Upload equations.jsonl
Browse files- equations.jsonl +100 -100
equations.jsonl
CHANGED
|
@@ -1,100 +1,100 @@
|
|
| 1 |
-
{"
|
| 2 |
-
{"
|
| 3 |
-
{"
|
| 4 |
-
{"
|
| 5 |
-
{"
|
| 6 |
-
{"
|
| 7 |
-
{"
|
| 8 |
-
{"
|
| 9 |
-
{"
|
| 10 |
-
{"
|
| 11 |
-
{"
|
| 12 |
-
{"
|
| 13 |
-
{"
|
| 14 |
-
{"
|
| 15 |
-
{"
|
| 16 |
-
{"
|
| 17 |
-
{"
|
| 18 |
-
{"
|
| 19 |
-
{"
|
| 20 |
-
{"
|
| 21 |
-
{"
|
| 22 |
-
{"
|
| 23 |
-
{"
|
| 24 |
-
{"
|
| 25 |
-
{"
|
| 26 |
-
{"
|
| 27 |
-
{"
|
| 28 |
-
{"
|
| 29 |
-
{"
|
| 30 |
-
{"
|
| 31 |
-
{"
|
| 32 |
-
{"
|
| 33 |
-
{"
|
| 34 |
-
{"
|
| 35 |
-
{"
|
| 36 |
-
{"
|
| 37 |
-
{"
|
| 38 |
-
{"
|
| 39 |
-
{"
|
| 40 |
-
{"
|
| 41 |
-
{"
|
| 42 |
-
{"
|
| 43 |
-
{"
|
| 44 |
-
{"
|
| 45 |
-
{"
|
| 46 |
-
{"
|
| 47 |
-
{"
|
| 48 |
-
{"
|
| 49 |
-
{"
|
| 50 |
-
{"
|
| 51 |
-
{"
|
| 52 |
-
{"
|
| 53 |
-
{"
|
| 54 |
-
{"
|
| 55 |
-
{"
|
| 56 |
-
{"
|
| 57 |
-
{"
|
| 58 |
-
{"
|
| 59 |
-
{"
|
| 60 |
-
{"
|
| 61 |
-
{"
|
| 62 |
-
{"
|
| 63 |
-
{"
|
| 64 |
-
{"
|
| 65 |
-
{"
|
| 66 |
-
{"
|
| 67 |
-
{"
|
| 68 |
-
{"
|
| 69 |
-
{"
|
| 70 |
-
{"
|
| 71 |
-
{"
|
| 72 |
-
{"
|
| 73 |
-
{"
|
| 74 |
-
{"
|
| 75 |
-
{"
|
| 76 |
-
{"
|
| 77 |
-
{"
|
| 78 |
-
{"
|
| 79 |
-
{"
|
| 80 |
-
{"
|
| 81 |
-
{"
|
| 82 |
-
{"
|
| 83 |
-
{"
|
| 84 |
-
{"
|
| 85 |
-
{"
|
| 86 |
-
{"
|
| 87 |
-
{"
|
| 88 |
-
{"
|
| 89 |
-
{"
|
| 90 |
-
{"
|
| 91 |
-
{"
|
| 92 |
-
{"
|
| 93 |
-
{"
|
| 94 |
-
{"
|
| 95 |
-
{"
|
| 96 |
-
{"
|
| 97 |
-
{"
|
| 98 |
-
{"
|
| 99 |
-
{"
|
| 100 |
-
{"
|
|
|
|
| 1 |
+
{"symbols": ["f", "sigma", "theta"], "symbol_descs": ["the probability density function value", "the standard deviation of the Gaussian distribution", "the variable of the Gaussian distribution"], "symbol_properties": ["O", "V", "V"], "expression": "exp(-(theta/sigma)**2/2)/(sqrt(2*pi)*sigma)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.6.2"}
|
| 2 |
+
{"symbols": ["f", "sigma", "theta", "theta1"], "symbol_descs": ["the result of the Gaussian distribution function", "the standard deviation of the Gaussian distribution", "the variable or input value for the Gaussian distribution", "the mean of the Gaussian distribution"], "symbol_properties": ["O", "V", "V", "V"], "expression": "exp(-((theta-theta1)/sigma)**2/2)/(sqrt(2*pi)*sigma)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.6.2b"}
|
| 3 |
+
{"symbols": ["x1", "x", "u", "c", "t"], "symbol_descs": ["the transformed x-coordinate in a relativistic frame of reference", "the original x-coordinate", "the relative velocity between the two frames of reference", "the speed of light", "time"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "(x-u*t)/sqrt(1-u**2/c**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.15.3x"}
|
| 4 |
+
{"symbols": ["t1", "x", "c", "u", "t"], "symbol_descs": ["the relativistic time in the observer's frame", "the position of the event in the observer's frame", "the speed of light", "the relative velocity between the observer's frame and the object's frame", "the time of the event in the object's frame"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "(t-u*x/c**2)/sqrt(1-u**2/c**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.15.3t"}
|
| 5 |
+
{"symbols": ["v1", "c", "v", "u"], "symbol_descs": ["the resultant velocity of two objects after a relativistic addition", "the speed of light", "the velocity of one of the objects", "the velocity of the other object"], "symbol_properties": ["O", "V", "V", "V"], "expression": "(u+v)/(1+u*v/c**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.16.6"}
|
| 6 |
+
{"symbols": ["theta1", "n", "theta2"], "symbol_descs": ["the angle of refraction", "the refractive index", "the angle of incidence"], "symbol_properties": ["O", "V", "V"], "expression": "arcsin(n*sin(theta2))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.26.2"}
|
| 7 |
+
{"symbols": ["foc", "d1", "d2", "n"], "symbol_descs": ["the focal length of a combination of two optical components", "the distance from the first optical component to the object", "the distance from the second optical component to the image", "the refractive index of the medium between the two optical components"], "symbol_properties": ["O", "V", "V", "V"], "expression": "1/(1/d1+n/d2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.27.6"}
