{ "metadata": { "name": "", "signature": "sha256:604dfd31225e3c2fe12afc104ed18461bd1bcabd558389f5cc69df386ba9091d" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "7: Motion of a charged particle" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 7.1, Page number 132" ] }, { "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 the electron(c)\n", "V=18; #potential difference(kV)\n", "m=9.1*10**-31; #mass of the electron(kg)\n", "\n", "#Calculation \n", "K=e*V*10**3; #Kinetic energy(J)\n", "v=math.sqrt((2*e*V*10**3)/m); #speed of electron(m/s)\n", "\n", "#Result\n", "print \"The kinetic energy of electron is\",K*10**16,\"*10**-16 J\"\n", "print \"Speed of the electron is\",round(v/10**7,3),\"*10**7 m/s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The kinetic energy of electron is 28.8 *10**-16 J\n", "Speed of the electron is 7.956 *10**7 m/s\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 7.2, Page number 133" ] }, { "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", "vx=4*10**6; #velocity along x-axis(m/s)\n", "E=1500; #electric field strength(N/C)\n", "l=0.07; #length in y-axis(m)\n", "q=1.6*10**-19; #charge of electron(c)\n", "\n", "#Calculation \n", "y=(-q*E*(l**2))/(2*m*(vx**2))*10**2; #vertical displacement of electron(cm)\n", "\n", "#Result\n", "print \"The vertical displacement of electron when it leaves the electric field is\",round(y,3),\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The vertical displacement of electron when it leaves the electric field is -4.038 cm\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 7.3, Page number 133" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "u=5*10**5; #velocity(m/s)\n", "m=1.67*10**-27; #mass of proton(kg)\n", "q=1.6*10**-19;\n", "E=500; #electric field(N/C)\n", "theta=42; #angle(degrees)\n", "\n", "#Calculation \n", "theta=theta*math.pi/180; #angle(radian)\n", "t=((u*m*math.sin(theta))/(q*E))*10**6; #time required for the proton(micro s)\n", "\n", "#Result\n", "print \"The time required for the proton is\",round(t,2),\"micro s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The time required for the proton is 6.98 micro s\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 7.4, Page number 133" ] }, { "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;\n", "B=0.36; #magnetic field(T)\n", "R=0.2; #radius(m)\n", "\n", "#Calculation \n", "v=(q*B*R)/m; #orbital speed of proton(m/s)\n", "\n", "#Result\n", "print \"The orbital speed of proton is\",round(v/10**6,1),\"*10**6 m/s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The orbital speed of proton is 6.9 *10**6 m/s\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 7.5, Page number 133" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "v=2*10**6; #speed(m/s)\n", "theta=30; #angle at which proton enters at the origin of coordinate system(degrees)\n", "B=0.3; #magnetic field(T)\n", "m=1.67*10**-27; #mass of proton(kg)\n", "q=1.6*10**-19;\n", "\n", "#Calculation \n", "theta=theta*math.pi/180; #angle(radian)\n", "vp=v*math.sin(theta); #v(perpendicular component)\n", "vpa=v*math.cos(theta); #v(parallel component)\n", "p=(vpa*2*math.pi*m)/(q*B); #pitch of the helix described by the proton\n", "R=((m*vp)/(q*B))*10**2; #radius of the trajectory\n", "\n", "#Result\n", "print \"the pitch of the helix is\",round(p,2),\"m\"\n", "print \"the radius of trajectory is\",round(R,2),\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "the pitch of the helix is 0.38 m\n", "the radius of trajectory is 3.48 cm\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 7.6, Page number 133" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "V=25; #deflecting voltage(V)\n", "l=0.03; #length of deflecting planes(m)\n", "d=0.75; #distance between 2 deflecting plates(cm)\n", "Va=800; #final anode voltage(V)\n", "D=0.2; #distance between the screen and the plates(m)\n", "e=1.6*10**-19;\n", "m=9.1*10**-31; #mass of electron(kg)\n", "\n", "#Calculation \n", "y=(((V*l)/(2*d*Va))*(D+(l/2)))*10**4; #displacement produced(cm)\n", "a=((V*l)/(2*d*Va))*10**2;\n", "alpha=math.atan(a); #angle made by the beam with the axis(radian)\n", "alpha1=alpha*180/math.pi; #angle(degrees)\n", "v=((math.sqrt((2*e*Va)/m))/math.cos(alpha)); #velocity of electron(v)\n", "\n", "#Result\n", "print \"the displacement produced is\",round(y,2),\"cm\"\n", "print \"the angle made by the beam with the axis is\",round(alpha1,2),\"degrees\"\n", "print \"velocity of electrons is\",round(v/10**7,2),\"*10**7 m/s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "the displacement produced is 1.34 cm\n", "the angle made by the beam with the axis is 3.58 degrees\n", "velocity of electrons is 1.68 *10**7 m/s\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 7.7, Page number 134" ] }, { "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;\n", "B=5*10**-5; #magnetic field(Wb/m**2)\n", "l=0.04; #length of magnetic field along the axis(m)\n", "m=9.1*10**-31; #mass of electron(kg)\n", "D=0.25; #distance of the screen from the field(m)\n", "Va=600; #final anode voltage(V)\n", "\n", "#Calculation \n", "y=(((e*B*l)/m)*math.sqrt(m/(2*e*Va))*(D+(l/2)))*10**2; #displacement of the electron(cm)\n", "\n", "#Result\n", "print \"the displacement of the electron beam spot on the screen is\",round(y,2),\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "the displacement of the electron beam spot on the screen is 0.65 cm\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 7.8, Page number 134" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "E=2.5*10**4; #electric field(V/m)\n", "B=0.18; #magnetic field(T)\n", "B1=0.22; #magnetic field in the main chamber(T)\n", "m2=13; #mass number of carbon(kg)\n", "m1=12; #mass number of carbon(kg)\n", "e=1.6*10**-9;\n", "q=1.67*10**-27;\n", "\n", "#Calculation \n", "v=E/B; #velocity of particles(m/s)\n", "s=((2*v*(m2-m1)*q)/(e*B1))*10**12; #seperation on photographic plate(cm)\n", "\n", "#Result\n", "print \"the seperation on photographic plate is\",round(s,3),\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "the seperation on photographic plate is 1.318 cm\n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 7.9, Page number 134" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "v=5.6*10**6; #speed of the electron(m/s)\n", "m=9.1*10**-31; #mass of electron(kg)\n", "e=1.6*10**-19;\n", "s=0.03; #distance travelled(m)\n", "\n", "#Calculation \n", "E=(m*(v)**2)/(2*e*s); #intensity of electric field(N/C)\n", "\n", "#Result\n", "print \"The intensity of electric field is\",round(E),\"N/C\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The intensity of electric field is 2973.0 N/C\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 7.10, Page number 134" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "v=5*10**7;\n", "B=0.4; #magnetic field(T)\n", "r=0.711*10**-3; #radius of the circle(m)\n", "\n", "#Calculation \n", "Q=v/(B*r); #charge to mass ratio(C/kg)\n", "\n", "#Result\n", "print \"The charge to mass ratio is\",round(Q/10**10,2),\"*10**10 C/kg\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The charge to mass ratio is 17.58 *10**10 C/kg\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 7.11, Page number 135" ] }, { "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", "v=3*10**7; #speed of electron(m/s)\n", "R=0.05; #radius of the circle(m)\n", "q=1.6*10**-31;\n", "\n", "#Calculation \n", "B=((m*v)/(q*R))*10**-9; #magnetic field(mT)\n", "\n", "#Result\n", "print \"The magnetic field to bend a beam is\",round(B,1),\"mT\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The magnetic field to bend a beam is 3.4 mT\n" ] } ], "prompt_number": 29 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 7.12, Page number 135" ] }, { "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", "q=1.6*10**-19;\n", "t=8*10**-9; #time(ns)\n", "\n", "#Calculation \n", "B=(2*math.pi*m*500)/(q*t); #magnetic field(T)\n", "\n", "#Result\n", "print \"The magnetic field is\",round(B,2),\"T\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The magnetic field is 2.23 T\n" ] } ], "prompt_number": 31 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 7.13, Page number 135" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "v=9.15*10**7; #cyclotron frequency of proton(Hz)\n", "m=1.67*10**-27; #mass of proton(kg)\n", "q=1.6*10**-19;\n", "\n", "#Calculation \n", "B=(2*math.pi*v*m)/q; #magnetic field(T)\n", "\n", "#Result\n", "print \"The magnetic field is\",int(B),\"T\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The magnetic field is 6 T\n" ] } ], "prompt_number": 33 } ], "metadata": {} } ] }