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authorThirumalesh-HS2015-12-20 19:15:22 +0530
committerThirumalesh-HS2015-12-20 19:15:22 +0530
commit731aaa62939d9a30493a43eb09298271d462b2d2 (patch)
treef07ddf2509988b995bb9000ee87c73f090023494
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Efield-due-to-point-charges
-rw-r--r--Physics_Textook_Part-I_for_class_XII_by_NCERT_by_Chief_Editor_-_Shveta_Uppal/Electric-field-lines-due-to-point-charges.ipynb117
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diff --git a/Physics_Textook_Part-I_for_class_XII_by_NCERT_by_Chief_Editor_-_Shveta_Uppal/Electric-field-lines-due-to-point-charges.ipynb b/Physics_Textook_Part-I_for_class_XII_by_NCERT_by_Chief_Editor_-_Shveta_Uppal/Electric-field-lines-due-to-point-charges.ipynb
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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Electric field lines due to point charges"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "### Code contributed by: Dr.Ajith Kumar"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Steps to run the file\n",
+ "* Find the line Charges (Value, x-cord, y-cord)\n",
+ "* Value indicates the charge type(+ve or -ve) and it's magnitude\n",
+ "* x-cord & y-cord indicates the position of the charge in 2D plane\n",
+ "* You may add or delete charges to the list `Q`. Choose charge type, it's magnitude and it's position in 2D plane\n",
+ "* For example: try adding `(-10, 3, 3)` to the list `Q` and run the file\n",
+ "* To change the color of the charge replace color-field 'r' in text function with 'k' for black, 'b' for blue, 'y' for yellow \n",
+ "* Similarly, you can change the color of field lines by changing color-field in streamplot function with appropriate color values"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Populating the interactive namespace from numpy and matplotlib\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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deqhWizJ9/jmklTp1INcMG0b0wQcIKMbGqoszZGfj+W3eTPTxx5BnunbFOT09Ua9duyJV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\nKIMBcZ7cXAzKPj5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VQhDws88s979yBUT+66941qNHi+tbK2LLFgjgt2/D7B43juXOWMAm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mw8r0cPBPR8fIzfRUdDsKxaBQvIx4fonXcghJYsQeDvzBm44nXrQtlWq4b3Vrbs051k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\nGcIILC8qV6YmnZvLlajqXg3q1uWYaN+ewnXmTL73s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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xa021cac>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Import pylab inline\n",
+ "%pylab inline\n",
+ "seterr(all='ignore') # ignore all floating point errors\n",
+ "\n",
+ "N = 101 # Number of points in x-coordinate and y-coordinate each\n",
+ "a, b = linspace(-5, 5, N), linspace(-5, 5, N) # Set evenly spaced points within the interval -5 and 5\n",
+ "xa, ya = meshgrid(a, b) # A meshgrid in the xy plane. xa contains the x-coordinates\n",
+ "Ex = zeros_like(xa) # 2D array to store the Ex and\n",
+ "Ey = zeros_like(ya) # Ey components\n",
+ "\n",
+ "Q = [(-15, 0, 3), (5, -2, -2), (5, 2, -2)] # Charges (Value, x-cord, y-cord)\n",
+ "\n",
+ "for q in Q: # mark charge locations\n",
+ " text(q[1], q[2], 'o', color = 'r', fontsize=15, va='center', ha='center')\n",
+ "\n",
+ "for i in range(N): # calculate Ex and Ey at each point in the grid, due to all charges\n",
+ " for j in range(N):\n",
+ " x, y = xa[i,j], ya[i,j]\n",
+ " for k in range(len(Q)): # sum over the charges, using equation from the text book\n",
+ " \n",
+ " Ex[i,j] += Q[k][0]*(x-Q[k][1])/ ((x-Q[k][1])**2+(y-Q[k][2])**2)**(1.5)\n",
+ " Ey[i,j] += Q[k][0]*(y-Q[k][2])/ ((x-Q[k][1])**2+(y-Q[k][2])**2)**(1.5)\n",
+ "\n",
+ "streamplot(xa, ya, Ex, Ey, color='b', density= 1.6) #plot the field lines using streamplot\n",
+ "show() # show the plot"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}