|
| 8 |
+
{"symbols": ["x", "x1", "x2", "theta1", "theta2"], "symbol_descs": ["the distance between two points", "the magnitude of the first vector", "the magnitude of the second vector", "the angle of the first vector", "the angle of the second vector"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "sqrt(x1**2+x2**2-2*x1*x2*cos(theta1-theta2))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.29.16"}
|
| 9 |
+
{"symbols": ["Int", "Int_0", "theta", "n"], "symbol_descs": ["the resulting intensity", "the initial intensity", "the angle of diffraction", "the number of slits"], "symbol_properties": ["O", "V", "V", "V"], "expression": "Int_0*sin(n*theta/2)**2/sin(theta/2)**2", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.30.3"}
|
| 10 |
+
{"symbols": ["theta", "lambd", "d", "n"], "symbol_descs": ["the angle of diffraction", "the wavelength of the incident light", "the distance between the slits or the grating spacing", "the order of the diffraction pattern"], "symbol_properties": ["O", "V", "V", "V"], "expression": "arcsin(lambd/(n*d))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.30.5"}
|
| 11 |
+
{"symbols": ["Pwr", "epsilon", "c", "Ef", "r", "omega", "omega_0"], "symbol_descs": ["the power of the scattered radiation", "the electric constant (permittivity of free space)", "the speed of light", "the strength of the external electric field", "the radius of the scattering object or atom", "the frequency of the external electric field", "the natural frequency of the oscillator or resonant frequency"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "(1/2*epsilon*c*Ef**2)*(8*pi*r**2/3)*(omega**4/(omega**2-omega_0**2)**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.32.17"}
|
| 12 |
+
{"symbols": ["Int", "I1", "I2", "delta"], "symbol_descs": ["the resultant intensity of two wave sources", "the intensity of the first wave source", "the intensity of the second wave source", "the phase difference between the two wave sources"], "symbol_properties": ["O", "V", "V", "V"], "expression": "I1+I2+2*sqrt(I1*I2)*cos(delta)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.37.4"}
|
| 13 |
+
{"symbols": ["x", "x1", "omega", "t", "alpha"], "symbol_descs": ["the resulting displacement", "the initial amplitude", "the angular frequency", "the time", "the non-linearity coefficient"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "x1*(cos(omega*t)+alpha*cos(omega*t)**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.50.26"}
|
| 14 |
+
{"symbols": ["Ef", "epsilon", "p_d", "r", "x", "y", "z"], "symbol_descs": ["the electric field strength at a point", "the electric constant (permittivity of free space)", "the electric dipole moment", "the distance from the dipole to the point where the field is being measured", "the x-coordinate of the point where the field is being measured", "the y-coordinate of the point where the field is being measured", "the z-coordinate of the point where the field is being measured"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "p_d/(4*pi*epsilon)*3*z/r**5*sqrt(x**2+y**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.6.15a"}
|
| 15 |
+
{"symbols": ["n", "n_0", "kb", "T", "theta", "p_d", "Ef"], "symbol_descs": ["the carrier density", "the equilibrium carrier density", "the Boltzmann constant", "the temperature in Kelvin", "the angle between the electric field and the carrier movement direction", "the dipole moment of the carrier", "the electric field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "n_0*(1+p_d*Ef*cos(theta)/(kb*T))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.11.17"}
|
| 16 |
+
{"symbols": ["Pol", "n", "alpha", "epsilon", "Ef"], "symbol_descs": ["the polarization of a material", "the number density of polarizable units", "the polarizability of a unit", "the permittivity of free space or a constant", "the external electric field"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "n*alpha/(1-(n*alpha/3))*epsilon*Ef", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.11.27"}
