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diff --git a/Elements_of_Electromagnetics/chapter_4.ipynb b/Elements_of_Electromagnetics/chapter_4.ipynb new file mode 100644 index 00000000..14ac4af2 --- /dev/null +++ b/Elements_of_Electromagnetics/chapter_4.ipynb @@ -0,0 +1,699 @@ +{
+ "metadata": {
+ "name": "chapter_4.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h1>Chapter 4: Electrostatic Fields<h1>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 4.1, Page number: 107<h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Point charges 1 mC and -2 mC are located at (3,2,-1) and (-1,-1,4),\n",
+ "respectively. Calculate the electric force on a 10 nC charge located\n",
+ "at (0,3,1) and the electric field intensity at that point. '''\n",
+ "\n",
+ "import scipy\n",
+ "from numpy import *\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "ax=array([1,0,0]) #Unit vector along x direction\n",
+ "ay=array([0,1,0]) #Unit vector along y direction\n",
+ "az=array([0,0,1]) #Unit vector along z direction\n",
+ "Q1=1*10**-3 #charge 1 at (-1,-1,4) in C\n",
+ "Q2=-2*10**-3 #charge 2 at (3,2,-1) in C\n",
+ "Q=10*10**-9 #charge 3 at (0,3,1) in C\n",
+ "P1=array([0,3,1])-array([3,2,-1]) #distance vector from charge 3 to 1\n",
+ "P2=array([0,3,1])-array([-1,-1,4]) #distance vector from charge 3 to 2\n",
+ "e=10**-9/(36*scipy.pi) #permittivity in Farad/m \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "modP1=scipy.sqrt(dot(P1,P1))\n",
+ "modP2=scipy.sqrt(dot(P2,P2))\n",
+ "F1=(Q*Q1)*P1*10**3/(4*scipy.pi*e*modP1**3) #force on charge 3 by 1 in mN\n",
+ "F2=(Q*Q2)*P2*10**3/(4*scipy.pi*e*modP2**3) #force on charge 3 by 2 in mN\n",
+ "\n",
+ " #Total force on charge 3\n",
+ " \n",
+ "Fx=round(dot(F1+F2,ax),3)\n",
+ "Fy=round(dot(F1+F2,ay),3)\n",
+ "Fz=round(dot(F1+F2,az),3)\n",
+ "F=array([Fx,Fy,Fz]) #Total force in mN\n",
+ "E=(10**-6)*(F/Q) #Electric field in kV/m\n",
+ "\n",
+ "#Results \n",
+ "\n",
+ "print 'Total force on charge at (0,3,1) =',F,'in mN'\n",
+ "print 'Electric field at (0,3,1) =',E,'kV/m'"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total force on charge at (0,3,1) = [-6.512 -3.713 7.509] in mN\n",
+ "Electric field at (0,3,1) = [-651.2 -371.3 750.9] kV/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 4.3, Page number: 109"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "A practical application of electrostatics is in electrostatic separation of solids. For example, \n",
+ "Florida phosphate ore, consisting of small panicles of quartz and phosphate rock, can be \n",
+ "separated into its components by applying a uniform electric field as in Figure 4.4. Assum- \n",
+ "ing zero initial velocity and displacement, determine the separation between the particles \n",
+ "after falling 80 cm. Take E = 500 kV/m and Q/m = 9 microC/kg for both positively and neg- \n",
+ "atively charged particles. '''\n",
+ "\n",
+ "import scipy\n",
+ "#Variable Declaration\n",
+ "\n",
+ "E=500*10**3 #electric field in V/m\n",
+ "Qm=9*10**-6 #Q/m in C/kg\n",
+ "y=0.8 #distance fallen in m\n",
+ "g=9.8 #acceleration due to gravity in m/s^2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "t=scipy.sqrt(2*y/g) #time taken to fall in seconds\n",
+ "x=Qm*E*t**2/2 #half the separation between particles in m\n",
