{
"metadata": {
"name": "",
"signature": "sha256:145edbfaabde16eb44fa3dc5f3d7e002b74573834c4739b553449ef2b9fabc14"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter7:SUPERCONDUCTIVITY"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg1:pg-272"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Tc=3.7 #critical temperature in K\n",
"Hc_0=0.0306 #critical magnetic field in Tesla at 0K\n",
"T=2 #temperature in K\n",
"Hc=Hc_0*(1-(T/Tc)**2)\n",
"print\"Critical field at 2 K is \",round(Hc,4),\"Tesla\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Critical field at 2 K is 0.0217 Tesla\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg2:pg-272"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Tc=7.2 #transition temperature in K\n",
"T=5 #temperature in K\n",
"Hc_T=3.3e4 #critical magnetic field at 5K in A/m\n",
"Hc_0=Hc_T/(1-(T/Tc)**2)\n",
"print\"Maximum value of H at 0 K is \",\"{:.2e}\".format(Hc_0),\"A/m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum value of H at 0 K is 6.37e+04 A/m\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg3:pg-273"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Tc=7.2 #critical temperature in K\n",
"Hc_0=1 #let,critical magnetic field at 0K\n",
"Hc_T=0.1*Hc_0 #critical magnetic field at T Kelvin\n",
"T=sqrt(1-Hc_T/Hc_0)*Tc\n",
"print\"Temperature is \",round(T,2),\"K\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Temperature is 6.83 K\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg4:pg-273"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"T=4.2 #temperature in K\n",
"Hc_0=0.0803 #critical magnetic field at 0K in Wb/m**2\n",
"Tc=7.2 #critical temperature for Pb in K\n",
"Hc_T=Hc_0*(1-(T/Tc)**2)\n",
"print\"Critical field at 4.2 K is \",round(Hc_T,5),\"Tesla\"#answer is wrong in book"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Critical field at 4.2 K is 0.05298 Tesla\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg5:pg-273"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Hc_T=105e3 #critical magnetic field at T Kelvin in A/m\n",
"Hc_0=150e3 #critical magnetic field at 0K in A/m\n",
"Tc=9.2 #critical temperature in K\n",
"T=sqrt(1-Hc_T/Hc_0)*Tc\n",
"print\"Temperature is \",round(T,2),\"K\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Temperature is 5.04 K\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6:pg-274"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Hc_T=1e5 #critical magnetic field at 8K in A/m\n",
"T=8 #temperature in K\n",
"Hc_0=2e5 #critical magnetic field at 0K in A/m\n",
"Tc=T/sqrt(1-Hc_T/Hc_0)\n",
"print\"Transition temperature is \",round(Tc,1),\"K\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Transition temperature is 11.3 K\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg7:pg-274"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Tc=7.26 #critical temperature in K\n",
"Hc_0=8e5 #critical magnetic field at 0K in A/m\n",
"Hc_T=4e4 #critical magnetic field at T kelvin in A/m\n",
"T=sqrt(1-Hc_T/Hc_0)*Tc\n",
"print\"T =\",round(T,2),\"K\",\"\\nThe temperature of the metal should be held below\",round(T,2),\"K\" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"T = 7.08 K \n",
"The temperature of the metal should be held below 7.08 K\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg8:pg-275"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"T1=14 #temperature in K\n",
"T2=12 #temperature in K\n",
"T=4.2 #temperature in K\n",
"Hc_T1=0.176 #critical magnetic field at temperature T1\n",
"Hc_T2=0.528 #critical magnetic field at temperature T2\n",
"Tc=sqrt((Hc_T2*T1**2-Hc_T1*T2**2)/(Hc_T2-Hc_T1))\n",
"Tc=int(Tc*10)/10. #rounding off\n",
"Hc_0=Hc_T1/(1-(T1/Tc)**2)\n",
"Hc_T=Hc_0*(1-(T/Tc)**2)\n",
"print\"Transition temperature is \",Tc,\"K\"\n",
"print\"Critical field at 0 K is \",round(Hc_0,3),\"Tesla\"\n",
"print\"Critical field at 4.2 K is \",round(Hc_T,2),\"Tesla\"\n",
"#answers in book are wrong because value of T2 is taken as 13K in calculation which is wrong."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Transition temperature is 14.8 K\n",
