{ "metadata": { "name": "", "signature": "sha256:3a0360df3c22e5e4c6f88ae6f9ab32945c496822bb8898446d53149d9f1116ec" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Chapter 8: Magnetic Forces, Materials and Devices

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 8.1, Page number: 308

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import scipy\n", "from numpy import *\n", "\n", "#Variable Declaration\n", "\n", "m=2 #mass in kg\n", "q=3 #charge in C\n", "v=array([4,0,3]) #initial velocity in m/s\n", "E=array([12,10,0]) #electric field in V/m\n", "t=1 #time in sec\n", "\n", "#Calculations\n", "\n", "a=q*E/m #acceleration in m/s^2 after 1 sec\n", "u=array([18*t+4,15*t,3]) #velocity in m/s after 1 sec\n", "modofu=scipy.sqrt(dot(u,u))\n", "KE=0.5*m*(modofu)**2 #kinetic energy in J at t=1 sec\n", "s=array([9*t**2+4*t+1,7.5*t**2-2,3*t]) #position after 1 sec in m\n", "\n", "#Results\n", "\n", "print 'At time t=1 sec,'\n", "print' The acceleration of the particle =',a,'m/s^2'\n", "print 'Its velocity =',u,'m/s' \n", "print 'Its kinetic energy =',KE,'J'\n", "print 'Its position =',s,'m'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "At time t=1 sec,\n", " The acceleration of the particle = [18 15 0] m/s^2\n", "Its velocity = [22 15 3] m/s\n", "Its kinetic energy = 718.0 J\n", "Its position = [ 14. 5.5 3. ] m\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 8.6, Page number: 322" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "\n", "import scipy\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", "x=4\n", "y=-3\n", "z=10\n", "muo=4*scipy.pi*10**-7 #permeability of free space\n", "m1=5 #magnetic moment in A/m^2\n", "\n", "#Calculations\n", "\n", "r=scipy.sqrt(x**2+y**2+z**2)\n", "p=scipy.sqrt(x**2+y**2)\n", "sinphi=y/p\n", "cosphi=x/p\n", "sintheta=1/scipy.sqrt(5)\n", "costheta=2/scipy.sqrt(5)\n", "B1=muo*m1*(2*costheta*ar+sintheta*ath)/(4*scipy.pi*r**3)\n", "m2=3*(sintheta*sinphi*ar+costheta*sinphi*ath+cosphi*aph)\n", "T2=cross(m2,B1)*10**9\n", "T2x=round(dot(T2,ar),3)\n", "T2y=round(dot(T2,ath),3)\n", "T2z=round(dot(T2,aph),3)\n", "T2r=array([T2x,T2y,T2z]) #torque in nNm\n", "\n", "#Result\n", "\n", "print 'Torque T2 =',T2r,'nNm'\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Torque T2 = [-0.384 1.536 0.902]\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 8.7, Page number: 330" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import scipy\n", "\n", "#Variable Declaration\n", "\n", "muo=4*scipy.pi*10**-7 #permeability of free space\n", "mur=2 #relative permeability\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", "\n", "\n", "#Calculations\n", "\n", "J=(-5-10)*10**-6/(4*scipy.pi*10**-7*2.5) #in kA/m^2\n", "Jb=1.5*J #in kA/m^2\n", "MbyB=(1.5)*10**4/(4*scipy.pi*2.5) \n", "Mv=MbyB*10*10**-3*ax+MbyB*5*10**-3*ay\n", "Kb=cross(az,Mv)\n", "\n", "#Results\n", "\n", "print 'J =',round(J,3),'kA/m^2'\n", "print 'Jb =',round(Jb,3),'kA/m^2'\n", "print 'M =(',round(dot(Mv,ax),3),'y,',round(dot(Mv,ay),3),'x, 0) kA/m'\n", "print 'Kb =(',round(dot(Kb,ax),3),'x,',round(dot(Kb,ay),3),'y, 0) kA/m' \n", " \n", "\n", " \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "J = -4.775 kA/m^2\n", "Jb = -7.162 kA/m^2\n", "M =( 4.775 y, 2.387 x, 0) kA/m\n", "Kb =( -2.387 x, 4.775 y, 0) kA/m\n" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 8.8, Page number: 332