|
| 17 |
+
{"symbols": ["theta", "n", "alpha"], "symbol_descs": ["the resulting angle or parameter", "the number of terms or iterations", "the angle of incidence or a constant factor"], "symbol_properties": ["O", "V", "V"], "expression": "1+n*alpha/(1-(n*alpha/3))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.11.28"}
|
| 18 |
+
{"symbols": ["Volt", "q", "epsilon", "r", "v", "c"], "symbol_descs": ["the electric potential", "the electric charge", "the electric constant (permittivity of free space)", "the distance from the charge", "the velocity of the charge", "the speed of light"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "q/(4*pi*epsilon*r*(1-v/c))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.21.32"}
|
| 19 |
+
{"symbols": ["E_n", "g_", "h", "Jz", "mom", "B"], "symbol_descs": ["the energy of the nth state", "the g-factor of the particle or atom", "the Planck constant", "the z-component of the total angular momentum", "the magnetic moment of the particle or atom", "the magnetic field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "g_*mom*B*Jz/(h/(2*pi))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.34.29b"}
|
| 20 |
+
{"symbols": ["n", "n_0", "kb", "T", "mom", "B"], "symbol_descs": ["the number of particles in a given state", "the number of particles at equilibrium", "the Boltzmann constant", "the temperature of the system", "the magnetic moment of a particle", "the magnetic field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "n_0/(exp(mom*B/(kb*T))+exp(-mom*B/(kb*T)))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.35.18"}
|
| 21 |
+
{"symbols": ["M", "n_rho", "mom", "B", "kb", "T"], "symbol_descs": ["the magnetization of a material", "the density of magnetic moments", "the magnetic moment of a particle", "the magnetic field strength", "the Boltzmann constant", "the temperature in Kelvin"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "n_rho*mom*tanh(mom*B/(kb*T))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.35.21"}
|
| 22 |
+
{"symbols": ["f", "mom", "H", "kb", "T", "alpha", "epsilon", "c", "M"], "symbol_descs": ["the resultant value of the function", "the momentum of an object or particle", "the magnetic field strength", "the Boltzmann constant", "the temperature in Kelvin", "the polarizability of a medium or molecule", "the electric permittivity of a medium", "the speed of light in vacuum", "the magnetization of a material"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V", "V", "V"], "expression": "mom*H/(kb*T)+(mom*alpha)/(epsilon*c**2*kb*T)*M", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.36.38"}
|
| 23 |
+
{"symbols": ["E_n", "h", "omega", "kb", "T"], "symbol_descs": ["the energy of the nth mode of a quantum harmonic oscillator", "the Planck constant", "the angular frequency of the oscillator", "the Boltzmann constant", "the temperature of the system"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "(h/(2*pi))*omega/(exp((h/(2*pi))*omega/(kb*T))-1)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.4.33"}
|
| 24 |
+
{"symbols": ["prob", "E_n", "t", "h"], "symbol_descs": ["the probability of finding a particle in a particular state", "the energy of the nth state of a quantum system", "time", "the Planck constant"], "symbol_properties": ["O", "V", "V", "V"], "expression": "sin(E_n*t/(h/(2*pi)))**2", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.8.54"}
|
| 25 |
+
{"symbols": ["prob", "p_d", "Ef", "t", "h", "omega", "omega_0"], "symbol_descs": ["the transition probability of an atomic system", "the dipole moment of the transition", "the amplitude of the external electric field", "the interaction time between the atomic system and the external field", "the Planck constant", "the frequency of the external field", "the resonant frequency of the atomic transition"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "(p_d*Ef*t/(h/(2*pi)))*sin((omega-omega_0)*t/2)**2/((omega-omega_0)*t/2)**2", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.9.52"}
|
| 26 |
+
