/2_potential_fields/newtons_principia.md | 48 +- .../spherical_shell_gravity.ipynb | 1139 +++++++++++++++++ book/_toc.yml | 1 + requirements.txt | 2 + 6 files changed, 1188 insertions(+), 2 deletions(-) create mode 100644 book/2_potential_fields/figures/spherical_shell_disturbance.png create mode 100644 book/2_potential_fields/figures/spherical_shell_field.png create mode 100644 book/2_potential_fields/spherical_shell_gravity.ipynb diff --git a/book/2_potential_fields/figures/spherical_shell_disturbance.png b/book/2_potential_fields/figures/spherical_shell_disturbance.png new file mode 100644 index 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