{
"metadata": {
"name": "",
"signature": "sha256:6c9d1e462fb51d212d5e8b8f597a34ef40452b9332c91d54e15e6a4dccd85074"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Dielectric materials"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 11.1, Page number 335"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"epsilon_0=8.854*10**-12;\n",
"A=10*10*10**-6; #area of capacitor in m^2\n",
"d=2*10**-3; #distance of seperation in m\n",
"C=10**-9; #capacitance in F\n",
"\n",
"#Calculation\n",
"epsilon_r=(C*d)/(epsilon_0*A);\n",
"epsilon_r=math.ceil(epsilon_r*10**2)/10**2; #rounding off to 2 decimals\n",
"\n",
"#Result\n",
"print(\"dielectric constant of material is\",epsilon_r);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"('dielectric constant of material is', 2258.87)\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 11.2, Page number 335"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable declaration\n",
"epsilon_0=8.854*10**-12;\n",
"epsilon_r=1.0000684; #dielectric constant of He gas\n",
"N=2.7*10**25; #concentration of dipoles per m^3\n",
"\n",
"#Calculation\n",
"#alpha_e=P/(N*E) and P=epsilon_0(epsilon_r-1)*E\n",
"#therefore alpha_e=epsilon_0(epsilon_r-1)/N\n",
"alpha_e=(epsilon_0*(epsilon_r-1))/N;\n",
"\n",
"#Result\n",
"print(\"electronic polarizability of He gas in Fm^2 is\",alpha_e);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"('electronic polarizability of He gas in Fm^2 is', 2.2430133333322991e-41)\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 11.3, Page number 336"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable declaration\n",
"epsilon_0=8.854*10**-12;\n",
"epsilon_r=6; #dielectric constant\n",
"E=100; #electric field intensity in V/m\n",
"\n",
"#Calculation\n",
"P=epsilon_0*(epsilon_r-1)*E;\n",
"\n",
"#Result\n",
"print(\"polarization in C/m^2 is\",P);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"('polarization in C/m^2 is', 4.426999999999999e-09)\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 11.4, Page number 336"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"epsilon_0=8.854*10**-12;\n",
"R=0.158; #radius of Ne in nm\n",
"\n",
"#Calculation\n",
"R=R*10**-9; #converting nm to m\n",
"alpha_e=4*math.pi*epsilon_0*R**3;\n",
"\n",
"#Result\n",
"print(\"electronic polarizability in Fm^2 is\",alpha_e);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"('electronic polarizability in Fm^2 is', 4.3885458748002144e-40)\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 11.5, Page number 336"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"epsilon_0=8.854*10**-12;\n",
"C=0.02; #capacitance in micro farad\n",
"epsilon_r=6; #dielectric constant\n",
"t=0.002; #thickness of mica in cm\n",
"d=0.002; #thickness of metal sheet in cm\n",
"\n",
"#Calculation\n",
"C=C*10**-6; #converting micro farad to farad\n",
"d=d*10**-2; #converting cm to m\n",
"A=(C*d)/(epsilon_0*epsilon_r);\n",
"A=A*10**3;\n",
"A=math.ceil(A*10**4)/10**4; #rounding off to 4 decimals\n",
"A1=A*10; #converting m**2 to cm**2\n",
"A1=math.ceil(A1*10**3)/10**3; #rounding off to 3 decimals\n",
"\n",
"#Result\n",
"print(\"area of metal sheet in m^2 is\",A,\"*10**-3\");\n",
"print(\"area of metal sheet in cm^2 is\",A1);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"('area of metal sheet in m^2 is', 7.5296, '*10**-3')\n",
"('area of metal sheet in cm^2 is', 75.296)\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 11.6, Page number 336"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"epsilon_0=8.854*10**-12;\n",
"E=1000; #electric field in V/m\n",
"P=4.3*10**-8; #polarization in C/m^2\n",
"\n",
"#Calculation\n",
"epsilon_r=(P/(E*epsilon_0)+1);\n",
"epsilon_r=math.ceil(epsilon_r*10**4)/10**4; #rounding off to 4 decimals\n",
"\n",
"#Result\n",
"print(\"dielectric constant is\",epsilon_r);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"('dielectric constant is', 5.8566)\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 11.7, Page number 337"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable declaration\n",
"epsilon_0=8.854*10**-12;\n",
"chi=4.94; #relative susceptibility\n",
"N=10**28; #number of dipoles per m^3\n",
"\n",
"#Calculation\n",
"#polarisation P=N*alpha*E and P=epsilon_0*chi*E. equate the two equations\n",
"#epsilon_0*chi*E=N*alpha*E\n",
"alpha=(epsilon_0*chi)/N;\n",
"\n",
"#Result\n",
"print(\"polarisability of material in F/m^2 is\",alpha);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"('polarisability of material in F/m^2 is', 4.373876e-39)\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}