{"symbols": ["v", "E_n", "d", "k", "h"], "symbol_descs": ["the velocity of a particle or wave", "the nth energy level of a quantum system", "the distance between particles or the diameter of a nanoparticle", "Boltzmann's constant, relating energy to temperature", "the Planck constant, relating energy to frequency"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "2*E_n*d**2*k/(h/(2*pi))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.13.18"}
|
| 27 |
+
{"symbols": ["E_n", "U", "k", "d"], "symbol_descs": ["the n-th energy level", "the characteristic potential energy", "the wave number", "the distance between potential energy wells"], "symbol_properties": ["O", "V", "V", "V"], "expression": "2*U*(1-cos(k*d))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.15.12"}
|
| 28 |
+
{"symbols": ["f", "beta", "alpha", "theta"], "symbol_descs": ["the resultant value of the function", "a scaling factor", "a coefficient modifying the cosine term", "the angle in radians"], "symbol_properties": ["O", "V", "V", "V"], "expression": "beta*(1+alpha*cos(theta))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.17.37"}
|
| 29 |
+
{"symbols": ["E_n", "m", "q", "h", "n", "epsilon"], "symbol_descs": ["the energy of the nth energy level", "the mass of the electron", "the elementary charge", "the Planck constant", "the principal quantum number", "the electric constant (permittivity of free space)"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "-m*q**4/(2*(4*pi*epsilon)**2*(h/(2*pi))**2)*(1/n**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.19.51"}
|
| 30 |
+
{"symbols": ["f", "theta"], "symbol_descs": ["the probability density function of a standard normal distribution", "the variable of the standard normal distribution, typically representing a z-score or standardized value"], "symbol_properties": ["O", "V"], "expression": "exp(-theta**2/2)/sqrt(2*pi)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.6.2a"}
|
| 31 |
+
{"symbols": ["d", "x1", "x2", "y1", "y2"], "symbol_descs": ["the distance between two points", "the x-coordinate of the first point", "the x-coordinate of the second point", "the y-coordinate of the first point", "the y-coordinate of the second point"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "sqrt((x2-x1)**2+(y2-y1)**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.8.14"}
|
| 32 |
+
{"symbols": ["F", "m1", "m2", "G", "x1", "x2", "y1", "y2", "z1", "z2"], "symbol_descs": ["the gravitational force between two objects", "the mass of the first object", "the mass of the second object", "the gravitational constant", "the x-coordinate of the first object", "the x-coordinate of the second object", "the y-coordinate of the first object", "the y-coordinate of the second object", "the z-coordinate of the first object", "the z-coordinate of the second object"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V", "V", "V", "V"], "expression": "G*m1*m2/((x2-x1)**2+(y2-y1)**2+(z2-z1)**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.9.18"}
|
| 33 |
+
{"symbols": ["m", "m_0", "v", "c"], "symbol_descs": ["the relativistic mass of an object", "the object's rest mass", "the object's velocity", "the speed of light"], "symbol_properties": ["O", "V", "V", "V"], "expression": "m_0/sqrt(1-v**2/c**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.10.7"}
|
| 34 |
+
{"symbols": ["A", "x1", "x2", "x3", "y1", "y2", "y3"], "symbol_descs": ["the resulting sum of products", "the first coefficient", "the second coefficient", "the third coefficient", "the first variable or value", "the second variable or value", "the third variable or value"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "x1*y1+x2*y2+x3*y3", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.11.19"}
|
| 35 |
+
{"symbols": ["F", "mu", "Nn"], "symbol_descs": ["the frictional force", "the coefficient of friction", "the normal force"], "symbol_properties": ["O", "V", "V"], "expression": "mu*Nn", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.12.1"}
|
| 36 |
+
{"symbols": ["F", "q1", "q2", "epsilon", "r"], "symbol_descs": ["the electrostatic force between two charges", "the first electric charge", "the second electric charge", "the electric constant (permittivity of free space)", "the distance between the centers of the two charges"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "q1*q2*r/(4*pi*epsilon*r**3)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.12.2"}
|
| 37 |
+
{"symbols": ["Ef", "q1", "epsilon", "r"], "symbol_descs": ["the electric field at a given point", "the charge of the object generating the electric field", "the electric constant (permittivity of free space)", "the distance from the charge to the point where the electric field is being measured"], "symbol_properties": ["O", "V", "V", "V"], "expression": "q1*r/(4*pi*epsilon*r**3)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.12.4"}
|
| 38 |
+
{"symbols": ["F", "q2", "Ef"], "symbol_descs": ["the force experienced by an object", "the charge of the object", "the electric field strength"], "symbol_properties": ["O", "V", "V"], "expression": "q2*Ef", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.12.5"}
|
| 39 |
+
{"symbols": ["F", "q", "Ef", "B", "v", "theta"], "symbol_descs": ["the resultant force on a charged particle", "the charge of the particle", "the external electric field strength", "the magnetic field strength", "the velocity of the charged particle", "the angle between the particle's velocity and the magnetic field"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "q*(Ef+B*v*sin(theta))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.12.11"}
|
| 40 |
+
{"symbols": ["K", "m", "v", "u", "w"], "symbol_descs": ["the kinetic energy of an object", "the mass of the object", "the object's velocity in the x-direction", "the object's velocity in the y-direction", "the object's velocity in the z-direction"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "1/2*m*(v**2+u**2+w**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.13.4"}
|
| 41 |
+
{"symbols": ["U", "m1", "m2", "r1", "r2", "G"], "symbol_descs": ["the potential energy of two objects", "the mass of the first object", "the mass of the second object", "the initial distance between the two objects", "the final distance between the two objects", "the gravitational constant"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "G*m1*m2*(1/r2-1/r1)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.13.12"}
|
| 42 |
+
{"symbols": ["U", "m", "g", "z"], "symbol_descs": ["the potential energy of an object", "the mass of the object", "the acceleration due to gravity", "the height of the object above a reference point"], "symbol_properties": ["O", "V", "V", "V"], "expression": "m*g*z", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.14.3"}
|
| 43 |
+
{"symbols": ["U", "k_spring", "x"], "symbol_descs": ["the potential energy of the spring", "the spring constant", "the displacement from the spring's equilibrium position"], "symbol_properties": ["O", "V", "V"], "expression": "1/2*k_spring*x**2", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.14.4"}
|
| 44 |
+
{"symbols": ["p", "m_0", "v", "c"], "symbol_descs": ["the relativistic momentum of an object", "the object's rest mass", "the object's velocity", "the speed of light"], "symbol_properties": ["O", "V", "V", "V"], "expression": "m_0*v/sqrt(1-v**2/c**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.15.1"}
|
| 45 |
+
{"symbols": ["r", "m1", "m2", "r1", "r2"], "symbol_descs": ["the center of mass of a system of two objects", "the mass of the first object", "the mass of the second object", "the position of the first object", "the position of the second object"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "(m1*r1+m2*r2)/(m1+m2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.18.4"}
|
| 46 |
+
{"symbols": ["tau", "r", "F", "theta"], "symbol_descs": ["the torque exerted on an object", "the distance from the axis of rotation to the point where the force is applied", "the magnitude of the force applied", "the angle between the force vector and the radius vector"], "symbol_properties": ["O", "V", "V", "V"], "expression": "r*F*sin(theta)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.18.12"}
|
| 47 |
+
{"symbols": ["L", "m", "r", "v", "theta"], "symbol_descs": ["the angular momentum of an object", "the mass of the object", "the radius of the circular path", "the velocity of the object", "the angle between the velocity vector and the radius vector"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "m*r*v*sin(theta)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.18.14"}
|
| 48 |
+
{"symbols": ["E_n", "m", "omega", "omega_0", "x"], "symbol_descs": ["the quantum mechanical energy of the nth state", "the mass of the object", "the angular frequency of the perturbation", "the natural angular frequency", "the displacement from the equilibrium position"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "1/2*m*(omega**2+omega_0**2)*1/2*x**2", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.24.6"}
|
| 49 |
+
{"symbols": ["Volt", "q", "C"], "symbol_descs": ["the voltage across a capacitor", "the electric charge stored on the capacitor", "the capacitance of the capacitor"], "symbol_properties": ["O", "V", "V"], "expression": "q/C", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.25.13"}
|
| 50 |
+
{"symbols": ["k", "omega", "c"], "symbol_descs": ["the wave number", "the angular frequency", "the speed of light"], "symbol_properties": ["O", "V", "V"], "expression": "omega/c", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.29.4"}
|
| 51 |
+
{"symbols": ["Pwr", "q", "a", "epsilon", "c"], "symbol_descs": ["the power of an electromagnetic wave", "the charge of a particle", "the acceleration of the charged particle", "the electric constant or permittivity of free space", "the speed of light"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "q**2*a**2/(6*pi*epsilon*c**3)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.32.5"}
|
| 52 |
+
{"symbols": ["omega", "q", "v", "B", "p"], "symbol_descs": ["the angular frequency of the particle", "the charge of the particle", "the velocity of the particle", "the magnetic field strength", "the momentum of the particle"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "q*v*B/p", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.34.8"}
|
| 53 |
+
{"symbols": ["omega", "c", "v", "omega_0"], "symbol_descs": ["the relativistic angular frequency of an object", "the speed of light", "the object's velocity", "the object's proper angular frequency (at rest)"], "symbol_properties": ["O", "V", "V", "V"], "expression": "omega_0/(1-v/c)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.34.1"}
|
| 54 |
+
{"symbols": ["omega", "c", "v", "omega_0"], "symbol_descs": ["the relativistic angular frequency", "the speed of light", "the object's velocity", "the object's rest angular frequency"], "symbol_properties": ["O", "V", "V", "V"], "expression": "(1+v/c)/sqrt(1-v**2/c**2)*omega_0", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.34.14"}
|
| 55 |
+
{"symbols": ["E_n", "omega", "h"], "symbol_descs": ["the quantized energy of a harmonic oscillator", "the angular frequency of the oscillator", "the Planck constant"], "symbol_properties": ["O", "V", "V"], "expression": "(h/(2*pi))*omega", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.34.27"}
|
| 56 |
+
{"symbols": ["r", "m", "q", "h", "epsilon"], "symbol_descs": ["the radius of the electron's orbit", "the mass of the electron", "the charge of the electron", "the Planck constant", "the electric constant (permittivity of free space)"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "4*pi*epsilon*(h/(2*pi))**2/(m*q**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.38.12"}
|
| 57 |
+
{"symbols": ["E_n", "pr", "V"], "symbol_descs": ["the average kinetic energy of the molecules in an ideal gas", "the pressure of the gas", "the volume of the gas"], "symbol_properties": ["O", "V", "V"], "expression": "3/2*pr*V", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.39.1"}
|
| 58 |
+
{"symbols": ["E_n", "gamma", "pr", "V"], "symbol_descs": ["the internal energy of an ideal gas", "the adiabatic index of the gas", "the pressure of the gas", "the volume of the gas"], "symbol_properties": ["O", "V", "V", "V"], "expression": "1/(gamma-1)*pr*V", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.39.11"}
