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| author | hardythe1 | 2015-07-03 12:23:43 +0530 |
|---|---|---|
| committer | hardythe1 | 2015-07-03 12:23:43 +0530 |
| commit | 5a86a20b9de487553d4ef88719fb0fd76a5dd6a7 (patch) | |
| tree | db67ac5738a18b921d9a8cf6e86f402703f30bdf /Engineering_Physics_by_Uma_Mukherji/Chapter9.ipynb | |
| parent | 37d315828bbfc0f5cabee669d2b9dd8cd17b5154 (diff) | |
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diff --git a/Engineering_Physics_by_Uma_Mukherji/Chapter9.ipynb b/Engineering_Physics_by_Uma_Mukherji/Chapter9.ipynb new file mode 100755 index 00000000..9aff9ae1 --- /dev/null +++ b/Engineering_Physics_by_Uma_Mukherji/Chapter9.ipynb @@ -0,0 +1,654 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:12b212fa69742f446e6918a565a72f52e2d9500de27031b4c21c41162a940ee1"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "9: Motion of the charged particle in electric and magnetic field"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.1, Page number 230"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=1.33*10**-22; #angular momentum(kg m**2/sec)\n",
+ "B=0.025; #magnetic field(Wb/m**2)\n",
+ "m=6.68*10**-27; #mass of alpha particle(kg)\n",
+ "q=3.2*10**-19; #charge of alpha particle(c)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "w=(B*q)/m; #angular velocity\n",
+ "E=0.5*L*w; #KE of particle(J)\n",
+ "E=E/e; #KE of particle(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"KE of particle is\",round(E,2),\"eV\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "KE of particle is 497.75 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.2, Page number 230"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "R=0.35; #radius of cyclotron(m)\n",
+ "n=1.38*10**7; #frequency(Hz)\n",
+ "m=1.67*10**-27; #mass of proton(kg)\n",
+ "q=1.6*10**-19; #charge of proton(c)\n",
+ "\n",
+ "#Calculation\n",
+ "B=(2*math.pi*n*m)/q; #magnetic field induction(Wb/m**2)\n",
+ "E=((B**2)*(q**2)*(R**2))/(2*m); #maximum energy of proton(J)\n",
+ "E=E/q; #maximum energy of proton(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"magnetic field induction is\",round(B,3),\"Wb/m**2\"\n",
+ "print \"maximum energy of proton is\",round(E/10**6,1),\"MeV\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "magnetic field induction is 0.905 Wb/m**2\n",
+ "maximum energy of proton is 4.8 MeV\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.3, Page number 231"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "m=9.1*10**-31; #mass of electron(kg)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "V=1000; #potential difference(V)\n",
+ "B=1.19*10**-3; #magnetic field of induction(Wb/m**2)\n",
+ "\n",
+ "#Calculation\n",
+ "#due to potential difference V, electron is accelerated\n",
+ "#eV=0.5*m*(v^2)\n",
+ "#due to transverse magnetic field B electron moves in circular path of radius R\n",
+ "#(m*(v^2))/R=BeV\n",
+ "v=math.sqrt((2*e*V)/m); #velocity(m/sec)\n",
+ "R=(m*v)/(B*e); #radius of electron trajectory(m)\n",
+ "L=m*v*R; #angular momentum(kg m**2/sec)\n",
+ "\n",
+ "#Result\n",
+ "print \"radius of electron trajectory is\",round(R*100,3),\"cm\"\n",
+ "print \"angular momentum of electron is\",round(L/10**-28,2),\"*10**-28 kg m**2/sec\"\n",
+ "print \"answer for angular momentum varies due to rounding off errors\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "radius of electron trajectory is 8.962 cm\n",
+ "angular momentum of electron is 15294.12 *10**-28 kg m**2/sec\n",
+ "answer for angular momentum varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.4, Page number 231"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "vx=1.7*10**7; #horizontal velociy(m/sec)\n",
+ "Ey=3.4*10**4; #electric field(V/m)\n",
+ "x=3*10**-2; #horizontal displacement(m)\n",
+ "m=9.1*10**-31; #mass of electron(kg)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "t=x/vx; #time(sec)\n",
+ "#y=0.5*ay*(t^2)\n",
+ "ay=(e*Ey)/m; #acceleration(m/sec**2)\n",
+ "y=0.5*ay*(t**2); #vertical displacement(m)\n",
+ "Bz=Ey/vx; #magnitude of magnetic field(Wb/m**2) \n",
+ "\n",
+ "#Result\n",
+ "print \"vertical displacement of electron is\",round(y*100,4),\"cm\"\n",
+ "print \"answer varies due to rounding off errors\"\n",
+ "print \"magnitude of magnetic field is\",Bz,\"Wb/m**2\"\n",
+ "print \"direction of field is upward as Ey is downward\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "vertical displacement of electron is 0.9308 cm\n",
+ "answer varies due to rounding off errors\n",