+ "sep=2*x #separation between particles in m\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print 'The separation between particles is',round(sep*100,2),'cm'\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The separation between particles is 73.47 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 4.5, Page number: 120"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "The finite sheet 0 <= x <= 1, 0 <= y <= 1 on the z = 0 plane has a charge density \n",
+ "Ps=xy(x^2 + y^2 + 25)^3/2 nC/m^2 . Find \n",
+ "\u001f\u001d",
+ "(a) The total charge on the sheet \n",
+ "(b) The e1ectric field at (0, 0, 5) \n",
+ "(c) The force experienced by a -1 mC charge located at (0, 0, 5) '''\n",
+ "\n",
+ "import scipy\n",
+ "import scipy.integrate\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "Eo=10**-9/(36*scipy.pi) #permittivity of free space\n",
+ "ax=array([1,0,0]) #Unit vector along x direction\n",
+ "ay=array([0,1,0]) #Unit vector along y direction\n",
+ "az=array([0,0,1]) #Unit vector along z direction\n",
+ "q=-1 #charge in mC\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "def charge(x,y): \n",
+ " return x*y*(x**2+y**2+25)**(1.5)\n",
+ "Q, errq = scipy.integrate.dblquad(lambda y , x: charge(x,y), #total charge in nC\n",
+ " 0, 1, lambda y: 0, lambda y: 1) \n",
+ "\n",
+ "d=(4*scipy.pi*Eo*(x**2+y**2+25)**(1.5))\n",
+ "\n",
+ "def elecx(x,y): \n",
+ " return 10**-9*x*y*(x**2+y**2+25)**(1.5)*(-x)/d #x component of electric field\n",
+ "Ex, errx = scipy.integrate.dblquad(lambda y , x: elecx(x,y), \n",
+ " 0, 1, lambda y: 0, lambda y: 1) \n",
+ "\n",
+ "def elecy(x,y): \n",
+ " return 10**-9*x*y*(x**2+y**2+25)**(1.5)*(-y)/d #y component of electric field\n",
+ "Ey, erry = scipy.integrate.dblquad(lambda y , x: elecy(x,y), \n",
+ " 0, 1, lambda y: 0, lambda y: 1) \n",
+ "\n",
+ "def elecz(x,y): \n",
+ " return 10**-9*x*y*(5)/(4*scipy.pi*Eo) #z component of electric field\n",
+ "Ez, errz = scipy.integrate.dblquad(lambda y , x: elecz(x,y), \n",
+ " 0, 1, lambda y: 0, lambda y: 1) \n",
+ "\n",
+ "E=array([round(Ex,1),round(Ey,1),round(Ez,2)]) #electric field in V/m\n",
+ "\n",
+ "F=q*E #force in mN \n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print 'Total charge =',round(Q,2),'nC'\n",
+ "print 'Electric field at (0,0,5) =',E,'V/m'\n",
+ "print 'Force experienced by -1mC =',F,'mN'"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total charge = 33.15 nC\n",
+ "Electric field at (0,0,5) = [ -1.5 -1.5 11.25] V/m\n",
+ "Force experienced by -1mC = [ 1.5 1.5 -11.25] mN\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 4.6, Page number: 121<h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Planes x=2 and y=-3, respectively, carry charges 10 nC/m^2 and 15 nC/m^2 .\n",
+ "If the line x=0, z=2 carries charge 10 pi nC/m, calculate E at (1,1,-1)\n",
+ "due to the three charge distributions. '''\n",
+ "\n",
+ "import scipy\n",
+ "from numpy import *\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "ax=array([1,0,0]) #Unit vector along x direction\n",
+ "ay=array([0,1,0]) #Unit vector along y direction\n",
+ "az=array([0,0,1]) #Unit vector along z direction\n",
+ "ps1=10*10**-9 #Surface charge density of plane 1\n",
+ "ps2=15*10**-9 #Surface charge density of plane 2\n",
+ "pl=10*scipy.pi*10**-9 #charge density of line\n",
+ "e=(10**-9)/(36*scipy.pi) #permittivity of free space in Farad/m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "E1=(ps1/(2*e))*-ax/scipy.pi #field due to plane 1 in multiples of pi in V/m\n",
+ "E2=(ps2/(2*e))*ay/scipy.pi #field due to plane 2 in multiples of pi in V/m\n",
+ "\n",
+ " #field due to line charge in multiples of pi in V/m\n",
+ " \n",
+ "a=(ax-3*az) \n",
+ "moda=scipy.sqrt(dot((ax-3*az),(ax-3*az)))\n",