|
| 59 |
+
{"symbols": ["pr", "n", "T", "V", "kb"], "symbol_descs": ["the pressure of an ideal gas", "the number of moles of gas", "the temperature of the gas in Kelvin", "the volume of the gas", "the Boltzmann constant"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "n*kb*T/V", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.39.22"}
|
| 60 |
+
{"symbols": ["n", "n_0", "m", "x", "T", "g", "kb"], "symbol_descs": ["the density of particles at a given point", "the density of particles at the reference point", "the mass of a particle", "the height or distance from the reference point", "the temperature in Kelvin", "the acceleration due to gravity", "the Boltzmann constant"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "n_0*exp(-m*g*x/(kb*T))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.40.1"}
|
| 61 |
+
{"symbols": ["L_rad", "omega", "T", "h", "kb", "c"], "symbol_descs": ["the radiated power per unit area per unit solid angle per unit frequency", "the angular frequency of the radiation", "the temperature of the blackbody", "the Planck constant", "the Boltzmann constant", "the speed of light"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "h/(2*pi)*omega**3/(pi**2*c**2*(exp((h/(2*pi))*omega/(kb*T))-1))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.41.16"}
|
| 62 |
+
{"symbols": ["v", "mu_drift", "q", "Volt", "d"], "symbol_descs": ["the drift velocity of a charged particle", "the mobility of the charged particle", "the charge of the particle", "the applied voltage", "the distance over which the voltage is applied"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "mu_drift*q*Volt/d", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.43.16"}
|
| 63 |
+
{"symbols": ["D", "mob", "T", "kb"], "symbol_descs": ["the diffusion coefficient", "the mobility of charge carriers", "the temperature in Kelvin", "the Boltzmann constant"], "symbol_properties": ["O", "V", "V", "V"], "expression": "mob*kb*T", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.43.31"}
|
| 64 |
+
{"symbols": ["kappa", "gamma", "kb", "A", "v"], "symbol_descs": ["the isentropic expansion factor", "the adiabatic index", "Boltzmann's constant", "a constant area", "the velocity"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "1/(gamma-1)*kb*v/A", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.43.43"}
|
| 65 |
+
{"symbols": ["E_n", "n", "kb", "T", "V1", "V2"], "symbol_descs": ["the energy change of an ideal gas", "the number of moles of the gas", "the Boltzmann constant", "the temperature of the gas in Kelvin", "the initial volume of the gas", "the final volume of the gas"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "n*kb*T*ln(V2/V1)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.44.4"}
|
| 66 |
+
{"symbols": ["c", "gamma", "pr", "rho"], "symbol_descs": ["the speed of sound", "the adiabatic index or heat capacity ratio", "the pressure of the gas or fluid", "the density of the gas or fluid"], "symbol_properties": ["O", "V", "V", "V"], "expression": "sqrt(gamma*pr/rho)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.47.23"}
|
| 67 |
+
{"symbols": ["E_n", "m", "v", "c"], "symbol_descs": ["the total energy of an object", "the relativistic mass of an object", "the object's velocity", "the speed of light"], "symbol_properties": ["O", "V", "V", "V"], "expression": "m*c**2/sqrt(1-v**2/c**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "I.48.2"}
|
| 68 |
+
{"symbols": ["Pwr", "kappa", "T1", "T2", "A", "d"], "symbol_descs": ["the power transferred", "the thermal conductivity of the material", "the initial temperature", "the final temperature", "the cross-sectional area of the material", "the distance over which the heat is transferred"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "kappa*(T2-T1)*A/d", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.2.42"}
|
| 69 |
+
{"symbols": ["flux", "Pwr", "r"], "symbol_descs": ["the radiant flux of an object", "the power emitted by the object", "the distance from the object"], "symbol_properties": ["O", "V", "V"], "expression": "Pwr/(4*pi*r**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.3.24"}