+ "magnitude of magnetic field is 0.002 Wb/m**2\n",
+ "direction of field is upward as Ey is downward\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.5, Page number 232"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "m=1.67*10**-27; #mass of proton(kg)\n",
+ "q=1.6*10**-19; #charge of proton(c)\n",
+ "B=0.5; #magnetic field(Wb/m**2)\n",
+ "R=1; #radius of cyclotron(m)\n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "n=((B*q)/(2*math.pi*m)); #frequency of oscillation voltage(Hz)\n",
+ "E=((B**2)*(q**2)*(R**2))/(2*m); #maximum energy of proton(J)\n",
+ "E=E/q; #maximum energy of proton(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"frequency of oscillation voltage is\",round(n/10**6,3),\"MHz\"\n",
+ "print \"maximum energy of proton is\",round(E/10**6,3),\"MeV\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "frequency of oscillation voltage is 7.624 MHz\n",
+ "maximum energy of proton is 11.976 MeV\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.6, Page number 232"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "q=3.2*10**-19 #charge of a9lpha particle(c)\n",
+ "m=6.68*10**-27; #mass(kg) \n",
+ "B=1.5; #magnetic field(Wb/m**2)\n",
+ "v=7.263*10**6; #velocity(m/s) \n",
+ "\n",
+ "#Calculation\n",
+ "F=B*q*v; #force on particle(N)\n",
+ "T=(2*math.pi*m)/(B*q); #periodic time(sec)\n",
+ "n=1/T; #resonance frequency(Hz)\n",
+ "\n",
+ "#Result\n",
+ "print \"force on particle is\",round(F*10**13,2),\"*10**-13 N\"\n",
+ "print \"periodic time is\",round(T*10**8,3),\"*10**-8 sec\"\n",
+ "print \"answer for periodic time varies due to rounding off errors\"\n",
+ "print \"resonance frequency is\",round(n/10**6,2),\"MHz\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "force on particle is 34.86 *10**-13 N\n",
+ "periodic time is 8.744 *10**-8 sec\n",
+ "answer for periodic time varies due to rounding off errors\n",
+ "resonance frequency is 11.44 MHz\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.7, Page number 233"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=1.2*10**7; #frequency(Hz)\n",
+ "mp=1.67*10**-27; #mass of proton(kg)\n",
+ "qp=1.6*10**-19; #charge of proton(c)\n",
+ "R=0.5; #radius(m)\n",
+ "malp=6.68*10**-27; #mass of alpha particle(kg)\n",
+ "\n",
+ "#Calculation\n",
+ "Bp=(2*math.pi*mp*n)/qp; #flux density for proton(Wb/m**2)\n",
+ "Ep=((Bp**2)*(qp**2)*(R**2))/(2*mp); #energy of proton(J)\n",
+ "Ep=Ep/qp; #energy of proton(eV)\n",
+ "qalp=2*qp; #charge of alpha particle(c)\n",
+ "Balp=(2*math.pi*malp*n)/qalp; #flux density of alpha particle(Wb/m**2)\n",
+ "Ealp=((Balp**2)*(qalp**2)*(R**2))/(2*malp); #energy of alpha particle(J)\n",
+ "Ealp=Ealp/qp; #energy of alpha particle(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"flux density for proton is\",round(Bp,5),\"Wb/m**2\"\n",
+ "print \"flux density for alpha particle is\",round(Balp,4),\"Wb/m**2\"\n",
+ "print \"energy of proton is\",round(Ep/10**6,2),\"MeV\"\n",
+ "print \"energy of alpha particle is\",round(Ealp/10**6,2),\"MeV\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "flux density for proton is 0.78697 Wb/m**2\n",
+ "flux density for alpha particle is 1.5739 Wb/m**2\n",
+ "energy of proton is 7.42 MeV\n",
+ "energy of alpha particle is 29.67 MeV\n"
+ ]
+ }
+ ],
+ "prompt_number": 42
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.8, Page number 233"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "e=1.6*10**-19; #charge of electron(c) \n",
+ "me=9.1*10**-31; #mass of electron(kg)\n",
+ "malp=6.68*10**-27; #mass of alpha particle(kg)\n",
+ "B=0.05; #magnetic field(Wb/m**2)\n",
+ "V=20*10**3; #potential difference(V)\n",
+ "\n",
+ "#Calculation\n",
+ "q=2*e; #charge of alpha particle(c)\n",
+ "#v=sqrt((2*q*V)/m)\n",
+ "#R=(1/B)*sqrt((2*m*V)/q)\n",
+ "Re=(1/B)*math.sqrt((2*me*V)/e); #radius of electron(m)\n",
+ "Ralp=(1/B)*math.sqrt((2*malp*V)/q); #radius of alpha particle(m)\n",
+ "S=2*Ralp-2*Re; #linear separation between two particles(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"linear separation between two particles on common boundary wall is\",round(S*100,1),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "linear separation between two particles on common boundary wall is 113.7 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 45
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.9, Page number 234"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "V1=200; #potential difference(V)\n",
+ "i=60; #angle(degrees)\n",
+ "r=45; #angle(degrees)\n",
+ "\n",
