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1 files changed, 20 insertions, 550 deletions
diff --git a/Engineering_Physics/Chapter8_1.ipynb b/Engineering_Physics/Chapter8_1.ipynb index 809f0bc8..54d83b1d 100755 --- a/Engineering_Physics/Chapter8_1.ipynb +++ b/Engineering_Physics/Chapter8_1.ipynb @@ -1,7 +1,6 @@ { "metadata": { - "name": "", - "signature": "sha256:6cf74f56ec30435213713191af54de81cab98f4f30811b6d81fe0fb6a9021553" + "name": "Chapter8" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,49 +11,25 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "8: Special Theory of Relativity" - ] + "source": "8: Magnetic Materials" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 8.1, Page number 171" - ] + "source": "Example number 8.1, Page number 238" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "L_0 = 1; #For simplicity, we assume classical length to be unity(m)\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "\n", - "#Calculation\n", - "L = (1-1/100)*L_0; #Relativistic length(m)\n", - "#Relativistic length contraction gives L = L_0*sqrt(1-v^2/c^2), solving for v\n", - "v = math.sqrt(1-(L/L_0)**2)*c; #Speed at which relativistic length is 1 percent of the classical length(m/s)\n", - "v = math.ceil(v*10**4)/10**4; #rounding off the value of v to 4 decimals\n", - "\n", - "#Result\n", - "print \"The speed at which relativistic length is 1 percent of the classical length is\",v, \"c\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nI = 12; #current(Ampere)\nA = 7.5*10**-4 #area of loop(m**2)\n\n#Calculation\nM = I*A; #magnetic moment(Am**2)\nM = M*10**3;\n\n#Result\nprint \"magnetic moment is\",M,\"*10**-3 Am**2\"\nprint \"magnetic moment is in opposite direction from the observer\"\nprint \"M is perpendicular to the plane\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The speed at which relativistic length is 1 percent of the classical length is 0.1411 c\n" - ] + "text": "magnetic moment is 9.0 *10**-3 Am**2\nmagnetic moment is in opposite direction from the observer\nM is perpendicular to the plane\n" } ], "prompt_number": 1 @@ -63,39 +38,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 8.2, Page number 171" - ] + "source": "Example number 8.2, Page number 238" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "delta_t = 5*10**-6; #Mean lifetime of particles as observed in the lab frame(s)\n", - "\n", - "#Calculation\n", - "v = 0.9*c; #Speed at which beam of particles travel(m/s)\n", - "delta_tau = delta_t*math.sqrt(1-(v/c)**2); #Proper lifetime of particle as per Time Dilation rule(s)\n", - "\n", - "#Result\n", - "print \"The proper lifetime of particle is\",delta_tau, \"s\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nr = 0.5; #radius of orbit(Angstrom)\ne = 1.6*10**-19; #charge of electron(C)\nnew = 10**16; #frequency(rps)\n\n#Calculation\nr = r*10**-10; #radius of orbit(m)\nI = e*new; #current(Ampere)\nA = math.pi*r**2; #area enclosed(m**2)\nM = I*A; #magnetic moment(Am**2)\n\n#Result\nprint \"magnetic moment is\",M,\"Am**2\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The proper lifetime of particle is 2.17944947177e-06 s\n" - ] + "text": "magnetic moment is 1.25663706144e-23 Am**2\n" } ], "prompt_number": 2 @@ -104,549 +59,64 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 8.3, Page number 171. theoritical proof" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.4, Page number 172" - ] + "source": "Example number 8.3, Page number 239" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "\n", - "#Calculation\n", - "v = 0.6*c; #Speed with which the rocket leaves the earth(m/s)\n", - "u_prime = 0.9*c; #Relative speed of second rocket w.r.t. the first rocket(m/s)\n", - "u1 = (u_prime+v)/(1+(u_prime*v)/c**2); #Speed of second rocket for same direction of firing as per Velocity Addition Rule(m/s)\n", - "u1 = math.ceil(u1*10**4)/10**4; #rounding off the value of u1 to 4 decimals\n", - "u2 = (-u_prime+v)/(1-(u_prime*v)/c**2); #Speed of second rocket for opposite direction of firing as per Velocity Addition Rule(m/s)\n", - "u2 = math.ceil(u2*10**4)/10**4; #rounding off the value of u2 to 4 decimals\n", - "\n", - "#Result\n", - "print \"The speed of second rocket for same direction of firing is\",u1,\"c\"\n", - "print \"The speed of second rocket for opposite direction of firing is\",u2,\"c\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nmew_r = 5000; #relative permeability\n\n#Calculation\nchi_m = mew_r-1; #magnetic susceptibility\n\n#Result\nprint \"magnetic susceptibility is\",chi_m", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The speed of second rocket for same direction of firing is 0.9741 c\n", - "The speed of second rocket for opposite direction of firing is -0.6521 c\n" - ] + "text": "magnetic susceptibility is 4999\n" } ], - "prompt_number": 4 + "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 8.5, Page number 172" - ] + "source": "Example number 8.4, Page number 239" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "L0 = 1; #For simplicity assume length in spaceship's frame to be unity(m)\n", - "tau = 1; #Unit time in the spaceship's frame(s)\n", - "\n", - "#Calculation\n", - "L = 1/2*L0; #Length as observed on earth(m)\n", - "#Relativistic length contraction gives L = L_0*sqrt(1-v^2/c^2), solving for v\n", - "v = math.sqrt(1-(L/L0)**2)*c; #Speed at which length of spaceship is observed as half from the earth frame(m/s)\n", - "t = tau/math.sqrt(1-(v/c)**2); #Time dilation of the spaceship's unit time(s)\n", - "v = math.ceil(v*10**4)/10**4; #rounding off the value of v to 4 decimals\n", - "\n", - "#Result\n", - "print \"The speed at which length of spaceship is observed as half from the earth frame is\",v, \"c\"\n", - "print \"The time dilation of the spaceship unit time is\",t,\"delta_tau\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nH = 1800; #magnetic field(A/m)\nphi = 3*10**-5; #magnetic flux(Wb)\nA = 0.2; #cross sectional area(cm**2)\n\n#Calculation\nA = A*10**-4; #cross sectional area(m**2)\nB = phi/A; #magnetic flux density(Wb/m**2)\nmew = B/H; #permeability(H/m)\nmew = mew*10**4;\nmew=math.ceil(mew*100)/100; #rounding off to 2 decimals\n\n#Result\nprint \"permeability is\",mew,\"*10**-4 H/m\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The speed at which length of spaceship is observed as half from the earth frame is 0.8661 c\n", - "The time dilation of the spaceship unit time is 2.0 delta_tau\n" - ] + "text": "permeability is 8.34 *10**-4 H/m\n" } ], - "prompt_number": 5 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.6, Page number 172" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 3*10**8; #Speed of light in vacuum(m/s)\n", - "t1 = 2*10**-7; #Time for which first event occurs(s)\n", - "t2 = 3*10**-7; #Time for which second event occurs(s)\n", - "x1 = 10; #Position at which first event occurs(m)\n", - "x2 = 40; #Position at which second event occurs(m)\n", - "\n", - "#Calculation\n", - "v = 0.6*c; #Velocity with which S2 frame moves relative to S1 frame(m/s)\n", - "L_factor = 1/math.sqrt(1-(v/c)**2); #Lorentz factor\n", - "delta_t = L_factor*(t2 - t1)+L_factor*v/c**2*(x1 - x2); #Time difference between the events(s)\n", - "delta_x = L_factor*(x2 - x1)-L_factor*v*(t2 - t1); #Distance between the events(m)\n", - "\n", - "#Result\n", - "print \"The time difference between the events is\",delta_t, \"s\" \n", - "print \"The distance between the events is\",delta_x, \"m\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The time difference between the events is 5e-08 s\n", - "The distance between the events is 15.0 m\n" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.7, Page number 173" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 3*10**8; #Speed of light in vacuum(m/s)\n", - "tau = 2.6*10**-8; #Mean lifetime the particle in its own frame(s)\n", - "d = 20; #Distance which the unstable particle travels before decaying(m)\n", - "\n", - "#Calculation\n", - "#As t = d/v and also t = tau/sqrt(1-(v/c)^2), so that\n", - "#d/v = tau/sqrt(1-(v/c)^2), solving for v\n", - "v = math.sqrt(d**2/(tau**2+(d/c)**2)); #Speed of the unstable particle in lab frame(m/s)\n", - "v = v/10**8;\n", - "v = math.ceil(v*10)/10; #rounding off the value of v to 1 decimal\n", - "\n", - "#Result\n", - "print \"The speed of the unstable particle in lab frame is\",v,\"*10**8 