+ "e3=(pl/(2*scipy.pi*e*moda**2))*a\n",
+ "E3=array([dot(e3,ax)/scipy.pi,0,dot(e3,az)/scipy.pi])\n",
+ "\n",
+ " #total field in multiples of pi in V/m\n",
+ " \n",
+ "E=E1+E2+E3 \n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print 'The total electric field at (1,1,-1) =',E,'Pi V/m'"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The total electric field at (1,1,-1) = [-162. 270. -54.] Pi V/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 4.7, Page number: 123<h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Determine D at (4, 0, 3) if there is a point charge - 5pi mC\n",
+ "at (4, 0, 0) and a line charge 3pi mC/m along the y-axis. '''\n",
+ "\n",
+ "import scipy\n",
+ "from numpy import *\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "ax=array([1,0,0]) #Unit vector along x direction\n",
+ "ay=array([0,1,0]) #Unit vector along y direction\n",
+ "az=array([0,0,1]) #Unit vector along z direction\n",
+ "Q=-5*scipy.pi*10**-3 #charge at (4,0,0) in C\n",
+ "pl=3*scipy.pi*10**-3 #charge density of line charge in C/m\n",
+ "r=array([4,0,3]) #point where D is to be found \n",
+ "rp=array([4,0,0]) #position of point charge\n",
+ "\n",
+ "#Calculations \n",
+ "\n",
+ "R=r-rp \n",
+ "modR=scipy.sqrt(dot(R,R)) \n",
+ "Dq=(Q*R)/(4*scipy.pi*modR**3) #flux density due to point charge in C/m^2\n",
+ "p=scipy.sqrt(dot(r,r))\n",
+ "ap=r/p \n",
+ "Dl=(pl/(2*scipy.pi*p))*ap #flux density due to line charge in C/m^2\n",
+ "D=(Dq+Dl)*10**6 #total flux density in micro C/m^2\n",
+ "Dz=round(dot(D,az),0)\n",
+ "Dx=round(dot(D,ax),0)\n",
+ "Dy=round(dot(D,ay),0)\n",
+ "Dround=array([Dx,Dy,Dz]) #value of D rounded to 0 decimal points\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print 'D at (4,0,0) due to point charge and line charge =',Dround,'micro C/m^2'\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "D at (4,0,0) due to point charge and line charge = [ 240. 0. 41.] micro C/m^2\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 4.8, Page number: 130<h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Given that D = zp cos^2(phi) a_z C/m^2 , calculate the charge density \n",
+ "at (1,pi/4, 3) and the total charge enclosed by the cylinder of \n",
+ "radius 1 m with -2< Z <2 m. '''\n",
+ "\n",
+ "import scipy\n",
+ "from numpy import *\n",
+ "import scipy.integrate\n",
+ "from fractions import Fraction\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "ap=array([1,0,0]) #Unit vector along rho direction\n",
+ "aph=array([0,1,0]) #Unit vector along phi direction\n",
+ "az=array([0,0,1]) #Unit vector along z direction\n",
+ "point=array([1,scipy.pi/4,3])\n",
+ "p1=0\n",
+ "p2=1\n",
+ "ph1=0\n",
+ "ph2=2*scipy.pi\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "pointp=dot(point,ap)\n",
+ "pointph=dot(point,aph)\n",
+ "pv=pointp*scipy.cos(pointph)**2 #charge density at (1,pi/4,3) in C/m^3\n",
+ "\n",
+ "def ctop(phi,p): \n",
+ " return 2*p**2*(scipy.cos(phi)**2)\n",
+ "psya, erra = scipy.integrate.dblquad(lambda p , phi: ctop(phi,p), \n",
+ " ph1, ph2, lambda p: p1, lambda p: p2)\n",
+ "\n",
+ "def cbot(phi,p): \n",
+ " return 2*p**2*(scipy.cos(phi)**2)\n",
+ "psyb, errb = scipy.integrate.dblquad(lambda p , phi: cbot(phi,p), \n",
+ " ph1, ph2, lambda p: p1, lambda p: p2)\n",
+ " \n",
+ "psy=psya+psyb #Charge in C\n",
+ "psyp=psy/scipy.pi #Charge in multiples of Pi in C\n",
+ "psyf=Fraction(psyp).limit_denominator(100) #converting to fraction\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print 'Charge density at (1,pi/4,3) =',pv,'C/m^3'\n",
+ "print 'Total charge enclosed by the cylinder =',psyf,'Pi C'"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Charge density at (1,pi/4,3) = 0.5 C/m^3\n",
+ "Total charge enclosed by the cylinder = 4/3 Pi C\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 4.10, Page number: 136<h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Two point charges -4 micro C and 5 micro C are located at (2, -1, 3) \n",
+ "and (0, 4, -2), respectively. Find the potential at (1, 0, 1) \n",
+ "assuming zero potential at infinity. '''\n",
+ "\n",
+ "import scipy\n",
+ "from numpy import *\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "Q1=-4 #charge 1 in micro C\n",
+ "Q2=5 #charge 2 in micro C\n",
+ "e=10**-9/(36*scipy.pi) #permittivity of free space in Farad/m \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "R1=array([1,0,1])-array([2,-1,3]) #distance vector from (1,0,1) to charge 1\n",
+ "R2=array([1,0,1])-array([0,4,-2]) #distance vector from (1,0,1) to charge 2\n",
+ "modR1=scipy.sqrt(dot(R1,R1))\n",
+ "modR2=scipy.sqrt(dot(R2,R2)) \n",
+ "V=10**-9*((Q1/modR1)+(Q2/modR2))/(4*scipy.pi*e) #potential in kV\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print 'The potential at (1, 0, 1) =',round(V,3),'kV'\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The potential at (1, 0, 1) = -5.872 kV\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 4.11, Page number: 136"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "A point charge 5 nC is located at (-3, 4, 0) while line y = 1, z = 1 carries uniform charge \n",
+ "2 nC/m. \n",
+ "\u001f\u001d",
+ "(a) If V = 0V at O(0, 0, 0), find V at A(5, 0, ]). \n",
+ "(b) If V = 100V at B(1, 2, 1), find V at C(-2, 5, 3). \n",
+ "(c) If V = -5V at O, find V_BC '''\n",
+ "\n",
+ "import scipy\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "Eo=10**-9/(36*scipy.pi) #permittivity of free space\n",
+ "Vo=0 #potential at O in V\n",
+ "Vb=100 #potential at B in V\n",
+ "po=scipy.sqrt(2)\n",
+ "ro=5\n",
+ "pa=1\n",
+ "ra=9\n",
+ "pb=1\n",
+ "rb=scipy.sqrt(21)\n",
+ "pc=scipy.sqrt(20)\n",
+ "rc=scipy.sqrt(11)\n",
+ "pl=2*10**-9 #charge density of the line in C/m\n",
+ "Q=5*10**-9 #point charge at (-3,4,0) in C\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "Va=Vo-(-pl*scipy.log(po/pa)/(2*scipy.pi*Eo)+Q*(ra-ro)/(4*scipy.pi*Eo*ra*ro))\n",
+ "Vc=Vb+(-pl*scipy.log(pc/pb)/(2*scipy.pi*Eo)+Q*(rb-rc)/(4*scipy.pi*Eo*rb*rc))\n",
+ "Vbc=Vc-Vb\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print 'Va =',round(Va,3),'V'\n",
+ "print 'Vc =',round(Vc,3),'V'\n",
+ "print 'Vbc =',round(Vbc,3),'V'"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Va = 8.477 V\n",
+ "Vc = 49.825 V\n",
+ "Vbc = -50.175 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 4.12, Page number: 140<h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Given the potential V = (10/r**2)sin(theta)cos(phi), \n",
+ "(a) Find the electric flux density D at (2, pi/2, 0). \n",
+ "(b) Calculate the work done in moving a 10 micro C charge from \n",
+ "point A( 1, 30\u00b0, 120\u00b0) to B( 4, 90\u00b0, 60\u00b0). '''\n",
+ "\n",
+ "import scipy\n",
+ "from numpy import *\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "ar=array([1,0,0]) #Unit vector along radial direction\n",
+ "ath=array([0,1,0]) #Unit vector along theta direction\n",
+ "aph=array([0,0,1]) #Unit vector along phi direction\n",
+ "e=(10**-9)/(36*scipy.pi) #permittivity of free space in Farad/m\n",
+ "\n",
+ " #The point (2, pi/2, 0)\n",