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \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", "H1=array([-2,6,4]) #in A/m\n", "mu0=4*scipy.pi*10**-7 #permeability of free space\n", "mur1=5 #relative permeabililty in region 1\n", "mur2=2 #relative permeabililty in region 2\n", "an=array([-1,1,0])/scipy.sqrt(2)\n", "\n", "#Calculatios\n", "\n", "mu1=mu0*mur1\n", "mu2=mu0*mur2\n", "M1=(mur1-1)*H1 # magnetisation in region 1 in A/m\n", "B1=mu1*H1*10**6 # field in micro Wb/m^2\n", "B1x=round(dot(B1,ax),2) # x component of B1\n", "B1y=round(dot(B1,ay),1) # y component of B1\n", "B1z=round(dot(B1,az),2) # z component of B1\n", "B1r=array([B1x,B1y,B1z]) # B1 rounded to 2 decimal places\n", "H1n=dot(H1,an)*an \n", "H1t=H1-H1n\n", "H2t=H1t # using transverse boundary condition\n", "H2n=(mu1/mu2)*H1n # using normal boundary condition\n", "H2=H2t+H2n # in A/m\n", "B2=mu2*H2*10**6 # field in micro Wb/m^2\n", "B2x=round(dot(B2,ax),2) # x component of B2\n", "B2y=round(dot(B2,ay),2) # y component of B2\n", "B2z=round(dot(B2,az),2) # z component of B2\n", "B2r=array([B2x,B2y,B2z]) # B2 rounded to 2 decimal places\n", "\n", "#Results\n", "\n", "print 'M1= ',M1,'A/m'\n", "print 'B1= ',B1r,'micro Wb/m^2'\n", "print 'H2= ',H2,'A/m'\n", "print 'B2= ',B2r,'micro Wb/m^2'\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "M1= [-8 24 16] A/m\n", "B1= [-12.57 37.7 25.13] micro Wb/m^2\n", "H2= [ -8. 12. 4.] A/m\n", "B2= [-20.11 30.16 10.05] micro Wb/m^2\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 8.14, Page number: 350

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import scipy\n", "from numpy import *\n", "\n", "#Variable declaration\n", "\n", "p=10*10**-2 #in m\n", "a=1*10**-2 #in m\n", "Ur=1000 #relative permeability\n", "Uo=4*scipy.pi*10**-7 #permeability of free space\n", "n=200 #number of turns\n", "phi=0.5*10**-3 #flux in the core in Wb\n", "U=Uo*Ur #permeability of steel core\n", "\n", "#Calculation\n", "\n", "I=phi*2*scipy.pi*p/(U*n*scipy.pi*a*a) #current in A\n", "\n", "#Result\n", "\n", "print 'The current that will produce a flux of 0.5 mWb =',round(I,3),'A'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The current that will produce a flux of 0.5 mWb = 3.979 A\n" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 8.15, Page number: 351

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "\n", "import scipy\n", "from numpy import *\n", "\n", "#Variable Declaration\n", "\n", "Uo=4*scipy.pi*10**-7 #permeability of free space\n", "Ur=50 #relative permeability of coil\n", "l1=30*10**-2\n", "s=10*10**-4 \n", "l3=9*10**-2\n", "la=1*10**-2 \n", "B=1.5 #flux density in Wb/m^2\n", "N=400 #number of turns\n", "\n", "#Calculations\n", "\n", "R1=l1/(Uo*Ur*s)\n", "R2=R1\n", "R3=l3/(Uo*Ur*s)\n", "Ra=la/(Uo*s)\n", "R=R1*R2/(R1+R2)\n", "Req=R3+Ra+R\n", "I=B*s*Req/N #current in A\n", "\n", "#Result\n", "\n", "print 'The current required =',round(I,3),'A'\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The current required = 44.165 A\n" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 8.16, Page number: 353

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "\n", "import scipy\n", "from numpy import *\n", "\n", "#Variable Declaration\n", "\n", "m=400 #mass in kg\n", "g=9.8 #acceleration due to gravity in m/s^2\n", "Ur=3000 #relative permeability of the iron yoke\n", "Uo=4*scipy.pi*10**-7 #permeability of free space\n", "S=40*10**-4 #cross sectional area of iron yoke in m^2\n", "la=1*10**-4 #air gaps in m\n", "li=50*10**-2 #mean length of yoke in m\n", "I=1 #excitation current in A \n", "\n", "#Calculations\n", "\n", "B=scipy.sqrt(m*g*Uo/S) #field in Wb/m^2\n", "Ra=2*la/(Uo*S) \n", "Ri=li/(Uo*Ur*S) \n", "N=(Ra+Ri)/(Ra*Uo)*B*la #number of turns\n", "\n", "#Result\n", "\n", "print 'The nmber of turns in the coil when the excitation current is 1 A ='\n", "print round(N,0)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The nmber of turns in the coil when the excitation current is 1 A =\n", "162.0\n" ] } ], "prompt_number": 5 } ], "metadata": {} } ] }