m/s\"\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The speed of the unstable particle in lab frame is 2.8 *10**8 m/s\n" - ] - } - ], - "prompt_number": 9 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.8, Page number 174" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "me = 1; #For simplicity assume mass of electron to be unity(kg)\n", - "tau = 2.3*10**-6; #Average lifetime of mu-meson in rest frame(s)\n", - "t = 6.9*10**-6; #Average lifetime of mu-meson in laboratory frame(s)\n", - "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", - "C = 3*10**8; #Speed of light in vacuum(m/s)\n", - "m_e = 9.1*10**-31; #Mass of an electron(kg)\n", - "\n", - "#Calculation\n", - "#Fromm Time Dilation Rule, tau = t*sqrt(1-(v/c)^2), solving for v\n", - "v = c*math.sqrt(1-(tau/t)**2); #Speed of mu-meson in the laboratory frame(m/s)\n", - "v = math.ceil(v*10**5)/10**5; #rounding off the value of v to 5 decimals\n", - "m0 = 207*me; #Rest mass of mu-meson(kg)\n", - "m = m0/math.sqrt(1-(v/c)**2); #Relativistic variation of mass with velocity(kg)\n", - "m = math.ceil(m*10)/10; #rounding off the value of m to 1 decimal\n", - "T = (m*m_e*C**2 - m0*m_e*C**2)/e; #Kinetic energy of mu-meson(eV)\n", - "T = T*10**-6; #Kinetic energy of mu-meson(MeV)\n", - "T = math.ceil(T*100)/100; #rounding off the value of T to 2 decimals\n", - " \n", - "#Result\n", - "print \"The speed of mu-meson in the laboratory frame is\",v, \"c\"\n", - "print \"The effective mass of mu-meson is\",m, \"me\"\n", - "print \"The kinetic energy of mu-meson is\",T, \"MeV\"\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The speed of mu-meson in the laboratory frame is 0.94281 c\n", - "The effective mass of mu-meson is 621.1 me\n", - "The kinetic energy of mu-meson is 211.97 MeV\n" - ] - } - ], - "prompt_number": 13 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.9, Page number 174" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "m0 = 1; #For simplicity assume rest mass to be unity(kg)\n", - "\n", - "#Calculation\n", - "m = (20/100+1)*m0; #Mass in motion(kg)\n", - "#As m = m0/sqrt(1-(u/c)^2), solving for u\n", - "u = math.sqrt(1-(m0/m)**2)*c; #Speed of moving mass(m/s) \n", - "u = math.ceil(u*10**3)/10**3; #rounding off the value of u to 3 decimals\n", - "\n", - "#Result\n", - "print \"The speed of moving body is\",u, \"c\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The speed of moving body is 0.553 c\n" - ] - } - ], - "prompt_number": 14 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.10, Page number 175" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 3*10**8; #Speed of light in vacuum(m/s)\n", - "dE = 4*10**26; #Energy radiated per second my the sun(J/s)\n", - "\n", - "#Calculation\n", - "dm = dE/c**2; #Rate of decrease of mass of sun(kg/s)\n", - "dm = dm/10**9;\n", - "dm = math.ceil(dm*10**3)/10**3; #rounding off the value of dm to 3 decimals\n", - "\n", - "#Result\n", - "print \"The rate of decrease of mass of sun is\",dm,\"*10**9 kg/s\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The rate of decrease of mass of sun is 4.445 *10**9 kg/s\n" - ] - } - ], - "prompt_number": 18 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.11, Page number 175" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", - "m0 = 9.1*10**-31; #Mass of the electron(kg)\n", - "E0 = 0.512; #Rest energy of electron(MeV)\n", - "T = 10; #Kinetic energy of electron(MeV)\n", - "\n", - "#Calculation\n", - "E = T + E0; #Total energy of electron(MeV)\n", - "# From Relativistic mass-energy relation E^2 = c^2*p^2 + m0^2*c^4, solving for p\n", - "p = math.sqrt(E**2-m0**2*c**4)/c; #Momentum of the electron(MeV)\n", - "p = math.ceil(p*100)/100; #rounding off the value of p to 2 decimals\n", - "#As E = E0/sqrt(1-(u/c)^2), solving for u\n", - "u = math.sqrt(1-(E0/E)**2)*c; #Velocity of the electron(m/s)\n", - "u = math.ceil(u*10**4)/10**4; #rounding off the value of u to 4 decimals\n", - "\n", - "#Result\n", - "print \"The momentum of the electron is\",p,\"/c MeV\"\n", - "print \"The velocity of the electron is\",u, \"c\"\n", - "\n", - "#answer for velocity given in the book is wrong" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The