"Critical field at 0 K is 1.673 Tesla\n",
"Critical field at 4.2 K is 1.54 Tesla\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg9:pg-275"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"D=1.0 #diameter of Pb wire in mm\n",
"Bc=0.0548 #in Tesla\n",
"mu_0=4*math.pi*1e-7 #absolute permeability of air in N/A**2\n",
"Ic=math.pi*D*1e-3*Bc/mu_0\n",
"print\"Current is \",int(Ic),\"amp\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current is 137 amp\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg10:pg-276"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Hc_0=6.5e3 #critical magnetic field at 0K in A/m\n",
"Tc=7.18 #critical temperature in K\n",
"Hc_T=4.5e3 #critical magnetic field at T Kelvin in A/m\n",
"T=sqrt(1-Hc_T/Hc_0)*Tc\n",
"print\"Temperature is \",round(T,2),\"K\"\n",
"D=2 #diameter of the lead wire in mm\n",
"r=D/2 \n",
"Ic=2*math.pi*r*1e-3*Hc_T\n",
"Jc=Ic/(math.pi*(r*1e-3)**2)\n",
"print\"Critical current density is \",\"{:.1e}\".format(Jc),\"A/m**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Temperature is 3.98 K\n",
"Critical current density is 9.0e+06 A/m**2\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg11:pg-281"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"T=3.5 #temperature in K\n",
"lamda_T=750 #penetration depth of Hg at 3.5K in Angstrom\n",
"Tc=4.153 #critical temperature in K\n",
"lamda_0=lamda_T*sqrt(round(1-(T/Tc)**4,3))\n",
"print\"Penetration depth at 0 K is\",round(lamda_0,1),\"Angstrom\"#answer is wrong in book because of calculation mistake "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Penetration depth at 0 K is 528.2 Angstrom\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg12:pg-281"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"m=9.1e-31 #mass of electron kg\n",
"mu_0=12.56e-7 #absolute permeability of air in N/A**2\n",
"e=1.6e-19 #charge of electron in coulomb\n",
"ns=1e28 #number of super electrons per meter cube\n",
"lamda_0=sqrt(m/(mu_0*ns*e**2))\n",
"lamda_0=round(lamda_0,9)*1e10\n",
"print\"Penetration depth at 0 K is \",int(lamda_0),\"Angstrom\"\n",
"Tc=3 #critical temperature in K\n",
"T=1. #temperature in K\n",
"lamda_T=lamda_0/sqrt(1-(T/Tc)**4)\n",
"print\"Penetration depth at 1 K is \",int(lamda_T),\"Angstrom\"\n",
"#in book lamda(at 3K) is printed,which is wrong. Correct notation is lamda(at 1K)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Penetration depth at 0 K is 530 Angstrom\n",
"Penetration depth at 1 K is 533 Angstrom\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg13:pg-286"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Tc=9.25 #critical temperature in K\n",
"T=0 #temperature in K\n",
"Kb=1.38e-23 #Boltzmann's constant in J/K\n",
"Eg=3.53*Kb*Tc/(1.6e-19)\n",
"h=6.63e-34 #planck constant joule-sec\n",
"c=3e8 #speed of light in m/sec\n",
"print\"Energy gap Eg is \",round(Eg*1e3,2),\"meV\"\n",
"lamda_min=h*c/round(Eg*1.6e-19,23)\n",
"print\"Minimum photon wavelength is \",\"{:.2e}\".format(lamda_min),\"m\"\n",
"print\" This wavelength lie in the far-infrared region of electromagnetic radiations.\"\n",
"v=round(Eg*1.6e-19,23)/h\n",
"print\"Frequency needed is \",\"{:.2e}\".format(v),\"s**-1\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Energy gap Eg is 2.82 meV\n",
"Minimum photon wavelength is 4.42e-04 m\n",
" This wavelength lie in the far-infrared region of electromagnetic radiations.\n",
"Frequency needed is 6.79e+11 s**-1\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg14:pg-286"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"M=200.59 #average atomic mass of Hg in amu\n",
"m=204 #mass of isotope in amu\n",
"T=4.153 #temperature in K\n",
"t=4.118 #temperature in K\n",
"dM=m-M\n",
"dTc=t-T\n",
"alpha=-(M*dTc/(dM*T))\n",
"print\"Isotope effect coefficient is \",round(alpha,3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Isotope effect coefficient is 0.496\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}