+ "r=2\n",
+ "th=scipy.pi/2\n",
+ "ph=0\n",
+ " #Point A\n",
+ "ra=1\n",
+ "tha=scipy.pi*30/180\n",
+ "pha=scipy.pi*120/180\n",
+ " #Point B\n",
+ "rb=4\n",
+ "thb=scipy.pi/2\n",
+ "phb=scipy.pi*60/180\n",
+ "\n",
+ "q=10*10**-6 \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "Er=(20.0/r**3)*scipy.sin(th)*scipy.cos(ph) #Radial component of E in V/m\n",
+ "Eth=-(10/r**3)*scipy.cos(th)*scipy.cos(ph) #Theta component of E in V/m\n",
+ "Eph=(10/r**3)*scipy.sin(ph) #Phi component of E in V/m\n",
+ "E=array([Er,Eth,Eph])\n",
+ "D=E*e*10**12 #Electric flux density D in pC/m^2\n",
+ "Dr=round(dot(D,ar),1) #Radial component of D in V/m rounded to 1 decimal\n",
+ "Dth=round(dot(D,ath),0) #Theta component of D in pC/m^2 rounded to 0 decimal\n",
+ "Dph=round(dot(D,aph),0) #Phi component of D in pC/m^2 rounded to 0 decimal\n",
+ "Dc=array([Dr,Dth,Dph]) #Rounded D in pC/m^2\n",
+ "\n",
+ "Va=10*scipy.sin(tha)*cos(pha)/ra**2 #potential at point A in V\n",
+ "Vb=10*scipy.sin(thb)*cos(phb)/rb**2 #potential at point B in V\n",
+ "W=q*(Vb-Va)*10**6 #work done in micro J\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print 'The electric flux density D at (2, pi/2, 0) =',Dc,'pC/m^2'\n",
+ "print 'Work done in moving the charge =',W,'micro J'\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The electric flux density D at (2, pi/2, 0) = [ 22.1 -0. 0. ] pC/m^2\n",
+ "Work done in moving the charge = 28.125 micro J\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 4.13, Page number: 145<h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Two dipoles with dipole moments -5 a_z nC/m and 9 a_z nC/m are\n",
+ "located at points (0,0,-2) and (0,0,3), respectively.\n",
+ "Find the potential at the origin. '''\n",
+ "\n",
+ "import scipy\n",
+ "from numpy import *\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "p1=-5*10**-9 #dipole moment of dipole 1 in C/m\n",
+ "p2=9*10**-9 #dipole moment of dipole 2 in C/m\n",
+ "z1=2 #z component of position vector of dipole 1\n",
+ "z2=-3 #z component of position vector of dipole 2\n",
+ "e=10**-9/(36*scipy.pi) #permittivity of free space in Farad/m\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "V=(1/(4*scipy.pi*e))*((p1*abs(z1)/z1**3)+(p2*abs(z2)/z2**3))\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print 'Potential at origin =',V, 'V'\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Potential at origin = -20.25 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h3>Example 4.14, Page number: 148<h3>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "'''\n",
+ "Three point charges - 1 nC, 4 nC, and 3 nC are located at (0, 0, 0), \n",
+ "(0, 0, 1), and (1, 0, 0), respectively. Find the energy in the system. '''\n",
+ "\n",
+ "import scipy\n",
+ "from numpy import *\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "Q1=-1*10**-9 #Charge 1 in C\n",
+ "Q2=4*10**-9 #Charge 2 in C\n",
+ "Q3=3*10**-9 #Charge 3 in C\n",
+ "e=10**-9/(36*scipy.pi) #permittivity of free space in farad/m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "V1=(1/(4*scipy.pi*e)*(Q2+Q3))\n",
+ "V2=(1/(4*scipy.pi*e)*(Q1+Q3/(2**.5)))\n",
+ "V3=(1/(4*scipy.pi*e)*(Q1+Q2/(2**.5)))\n",
+ "W=0.5*((V1*Q1)+(V2*Q2)+(V3*Q3))*10**9 #Energy in nJ\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print 'Energy in the system =',round(W,2),'nJ'"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Energy in the system = 13.37 nJ\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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