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Diffstat (limited to 'Engineering_Physics/Chapter13_1.ipynb')
| -rw-r--r-- | Engineering_Physics/Chapter13_1.ipynb | 213 |
1 files changed, 189 insertions, 24 deletions
diff --git a/Engineering_Physics/Chapter13_1.ipynb b/Engineering_Physics/Chapter13_1.ipynb index 2366432d..75d0d1f7 100644 --- a/Engineering_Physics/Chapter13_1.ipynb +++ b/Engineering_Physics/Chapter13_1.ipynb @@ -1,6 +1,7 @@ { "metadata": { - "name": "Chapter13" + "name": "", + "signature": "sha256:be254bf95838dd01a87a63582117a886c3167a80cf387f9901b2e2de7a990b8e" }, "nbformat": 3, "nbformat_minor": 0, @@ -11,25 +12,48 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": "13: Dielectric Properties of Materials" + "source": [ + "13: Dielectric Properties of Materials" + ] }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 13.1, Page number 287" + "source": [ + "Example number 13.1, Page number 287" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the electronic polarizability \n\n#importing modules\nimport math\n\n#Variable declaration\nepsilon_0 = 8.85*10**-12; #Absolute electrical permittivity of free space(F/m)\nR = 0.52; #Radius of hydrogen atom(A)\nn = 9.7*10**26; #Number density of hydrogen(per metre cube)\n\n#Calculation\nR = R*10**-10; #Radius of hydrogen atom(m)\nalpha_e = 4*math.pi*epsilon_0*R**3; #Electronic polarizability of hydrogen atom(Fm**2)\n\n#Result\nprint \"The electronic polarizability of hydrogen atom is\", alpha_e, \"Fm**2\"", + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "epsilon_0 = 8.85*10**-12; #Absolute electrical permittivity of free space(F/m)\n", + "R = 0.52; #Radius of hydrogen atom(A)\n", + "n = 9.7*10**26; #Number density of hydrogen(per metre cube)\n", + "\n", + "#Calculation\n", + "R = R*10**-10; #Radius of hydrogen atom(m)\n", + "alpha_e = 4*math.pi*epsilon_0*R**3; #Electronic polarizability of hydrogen atom(Fm**2)\n", + "\n", + "#Result\n", + "print \"The electronic polarizability of hydrogen atom is\", alpha_e, \"Fm**2\"" + ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": "The electronic polarizability of hydrogen atom is 1.56373503182e-41 Fm**2\n" + "text": [ + "The electronic polarizability of hydrogen atom is 1.56373503182e-41 Fm**2\n" + ] } ], "prompt_number": 1 @@ -38,19 +62,46 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 13.2, Page number 287" + "source": [ + "Example number 13.2, Page number 287" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the capacitance of capacitor and charge on the plates\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nepsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\nA = 100; #Area of a plate of parallel plate capacitor(cm**2)\nd = 1; #Distance between the plates of the capacitor(cm)\nV = 100; #Potential applied to the plates of the capacitor(V)\n\n#Calculation\nA= A*10**-4; #Area of a plate of parallel plate capacitor(m**2)\nd = d*10**-2; #Distance between the plates of the capacitor(m)\nC = epsilon_0*A/d; #Capacitance of parallel plate capacitor(F)\nQ = C*V; #Charge on the plates of the capacitor(C)\n\n#Result\nprint \"The capacitance of parallel plate capacitor is\",C, \"F\"\nprint \"The charge on the plates of the capacitor is\",Q, \"C\"\n", + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n", + "A = 100; #Area of a plate of parallel plate capacitor(cm**2)\n", + "d = 1; #Distance between the plates of the capacitor(cm)\n", + "V = 100; #Potential applied to the plates of the capacitor(V)\n", + "\n", + "#Calculation\n", + "A= A*10**-4; #Area of a plate of parallel plate capacitor(m**2)\n", + "d = d*10**-2; #Distance between the plates of the capacitor(m)\n", + "C = epsilon_0*A/d; #Capacitance of parallel plate capacitor(F)\n", + "Q = C*V; #Charge on the plates of the capacitor(C)\n", + "\n", + "#Result\n", + "print \"The capacitance of parallel plate capacitor is\",C, \"F\"\n", + "print \"The charge on the plates of the capacitor is\",Q, \"C\"\n" + ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": "The capacitance of parallel plate capacitor is 8.854e-12 F\nThe charge on the plates of the capacitor is 8.854e-10 C\n" + "text": [ + "The capacitance of parallel plate capacitor is 8.854e-12 F\n", + "The charge on the plates of the capacitor is 8.854e-10 C\n" + ] } ], "prompt_number": 2 @@ -59,19 +110,43 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 13.3, Page number 288" + "source": [ + "Example number 13.3, Page number 288" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the dielectric displacement\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nepsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\nepsilon_r = 5.0; #Dielectric constant of the material between the plates of capacitor\nV = 15; #Potential difference applied between the plates of the capacitor(V)\nd = 1.5; #Separation between the plates of the capacitor(mm)\n\n#Calculation\nd = d*10**-3; #Separation between the plates of the capacitor(m)\n#Electric displacement, D = epsilon_0*epsilon_r*E, as E = V/d, so \nD = epsilon_0*epsilon_r*V/d; #Dielectric displacement(C/m**2)\n\n#Result\nprint \"The dielectric displacement is\",D, \"C/m**2\"", + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n", + "epsilon_r = 5.0; #Dielectric constant of the material between the plates of capacitor\n", + "V = 15; #Potential difference applied between the plates of the capacitor(V)\n", + "d = 1.5; #Separation between the plates of the capacitor(mm)\n", + "\n", + "#Calculation\n", + "d = d*10**-3; #Separation between the plates of the capacitor(m)\n", + "#Electric displacement, D = epsilon_0*epsilon_r*E, as E = V/d, so \n", + "D = epsilon_0*epsilon_r*V/d; #Dielectric displacement(C/m**2)\n", + "\n", + "#Result\n", + "print \"The dielectric displacement is\",D, \"C/m**2\"" + ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": "The dielectric displacement is 4.427e-07 C/m**2\n" + "text": [ + "The dielectric displacement is 4.427e-07 C/m**2\n" + ] } ], "prompt_number": 3 @@ -80,19 +155,40 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 13.4, Page number 288" + "source": [ + "Example number 13.4, Page number 288" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the relative dielectric constant\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nepsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\nN = 3*10**28; #Number density of solid elemental dielectric(atoms/metre cube)\nalpha_e = 10**-40; #Electronic polarizability(Fm**2)\n\n#Calculation\nepsilon_r = 1 + (N*alpha_e/epsilon_0); #Relative dielectric constant of the material\nepsilon_r = math.ceil(epsilon_r*10**3)/10**3; #rounding off the value of epsilon_r to 3 decimals\n\n#Result\nprint \"The Relative dielectric constant of the material is\",epsilon_r\n", + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n", + "N = 3*10**28; #Number density of solid elemental dielectric(atoms/metre cube)\n", + "alpha_e = 10**-40; #Electronic polarizability(Fm**2)\n", + "\n", + "#Calculation\n", + "epsilon_r = 1 + (N*alpha_e/epsilon_0); #Relative dielectric constant of the material\n", + "epsilon_r = math.ceil(epsilon_r*10**3)/10**3; #rounding off the value of epsilon_r to 3 decimals\n", + "\n", + "#Result\n", + "print \"The Relative dielectric constant of the material is\",epsilon_r\n" + ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": "The Relative dielectric constant of the material is 1.339\n" + "text": [ + "The Relative dielectric constant of the material is 1.339\n" + ] } ], "prompt_number": 5 @@ -101,19 +197,46 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 13.5, Page number 288" + "source": [ + "Example number 13.5, Page number 288" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the electronic polarizability\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nN_A = 6.02*10**23; #Avogadro's number(per mole)\nepsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\nepsilon_r = 3.75; #Relative dielectric constant\nd = 2050; #Density of sulphur(kg/metre cube)\ny = 1/3; #Internal field constant\nM = 32; #Atomic weight of sulphur(g/mol)\n\n#Calculation\nN = N_A*10**3*d/M; #Number density of atoms of sulphur(per metre cube)\n#Lorentz relation for local fields give E_local = E + P/(3*epsilon_0) which gives\n#(epsilon_r - 1)/(epsilon_r + 2) = N*alpha_e/(3*epsilon_0), solving for alpha_e\nalpha_e = (epsilon_r - 1)/(epsilon_r + 2)*3*epsilon_0/N; #Electronic polarizability of sulphur(Fm**2)\n\n#Result\nprint \"The electronic polarizability of sulphur is\",alpha_e, \"Fm**2\"", + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "N_A = 6.02*10**23; #Avogadro's number(per mole)\n", + "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n", + "epsilon_r = 3.75; #Relative dielectric constant\n", + "d = 2050; #Density of sulphur(kg/metre cube)\n", + "y = 1/3; #Internal field constant\n", + "M = 32; #Atomic weight of sulphur(g/mol)\n", + "\n", + "#Calculation\n", + "N = N_A*10**3*d/M; #Number density of atoms of sulphur(per metre cube)\n", + "#Lorentz relation for local fields give E_local = E + P/(3*epsilon_0) which gives\n", + "#(epsilon_r - 1)/(epsilon_r + 2) = N*alpha_e/(3*epsilon_0), solving for alpha_e\n", + "alpha_e = (epsilon_r - 1)/(epsilon_r + 2)*3*epsilon_0/N; #Electronic polarizability of sulphur(Fm**2)\n", + "\n", + "#Result\n", + "print \"The electronic polarizability of sulphur is\",alpha_e, \"Fm**2\"" + ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": "The electronic polarizability of sulphur is 3.2940125351e-40 Fm**2\n" + "text": [ + "The electronic polarizability of sulphur is 3.2940125351e-40 Fm**2\n" + ] } ], "prompt_number": 6 @@ -122,19 +245,39 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 13.6, Page number 289" + "source": [ + "Example number 13.6, Page number 289" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the electronic polarizability\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nN = 3*10**28; #Number density of atoms of dielectric material(per metre cube)\nepsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\nn = 1.6; #Refractive index of dielectric material\n\n#Calculation\n#As (n^2 - 1)/(n^2 + 2) = N*alpha_e/(3*epsilon_0), solving for alpha_e\nalpha_e = (n**2 - 1)/(n**2 + 2)*3*epsilon_0/N; #Electronic polarizability of dielectric material(Fm**2)\n\n#Result\nprint \"The electronic polarizability of dielectric material is\",alpha_e, \"Fm**2\"", + "input": [ + " \n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "N = 3*10**28; #Number density of atoms of dielectric material(per metre cube)\n", + "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n", + "n = 1.6; #Refractive index of dielectric material\n", + "\n", + "#Calculation\n", + "#As (n^2 - 1)/(n^2 + 2) = N*alpha_e/(3*epsilon_0), solving for alpha_e\n", + "alpha_e = (n**2 - 1)/(n**2 + 2)*3*epsilon_0/N; #Electronic polarizability of dielectric material(Fm**2)\n", + "\n", + "#Result\n", + "print \"The electronic polarizability of dielectric material is\",alpha_e, \"Fm**2\"" + ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": "The electronic polarizability of dielectric material is 3.029e-40 Fm**2\n" + "text": [ + "The electronic polarizability of dielectric material is 3.029e-40 Fm**2\n" + ] } ], "prompt_number": 8 @@ -143,19 +286,41 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 13.7, Page number 289" + "source": [ + "Example number 13.7, Page number 289" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the ratio of electronic polarizability to ionic polarizability\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nepsilon_r = 4.9; #Absolute relative dielectric constant of material(F/m)\nn = 1.6; #Refractive index of dielectric material\n\n#Calculation\n#As (n^2 - 1)/(n^2 + 2)*(alpha_e + alpha_i)/alpha_e = N*(alpha_e + alpha_i)/(3*epsilon_0) = (epsilon_r - 1)/(epsilon_r + 2)\n#let alpha_ratio = alpha_i/alpha_e\nalpha_ratio = ((epsilon_r - 1)/(epsilon_r + 2)*(n**2 + 2)/(n**2 - 1) - 1)**(-1); #Ratio of electronic polarizability to ionic polarizability\nalpha_ratio = math.ceil(alpha_ratio*10**3)/10**3; #rounding off the value of alpha_ratio to 3 decimals\n\n#Result\nprint \"The ratio of electronic polarizability to ionic polarizability is\",alpha_ratio", + "input": [ + " \n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "epsilon_r = 4.9; #Absolute relative dielectric constant of material(F/m)\n", + "n = 1.6; #Refractive index of dielectric material\n", + "\n", + "#Calculation\n", + "#As (n^2 - 1)/(n^2 + 2)*(alpha_e + alpha_i)/alpha_e = N*(alpha_e + alpha_i)/(3*epsilon_0) = (epsilon_r - 1)/(epsilon_r + 2)\n", + "#let alpha_ratio = alpha_i/alpha_e\n", + "alpha_ratio = ((epsilon_r - 1)/(epsilon_r + 2)*(n**2 + 2)/(n**2 - 1) - 1)**(-1); #Ratio of electronic polarizability to ionic polarizability\n", + "alpha_ratio = math.ceil(alpha_ratio*10**3)/10**3; #rounding off the value of alpha_ratio to 3 decimals\n", + "\n", + "#Result\n", + "print \"The ratio of electronic polarizability to ionic polarizability is\",alpha_ratio" + ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": "The ratio of electronic polarizability to ionic polarizability is 1.534\n" + "text": [ + "The ratio of electronic polarizability to ionic polarizability is 1.534\n" + ] } ], "prompt_number": 9 @@ -163,7 +328,7 @@ { "cell_type": "code", "collapsed": false, - "input": "", + "input": [], "language": "python", "metadata": {}, "outputs": [] |