momentum of the electron is 10.52 /c MeV\n", - "The velocity of the electron is 0.9989 c\n" - ] - } - ], - "prompt_number": 19 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.12, Page number 175. theoritical proof" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.13, Page number 176" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 3*10**8; #Speed of light in vacuum(m/s)\n", - "E = 4.5*10**17; #Total energy of object(J)\n", - "px = 3.8*10**8; #X-component of momentum(kg-m/s)\n", - "py = 3*10**8; #Y-component of momentum(kg-m/s)\n", - "pz = 3*10**8; #Z-component of momentum(kg-m/s)\n", - "\n", - "#Calculation\n", - "p = math.sqrt(px**2+py**2+pz**2); #Total momentum of the object(kg-m/s)\n", - "#From Relativistic mass-energy relation E^2 = c^2*p^2 + m0^2*c^4, solving for m0\n", - "m0 = math.sqrt(E**2/c**4 - p**2/c**2); #Rest mass of the body(kg)\n", - "m0 = math.ceil(m0*100)/100; #rounding off the value of m0 to 2 decimals\n", - "\n", - "#Result\n", - "print \"The rest mass of the body is\",m0, \"kg\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The rest mass of the body is 4.63 kg\n" - ] - } - ], - "prompt_number": 20 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example number 8.14, Page number 176" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "c = 3*10**8; #Speed of light in vacuum(m/s)\n", - "m = 50000; #Mass of high speed probe(kg)\n", - "\n", - "#Calculation\n", - "u = 0.8*c; #Speed of the probe(m/s)\n", - "p = m*u/math.sqrt(1-(u/c)**2); #Momentum of the probe(kg-m/s)\n", - "\n", - "#Result\n", - "print \"The momentum of the high speed probe is\",p, \"kg-m/s\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "The momentum of the high speed probe is 2e+13 kg-m/s\n" - ] - } - ], - "prompt_number": 21 + "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 8.15, Page number 177" - ] + "source": "Example number 8.5, Page number 239" }, { "cell_type": "code", "collapsed": false, - "input": [ - "\n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "e = 1.6*10**-19; #Electronic charge, C = Energy equivalent of 1 eV(J/eV)\n", - "m0 = 9.11*10**-31; #Rest mass of electron(kg)\n", - "c = 3*10**8; #Speed of light in vacuum(m/s)\n", - "\n", - "#Calculation\n", - "u1 = 0.98*c; #Inital speed of electron(m/s)\n", - "u2 = 0.99*c; #Final speed of electron(m/s)\n", - "m1 = m0/math.sqrt(1-(u1/c)**2); #Initial relativistic mass of electron(kg)\n", - "m2 = m0/math.sqrt(1-(u2/c)**2); #Final relativistic mass of electron(kg)\n", - "dm = m2 - m1; #Change in relativistic mass of the electron(kg)\n", - "W = dm*c**2/e; #Work done on the electron to change its velocity(eV)\n", - "W = W*10**-6; #Work done on the electron to change its velocity(MeV)\n", - "W = math.ceil(W*100)/100; #rounding off the value of W to 2 decimals\n", - "#As W = eV, V = accelerating potential, solving for V\n", - "V = W*10**6; #Accelerating potential(volt)\n", - "V = V/10**6;\n", - "\n", - "#Result\n", - "print \"The change in relativistic mass of the electron is\",dm, \"kg\"\n", - "print \"The work done on the electron to change its velocity is\",W, \"MeV\"\n", - "print \"The accelerating potential is\",V, \"*10**6 volt\"\n", - "\n", - "#answers given in the book are wrong" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nB = 0.65; #magnetic induction(Wb/m**2)\nrho = 8906; #density(kg/m**3)\nM = 58.7; #atomic weight\nmew0 = 4*math.pi*10**-7;\nmb = 9.27*10**-24;\nNa = 6.023*10**26; #avagadro constant\n\n#Calculation\nN = rho*Na/M; #number of atoms per unit volume(atoms/m**3)\nmew_r = B/(N*mew0); #relative permeability(A/m**2)\nM = mew_r/mb; #magnetic moment in mew_B \nM=math.ceil(M*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"magnetic moment is\",M,\"mew_B\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The change in relativistic mass of the electron is 1.87996052912e-30 kg\n", - "The work done on the electron to change its velocity is 1.06 MeV\n", - "The accelerating potential is 1.06 *10**6 volt\n" - ] + "text": "magnetic moment is 0.611 mew_B\n" } ], - "prompt_number": 24 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] + "prompt_number": 5 } ], "metadata": {} |