{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "name": "VectorPlot.ipynb", "provenance": [], "collapsed_sections": [] }, "language_info": { "name": "python" }, "kernelspec": { "name": "python3", "display_name": "Python 3" } }, "cells": [ { "cell_type": "markdown", "source": [ "#Making Vector Field Plots with Python" ], "metadata": { "id": "q43p7oDmcomA" } }, { "cell_type": "markdown", "source": [ "Making a 2-D vector field (or “quiver”) plot is somewhat similar to making a contour plot because the vectors must be calculated on a grid. This type of plot is most useful when the vectors do not have a third component. \n", "The first step is to find the Cartesian components of the field to be plotted. The example program will plot the magnetic field of a long wire along z axis carrying a current of I = 50 A in the +z direction. In cylindrical coordinates, the magnetic field is \n", "\n", "$$ \\vec{B} = \\frac{\\mu_0 I}{2\\pi s}\\hat{\\theta}, $$ \n", "where s is the distance from the wire and $\\mu_0 I/2\\pi = 1 \\rm{\\ mT\\cdot cm}$. If distances are in centimeters, the magnetic field is in mT." ], "metadata": { "id": "WHVsOQ8ucomB" } }, { "cell_type": "markdown", "source": [ "
" ], "metadata": { "id": "jNofvoH7dvOJ" } }, { "cell_type": "markdown", "source": [ "From the diagram above, the Cartesian components are \n", "\n", "$$\n", "\\vec{B} = \\frac{\\mu_0 I}{2\\pi s}\\left(-\\sin\\theta\\hat{x}+\\cos\\theta\\hat{y}\\right)\n", "= \\frac{\\mu_0 I}{2\\pi}\\frac{1}{s}\\left(-\\frac{y}{s}\\hat{x}+\\frac{x}{s}\\hat{y}\\right)\n", "= \\frac{\\mu_0 I}{2\\pi}\\left(-\\frac{y}{s^2}\\hat{x}+\\frac{x}{s^2}\\hat{y}\\right),\n", "$$ \n", "where $s^2=x^2+y^2$. \n", " \n", "The meshgrid command is used to make the two grids where **`X`** and **`Y`** which contain the x and y coordinates for each point. Two additional grids (called **`Bx`** and **`By`** in the example program) are filled with the values of the x and y components of the vector. \n", " \n", "The **`quiver`** command from the pylab library makes the 2-D vector field plot, which is assigned the name **`QP`** in the example program below. \n", " \n", "The **`quiverkey`** command adds a “key” which shows the scale for the lengths of the vectors in the plot. The first argument (**`QP`**) is the name of the plot. The second and third arguments give the position of the key in the horizontal and vertical directions from the lower, right corner as fractions of the size of the plot. The “1.1” places the key above the plot, which makes it easier to see. The fourth and fifth arguments are the length of the vector and its text label. The final argument is for the placement of the label (**`N`** = above, **`S`** = below, **`W`** = left, and **`E`** = right). \n", " \n", "The **`axis`** command is used to set the left, right, bottom, and top limits (in that order) of the axes. It helps to extend the axes beyond the limits of the grid to make room for the vectors near the edges." ], "metadata": { "id": "OSjvfMW4comF" } }, { "cell_type": "code", "source": [ "import pylab as pl\n", "# Set limits and number of points in grid\n", "xmax = 2.0\n", "xmin = -xmax\n", "NX = 10\n", "ymax = 2.0\n", "ymin = -ymax\n", "NY = 10\n", "# Make grid and calculate vector components\n", "x = pl.linspace(xmin, xmax, NX)\n", "y = pl.linspace(ymin, ymax, NY)\n", "X, Y = pl.meshgrid(x, y)\n", "S2 = X**2 + Y**2 # This is the radius squared\n", "Bx = -Y/S2\n", "By = +X/S2\n", "pl.figure()\n", "QP = pl.quiver(X,Y,Bx,By)\n", "pl.quiverkey(QP, 0.85, 1.02, 1.0, '1 mT', labelpos='N')\n", "# Set the left, right, bottom, top limits of axes\n", "dx = (xmax - xmin)/(NX - 1) # One less gap than points\n", "dy = (ymax - ymin)/(NY - 1)\n", "pl.axis([xmin-dx, xmax+dx, ymin-dy, ymax+dy])\n", "pl.title('Magnetic Field of a Wire')\n", "pl.xlabel('x (cm)')\n", "pl.ylabel('y (cm)')\n", "pl.show()" ], "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": { "needs_background": "light" } } ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 295 }, "id": "goco8SBJcomH", "outputId": "b0b8b40a-2610-47b5-dcac-2c792a519074" }, "execution_count": 1 }, { "cell_type": "markdown", "source": [ "##Additional Documentation" ], "metadata": { "id": "y00h7LZccomI" } }, { "cell_type": "markdown", "source": [ "https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.quiver.html" ], "metadata": { "id": "P4aLOjnkcomJ" } } ] }