+ "#Calculation\n",
+ "#electrostatic focusing condition (sini/sinr)=(v2/v1)=sqrt(V2/V1)\n",
+ "#0.5mv2=eV\n",
+ "i=i*(math.pi/180); #angle(radian)\n",
+ "r=r*(math.pi/180); #angle(radian)\n",
+ "V2=V1*((math.sin(i)/math.sin(r))**2); #potential difference(V)\n",
+ "pd=V2-V1; #potential difference(V)\n",
+ "\n",
+ "#Result\n",
+ "print \"potential difference between two regions is\",pd,\"V\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "potential difference between two regions is 100.0 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 46
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.10, Page number 235"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "E=250; #electric field(V/m)\n",
+ "R=10**-8; #radius of drop(m)\n",
+ "rho=10**3; #density of water(kg/m**3)\n",
+ "\n",
+ "#Calculation\n",
+ "#F=mg=qE\n",
+ "m=(4/3)*math.pi*(R**3)*rho; #mass of water drop(kg)\n",
+ "W=m*9.8; #weight of drop\n",
+ "q=W/E; #charge on water drop(C)\n",
+ "\n",
+ "#Result\n",
+ "print \"charge on water drop is\",round(q*10**21,3),\"*10**-21 C\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "charge on water drop is 0.164 *10**-21 C\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.11, Page number 235"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "v=5*10**5; #velocity(m/s)\n",
+ "B=0.3; #flux density(Wb/m**2)\n",
+ "N=6.025*10**26; #avagadro number\n",
+ "M72=72/N; #mass(kg)\n",
+ "M74=74; #mass(kg)\n",
+ "\n",
+ "#Calculation\n",
+ "R72=(M72*v)/(B*e); #radius(m)\n",
+ "R74=(R72/72)*M74; #radius(m)\n",
+ "S=2*(R74-R72); #linear separation of two lines(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"linear separation of two lines is\",round(S,3),\"m\"\n",
+ "print \"answer given in the book is wrong\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "linear separation of two lines is 0.069 m\n",
+ "answer given in the book is wrong\n"
+ ]
+ }
+ ],
+ "prompt_number": 58
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.12, Page number 236"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "l=5*10**-2; #length(m)\n",
+ "d=0.3; #distance of screen from end of magnetic field(m)\n",
+ "y=0.01; #deflection on screen(m)\n",
+ "m=9.1*10**-31; #mass of electron(kg)\n",
+ "e=1.6*10**-19; #charge of electron(C)\n",
+ "Va=1000; #anode voltage(V)\n",
+ "\n",
+ "#Calculation\n",
+ "D=d+(l/2); #distance(m)\n",
+ "B=(y/(D*l))*math.sqrt((2*m*Va)/e); #flux density(Wb/m**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"flux density is\",round(B*10**6,1),\"*10**-6 Wb/m**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "flux density is 65.6 *10**-6 Wb/m**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.13, Page number 236"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "e=1.6*10**-19; #charge of electron(C)\n",
+ "Va=150; #potential difference(V)\n",
+ "m=9.1*10**-31; #mass of electron(kg)\n",
+ "V=20; #potential(V)\n",
+ "D=1/2;\n",
+ "d=10**-2; #distance of seperation(m)\n",
+ "l=10*10**-2; #length(m)\n",
+ "\n",
+ "#Calculation\n",
+ "vx=math.sqrt((2*e*Va)/m); #velocity of electron reacting the field(m/s)\n",
+ "ay=(e/m)*(V/d); #acceleration due to deflecting field(m/s**2)\n",
+ "vy=ay*(l/vx); #final velocity attained by deflecting field(m/s)\n",
+ "theta=math.atan(vy/vx); #angle of deflection(radian)\n",
+ "thetaD=theta*(180/math.pi); #angle of deflection(degrees)\n",
+ "Y=D*math.tan(theta); #deflection on screen(m)\n",
+ "S=(Y/V); #deflection senstivity(m/V)\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print \"velocity of electron reacting the field is\",round(vx/10**6,2),\"*10**6 m/s\"\n",
+ "print \"acceleration due to deflecting field is\",round(ay*10**-14,3),\"*10**14 m/s**2\"\n",
+ "print \"final velocity attained by deflecting field is\",round(vy/10**6,1),\"*10**6 m/s\"\n",
+ "print \"angle of deflection is\",round(thetaD,2),\"degrees\"\n",
+ "print \"answer varies due to rounding off errors\"\n",
+ "print \"deflection on screen is\",round(Y,2),\"m\"\n",
+ "print \"deflection senstivity is\",round(S,4),\"m/V\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "velocity of electron reacting the field is 7.26 *10**6 m/s\n",
+ "acceleration due to deflecting field is 3.516 *10**14 m/s**2\n",
+ "final velocity attained by deflecting field is 4.8 *10**6 m/s\n",
+ "angle of deflection is 33.69 degrees\n",
+ "answer varies due to rounding off errors\n",
+ "deflection on screen is 0.33 m\n",
+ "deflection senstivity is 0.0167 m/V\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |