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diff --git a/modern_physics_by_Satish_K._Gupta/chap16.ipynb b/modern_physics_by_Satish_K._Gupta/chap16.ipynb deleted file mode 100755 index a6266584..00000000 --- a/modern_physics_by_Satish_K._Gupta/chap16.ipynb +++ /dev/null @@ -1,964 +0,0 @@ -{
- "metadata": {
- "name": "",
- "signature": "sha256:03e25d70b6f5039934ebff67f76c18265eda838017719c81d51174de65a0d0cb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 16 Electromagnetic induction"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.1 Page no 508"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "R=5.0 #ohm\n",
- "t=2\n",
- "a=15\n",
- "b=8\n",
- "\n",
- "#Calculation\n",
- "e=-a*t**2-(b*t)-t\n",
- "I=-e/R\n",
- "\n",
- "#Result\n",
- "print\"Induced current is\", I,\"A\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Induced current is 15.6 A\n"
- ]
- }
- ],
- "prompt_number": 6
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.2 Page no 508"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "S1=75*10**-4 #m**2\n",
- "B1=0.8 #wb/m**2\n",
- "S2=100*10**-4\n",
- "B2=1.4\n",
- "t=0.05\n",
- "\n",
- "#Calculation\n",
- "a1=B1*S1\n",
- "a2=B2*S2\n",
- "a=a2-a1\n",
- "e=-a/t\n",
- "\n",
- "#Result\n",
- "print\"Induced e.m.f is\", e,\"Volt\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Induced e.m.f is -0.16 Volt\n"
- ]
- }
- ],
- "prompt_number": 9
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.3 Page no 508"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "a1=5.5*10**-4 #Wb\n",
- "a2=0.5*10**-4\n",
- "N=1000\n",
- "t=0.1\n",
- "R=10 #ohm\n",
- "\n",
- "#Calculation\n",
- "a=a2-a1\n",
- "a11=N*a\n",
- "e=-(a11/t)\n",
- "I1=e/R\n",
- "I2=I1*t\n",
- "\n",
- "#Result\n",
- "print\" Induced e.m.f produced is\",e,\"V\"\n",
- "print\" Charge flowing through the coil in 0.1 is\",I2,\"C\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- " Induced e.m.f produced is 5.0 V\n",
- " Charge flowing through the coil in 0.1 is 0.05 C\n"
- ]
- }
- ],
- "prompt_number": 27
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.5 Page no 509"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "B=2.5*10**-3 #Wb**-2\n",
- "L=1 #m\n",
- "v=30 #r.p.s\n",
- "\n",
- "#Calculation\n",
- "import math\n",
- "e=-B*math.pi*L**2*v\n",
- "\n",
- "#Result\n",
- "print\"The produced e.m.f. between its ends is\",round(e,3),\"V\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The produced e.m.f. between its ends is -0.236 V\n"
- ]
- }
- ],
- "prompt_number": 31
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.6 Page no 509"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "L=1.2 #m\n",
- "e=10**-2 #v\n",
- "B=5*10**-5 #tesla\n",
- "\n",
- "#Calculation\n",
- "import math\n",
- "V=e/(B*math.pi*L**2)\n",
- "\n",
- "#Result\n",
- "print\"The rate of rotation of the wheel is\",round(V,1),\"Rotation a**-1\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The rate of rotation of the wheel is 44.2 Rotation a**-1\n"
- ]
- }
- ],
- "prompt_number": 37
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.7 Page no 509"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "D=10\n",
- "L=0.50 #m\n",
- "B=0.40*10**-4 #T\n",
- "V=2 #r.p.s.\n",
- "\n",
- "#Calculation\n",
- "import math\n",
- "E=-B*math.pi*L**2*V\n",
- "\n",
- "#Result\n",
- "print\"The induced e.m.f. between the axle and the rim of the wheel is\",round(E*10**5,3),\"10**-5\",\"V\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The induced e.m.f. between the axle and the rim of the wheel is -6.283 10**-5 V\n"
- ]
- }
- ],
- "prompt_number": 45
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.8 Page no 509"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "B=0.2 #T\n",
- "r=0.1 #m\n",
- "R=2 #ohm\n",
- "D=20*math.pi #rad s**-1\n",
- "\n",
- "#Calculation\n",
- "import math\n",
- "V=D/(2*math.pi)\n",
- "E=-B*math.pi*r**2*V\n",
- "I=E/R\n",
- "\n",
- "#Result\n",
- "print\"(i) The potential difference is\",round(E,4),\"V\"\n",
- "print\"(ii) The induced current is\",round(I,4),\"A\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "(i) The potential difference is -0.0628 V\n",
- "(ii) The induced current is -0.0314 A\n"
- ]
- }
- ],
- "prompt_number": 56
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.9 Page no 509"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "B=8.0*10**-5 #Wb m**-2\n",
- "L=2 #m\n",
- "v=30 #m s**-1\n",
- "\n",
- "#Calculation\n",
- "e=B*L*v\n",
- "\n",
- "#Result\n",
- "print\"The vertical component of earth's field is\",e*10**3,\"10**-3\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The vertical component of earth's field is 4.8 10**-3\n"
- ]
- }
- ],
- "prompt_number": 61
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.10 Page no 509"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Givem\n",
- "l=10 #m\n",
- "v=5 #m/s\n",
- "Bh=0.30*10**-4 #Wb/m**2\n",
- "\n",
- "#Calculation\n",
- "e=Bh*l*v\n",
- "\n",
- "#Result\n",
- "print \"Instantaneous value of e.m.f. induced is\",e*10**3,\"*10**-3 V\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Instantaneous value of e.m.f. induced is 1.5 *10**-3 V\n"
- ]
- }
- ],
- "prompt_number": 64
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.11 Page no 509"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "B=0.3 #T\n",
- "v=10**-2 #m/s\n",
- "l=8*10**-2\n",
- "L=1\n",
- "v1=1.0\n",
- "l2=2*10**-2\n",
- "L1=8\n",
- "\n",
- "#Calculation\n",
- "e=B*l*v\n",
- "l=L/v1\n",
- "e1=B*l2*v\n",
- "t1=L1/v1\n",
- "\n",
- "#Result\n",
- "print\"(i) Voltage developed in the direction of motion normal to the longer side is\", e*10**3,\"mv\"\n",
- "print\"(ii) Voltage developed in the direction of motion normal to the shorter side is\",e1*10**3,\"mV\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "(i) Voltage developed in the direction of motion normal to the longer side is 0.24 mv\n",
- "(ii) Voltage developed in the direction of motion normal to the shorter side is 0.06 mV\n"
- ]
- }
- ],
- "prompt_number": 72
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.12 Page no 510"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "B=0.4 #T\n",
- "v=5 #m/s\n",
- "l=0.25 #m\n",
- "e=0.5\n",
- "R=5.0\n",
- "\n",
- "#Calculation\n",
- "e=B*l*v\n",
- "I=e/R\n",
- "\n",
- "#Result\n",
- "print\"New current is\",I,\"A\"\n",
- "print\"Direction is from the end S to R\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "New current is 0.1 A\n",
- "Direction is from the end S to R\n"
- ]
- }
- ],
- "prompt_number": 75
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.13 Page no 510"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "v=500 #m/s\n",
- "B=5*10**-4 #t\n",
- "a=30 #degree\n",
- "l=25 #m\n",
- "\n",
- "#Calculation\n",
- "import math\n",
- "Bv=B*math.sin(a*3.14/180.0)\n",
- "e=Bv*l*v\n",
- "\n",
- "#Result\n",
- "print\"Voltage difference is\", round(e,3),\"V\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Voltage difference is 3.124 V\n"
- ]
- }
- ],
- "prompt_number": 80
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.14 Page no 510"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "L=10*10**-3 #H\n",
- "I=4*10**-3 #A\n",
- "N=200.0\n",
- "\n",
- "#Calculation\n",
- "a=L*I\n",
- "A=a/N\n",
- "\n",
- "#Result\n",
- "print\"Total magnetic flux is\",a,\"Weber\"\n",
- "print\"Magnetic flux through the cross section is\",A,\"Weber\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Total magnetic flux is 4e-05 Weber\n",
- "Magnetic flux through the cross section is 2e-07 Weber\n"
- ]
- }
- ],
- "prompt_number": 85
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.15 Page no 510"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "L=10**-2 #H\n",
- "I1=0\n",
- "I2=1 #A\n",
- "l=1 \n",
- "t=0.01\n",
- "\n",
- "#Calculation\n",
- "e=-L*(l/t)\n",
- "\n",
- "#Result\n",
- "print\"Self induced e.m.f is\", e,\"V\"\n",
- "print\"The self-induced e.m.f. will act so as to oppose the growth of current.\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Self induced e.m.f is -1.0 V\n",
- "The self-induced e.m.f. will act so as to oppose the growth of current.\n"
- ]
- }
- ],
- "prompt_number": 89
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.16 Page no 510"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "n=1500 #turns/m\n",
- "A=2*10**-4 #m**2\n",
- "l=20 #A/s\n",
- "\n",
- "#Calculation\n",
- "import math\n",
- "e=-4*math.pi*n*A*l*10**-7\n",
- "\n",
- "#Result\n",
- "print\"Induced e.m.f. is\",round(e*10**6,2)*10**-6,\"V\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Induced e.m.f. is -7.54e-06 V\n"
- ]
- }
- ],
- "prompt_number": 97
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.17 Page no 511"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "e=50*10**-3 #V\n",
- "a=8\n",
- "b=4\n",
- "t=0.5\n",
- "\n",
- "#Calculation\n",
- "l=a-b\n",
- "M=e*t/l\n",
- "\n",
- "#Result\n",
- "print\"Mutual inductance is\",M*10**3,\"*10**-3 H\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Mutual inductance is 6.25 *10**-3 H\n"
- ]
- }
- ],
- "prompt_number": 101
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.18 Page no 511"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "n1=5000 #turns/m\n",
- "A=4*10**-4 #m**2\n",
- "n2l=200\n",
- "u=10**-7\n",
- "\n",
- "#Calculation\n",
- "import math\n",
- "M=4*math.pi*u*n1*n2l*A\n",
- "\n",
- "#Result\n",
- "print\"Mutual inductance is\", round(M*10**4,3),\"*10**-4 H\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Mutual inductance is 5.027 *10**-4 H\n"
- ]
- }
- ],
- "prompt_number": 109
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.19 Page no 511"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "N=1200\n",
- "A=12*10**-4\n",
- "r=15*10**-2 #m\n",
- "u=10**-7\n",
- "I=1.0\n",
- "N2=300\n",
- "I1=0\n",
- "I2=2\n",
- "t=0.05\n",
- "\n",
- "#Calculation\n",
- "import math\n",
- "n=N/(2*math.pi*r)\n",
- "B=4*math.pi*u*n\n",
- "a=B*A*N\n",
- "L=a/I\n",
- "a1=B*A*N2\n",
- "a11=a1*I1\n",
- "a12=a1*I2\n",
- "a13=a12-a11\n",
- "e=-a13/t\n",
- "\n",
- "#Result\n",
- "print\"(a) Self inductance is\", L*10**3,\"*10**-3 H\"\n",
- "print\"(b) Induced e.m.f is\", round(e,3),\"V\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "(a) Self inductance is 2.304 *10**-3 H\n",
- "(b) Induced e.m.f is -0.023 V\n"
- ]
- }
- ],
- "prompt_number": 124
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.20 Page no 511"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "A=25*10**-4\n",
- "N=500\n",
- "l=30.0*10**-2 #m\n",
- "I=2.5\n",
- "u=10**-7\n",
- "t=10.0**-3\n",
- "\n",
- "#Calculation\n",
- "import math\n",
- "n=N/l\n",
- "B=4*math.pi*u*n*I\n",
- "a=B*A*N\n",
- "a1=0-a\n",
- "e=-a1/t\n",
- "\n",
- "#Result\n",
- "print\"Average induced e.m.f. produced is\", round(e,3),\"V\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Average induced e.m.f. produced is 6.545 V\n"
- ]
- }
- ],
- "prompt_number": 130
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.21 Page no 511"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "N=25.0\n",
- "A=2*10**-4 #m**2\n",
- "q=7.5*10**-3\n",
- "R=0.50\n",
- "\n",
- "#Calculation\n",
- "B=R*q/(N*A)\n",
- "\n",
- "#Result\n",
- "print\"Field strength of the magnet is\" ,B,\"T\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Field strength of the magnet is 0.75 T\n"
- ]
- }
- ],
- "prompt_number": 136
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.22 Page no 512"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "B=0.50 #T\n",
- "l=15*10**-2 #m\n",
- "R=9.0*10**-3 #ohm\n",
- "v=12*10**-2 #m/s\n",
- "\n",
- "#Calculation\n",
- "e=B*v*l\n",
- "F=B*l*(e/R)\n",
- "P=F*v\n",
- "P1=e**2/R\n",
- "\n",
- "#Result\n",
- "print\"(a) Induced e.m.f is\", e*10**3,\"*10**3 V\"\n",
- "print\"The end P of the rod will become positive and the end Q will become negative\"\n",
- "print\"(b) on closing the switch, electrons collects at the end Q. Therefore , excess charge is built up i.e it doesn't open when switch is open\" \n",
- "print\"(c) The magnetic lorentz force on electron is cancelled due to the electric field set up across the two end\"\n",
- "print\"(d) Retarding force is\",F*10**2,\"*10**-2 N\"\n",
- "print\"(e) Power is\",P*10**3,\"*10*-3 W\"\n",
- "print\"(f) Dissipated power is\",P*10**3,\"*10**-3 W\"\n",
- "print\"(g) The motion of the rod does not cut field lines,hence no induced e.m.f. is produced\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "(a) Induced e.m.f is 9.0 *10**3 V\n",
- "The end P of the rod will become positive and the end Q will become negative\n",
- "(b) on closing the switch, electrons collects at the end Q. Therefore , excess charge is built up i.e it doesn't open when switch is open\n",
- "(c) The magnetic lorentz force on electron is cancelled due to the electric field set up across the two end\n",
- "(d) Retarding force is 7.5 *10**-2 N\n",
- "(e) Power is 9.0 *10*-3 W\n",
- "(f) Dissipated power is 9.0 *10**-3 W\n",
- "(g) The motion of the rod does not cut field lines,hence no induced e.m.f. is produced\n"
- ]
- }
- ],
- "prompt_number": 156
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.23 Page no 512"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "a1=20*10**-2\n",
- "a2=0.3*10**-2 #m\n",
- "x=15*10**-2\n",
- "I=2.0 #A\n",
- "u=10**-7\n",
- "\n",
- "#Calculation\n",
- "import math\n",
- "B1=u*2*math.pi*I*a1**2/((a1**2+x**2)**1.5)\n",
- "a=B1*math.pi*a2**2\n",
- "M=a/I\n",
- "\n",
- "#Result\n",
- "print\"(a) Flux is\", round(B1*10**6,3)*10**-6 ,\"T\"\n",
- "print\"(b) Mutual inductance is\",round(M*10**11,3)*10**-11,\"H\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "(a) Flux is 3.217e-06 T\n",
- "(b) Mutual inductance is 4.548e-11 H\n"
- ]
- }
- ],
- "prompt_number": 168
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 16.25 Page no 513"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Given\n",
- "N1=1500\n",
- "l1=80.0*10**-2\n",
- "l2=4*10**-2\n",
- "r2=2*10**-2\n",
- "I=3.0 #A\n",
- "\n",
- "#Calculation\n",
- "import math\n",
- "A2=math.pi*r**2\n",
- "n1=N1/l1\n",
- "a=4*math.pi*10**-7*n1*I*4*math.pi*10**-4*100\n",
- "M=a/I\n",
- "\n",
- "#Result\n",
- "print\"Flux is\",round( a*10**4,3),\"*10**-4 Wb\"\n",
- "print\"Mutual inductance is\",round(M*10**4,2),\"*10**-4 H\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Flux is 8.883 *10**-4 Wb\n",
- "Mutual inductance is 2.96 *10**-4 H\n"
- ]
- }
- ],
- "prompt_number": 181
- }
- ],
- "metadata": {}
- }
- ]
-}
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