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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 19: Superconductivity"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.1, Page 959"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"T_c = 6.2; # Critical temperature of lead in superconducting state, K\n",
"T = 4; # Temperature at which critical field of lead is to be found out, K\n",
"H_c0 = 0.064; # Critical field for lead at 0 K, MA/m\n",
"\n",
"#Calculation\n",
"H_cT = H_c0*(1-(T/T_c)**2); # Critical field for lead at 4 K, MA/m\n",
"\n",
"#Result\n",
"print \"The critical field for lead at 4 K = %5.3f MA/m\"%H_cT\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The critical field for lead at 4 K = 0.037 MA/m\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.2, Page 959"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import *\n",
"\n",
"#Variable declaration\n",
"T_c1 = 4.153; # Critical temperature of mercury for its one isotope, K\n",
"M1 = 200.59; # Mass of first isotope of mercury, amu\n",
"M2 = 204; # Mass of second isotope of mercury, amu \n",
"\n",
"#Calculation \n",
"# From isotopic effect of superconductivity,\n",
"# T_c2/T_c1 = sqrt(M1/M2), solving for T_c2\n",
"T_c2 = T_c1*sqrt(M1/M2); # Critical temperature of mercury for second isotope, K\n",
"\n",
"#Result\n",
"print \"The critical temperature of mercury for its isotope of mass 204 amu = %5.3f K\"%T_c2\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The critical temperature of mercury for its isotope of mass 204 amu = 4.118 K\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.3, Page 960"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"d = 1e-003; # Diameter of aluminium wire, m\n",
"r = d/2; # Radius of aluminium wire, m\n",
"H_c = 7.9e+003; # Critical magnetic field for Al, A/m\n",
"\n",
"#Calculation\n",
"I_c = 2*3.14*r*H_c; # Critical current through superconducting aluminium wire, A\n",
"\n",
"#Result\n",
"print \"The critical current through superconducting aluminium wire = %6.3f A\"%I_c\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The critical current through superconducting aluminium wire = 24.806 A\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.4, Page 960"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"T_c = 7.18; # Critical temperature of lead in superconducting state, K\n",
"H_c0 = 6.5e+004; # Critical field for lead at 0 K, A/m\n",
"# At T = 4.2 K\n",
"T = 4.2; # Temperature at which critical field of lead is to be found out, K\n",
"H_cT = H_c0*(1-(T/T_c)**2); # Critical field for lead at 4 K, A/m\n",
"d = 1e-003; # Diameter of lead wire, m\n",
"r = d/2; # Radius of lead wire, m\n",
"I_c = 2*3.14*r*H_cT; # Critical current through superconducting lead wire, A\n",
"J_c = I_c/(3.14*r**2); # Critical current density for superconducting lead wire, A/Sq. meter\n",
"print \"The critical current density at %3.1f K = %5.3e A/Sq.m\"%(T, J_c)\n",
"# At T = 7 K\n",
"T = 7; # Temperature at which critical field of lead is to be found out, K\n",
"H_cT = H_c0*(1-(T/T_c)**2); # Critical field for lead at 4 K, A/m\n",
"d = 1e-003; # Diameter of lead wire, m\n",
"r = d/2; # Radius of lead wire, m\n",
"I_c = 2*3.14*r*H_cT; # Critical current through superconducting lead wire, A\n",
"J_c = I_c/(3.14*r**2); # Critical current density for superconducting lead wire, A/Sq. meter\n",
"print \"The critical current density at %3.1f K = %4.2e A/Sq.m\"%(T, J_c)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The critical current density at 4.2 K = 1.710e+08 A/Sq.m\n",
"The critical current density at 7.0 K = 1.29e+07 A/Sq.m\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.5, Page 961"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"T1 = 3; # Initial temperature of lead wire, K\n",
"T2 = 7.1; # Final temperature of lead wire, K\n",
"lambda1 = 39.6; # Initial London penetration depth for lead, mm\n",
"lambda2 = 173; # Final London penetration depth for lead, mm\n",
"\n",
"#Calculations\n",
"# As lambda_T = lambda_0*(1-(T/T_c)^4)^(-1/2) so\n",
"# (lambda1/lambda2)^2 = (T_c^4 - T2^4)/(T_c^4 - T1^4)\n",
"# Solving for T_c\n",
"T_c = ((T2**4-T1**4*(lambda1/lambda2)**2)/(1-(lambda1/lambda2)**2))**(1./4);\n",
"\n",
"#Result\n",
"print \"The critical temperature of lead = %5.3f K\"%T_c\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The critical temperature of lead = 7.193 K\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.6, Page 962"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"T_c = 7.2; # Critical temperature of lead in superconducting state, K\n",
"T = 5; # Temperature at which lead loses its superconducting state, K\n",
"H_cT = 3.3e+004; # Critical magnetic field for superconducting lead at 5 K, A/m\n",
"\n",
"#Calculation\n",
"# As H_cT = H_c0*(1-(T/T_c)^2), solving for H_c0\n",
"H_c0 = H_cT/(1-(T/T_c)**2); # Critical field for lead at 0 K, A/m \n",
"\n",
"#Result\n",
"print \"The critical magnetic field for lead at 0 K = %4.2e A/m\"%H_c0\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The critical magnetic field for lead at 0 K = 6.37e+04 A/m\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.7, Page 962"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"H_c0 = 2e+005; # Critical field for niobium at 0 K, A/m \n",
"H_cT = 1e+005; # Critical magnetic field for superconducting niobium at 5 K, A/m\n",
"T = 8; # Temperature at which lead loses its superconducting state, K\n",
"\n",
"#Calculation\n",
"# As H_cT = H_c0*(1-(T/T_c)^2), solving for T_c\n",
"T_c = T/(1-H_cT/H_c0)**(1./2);\n",
"\n",
"#Result\n",
"print \"The critical temperature for niobium = %6.3f K\"%T_c\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The critical temperature for niobium = 11.314 K\n"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}
|