|
| 70 |
+
{"symbols": ["Volt", "q", "epsilon", "r"], "symbol_descs": ["the electric potential at a given point", "the charge of an object", "the electric constant (permittivity of free space)", "the distance from the charge to the point where the potential is being measured"], "symbol_properties": ["O", "V", "V", "V"], "expression": "q/(4*pi*epsilon*r)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.4.23"}
|
| 71 |
+
{"symbols": ["Volt", "epsilon", "p_d", "theta", "r"], "symbol_descs": ["the electric potential at a given point", "the electric constant (permittivity of free space)", "the dipole moment", "the angle between the dipole axis and the vector to the point", "the distance from the dipole to the point"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "1/(4*pi*epsilon)*p_d*cos(theta)/r**2", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.6.11"}
|
| 72 |
+
{"symbols": ["Ef", "epsilon", "p_d", "theta", "r"], "symbol_descs": ["the electric field", "the electric constant or permittivity of the medium", "the dipole moment", "the angle between the dipole axis and the position vector", "the distance from the dipole to the point where the electric field is being measured"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "p_d/(4*pi*epsilon)*3*cos(theta)*sin(theta)/r**3", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.6.15b"}
|
| 73 |
+
{"symbols": ["E_n", "q", "epsilon", "d"], "symbol_descs": ["the electric potential energy", "the charge of an object", "the electric constant (permittivity of free space)", "the distance between charges"], "symbol_properties": ["O", "V", "V", "V"], "expression": "3/5*q**2/(4*pi*epsilon*d)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.8.7"}
|
| 74 |
+
{"symbols": ["E_den", "epsilon", "Ef"], "symbol_descs": ["the energy density", "the electric permittivity", "the electric field strength"], "symbol_properties": ["O", "V", "V"], "expression": "epsilon*Ef**2/2", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.8.31"}
|
| 75 |
+
{"symbols": ["Ef", "sigma_den", "epsilon", "chi"], "symbol_descs": ["the electric field", "the surface charge density", "the electric constant (permittivity of free space)", "the electric susceptibility of the medium"], "symbol_properties": ["O", "V", "V", "V"], "expression": "sigma_den/epsilon*1/(1+chi)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.10.9"}
|
| 76 |
+
{"symbols": ["x", "q", "Ef", "m", "omega_0", "omega"], "symbol_descs": ["the displacement of an object from its equilibrium position", "the electric charge of the object", "the external electric field strength", "the mass of the object", "the natural angular frequency of the oscillation", "the angular frequency of the external force"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "q*Ef/(m*(omega_0**2-omega**2))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.11.3"}
|
| 77 |
+
{"symbols": ["Pol", "n_rho", "p_d", "Ef", "kb", "T"], "symbol_descs": ["the polarization of a medium", "the density of molecules or dipoles", "the dipole moment of a molecule", "the external electric field strength", "the Boltzmann constant", "the temperature in Kelvin"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "n_rho*p_d**2*Ef/(3*kb*T)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.11.20"}
|
| 78 |
+
{"symbols": ["B", "epsilon", "c", "I", "r"], "symbol_descs": ["the magnetic field", "the electric constant (permittivity of free space)", "the speed of light", "the electric current", "the distance from the current-carrying wire"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "1/(4*pi*epsilon*c**2)*2*I/r", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.13.17"}
|
| 79 |
+
{"symbols": ["rho_c", "rho_c_0", "v", "c"], "symbol_descs": ["the critical density of the universe at a given velocity", "the critical density of the universe at rest", "the velocity of the object or frame of reference", "the speed of light"], "symbol_properties": ["O", "V", "V", "V"], "expression": "rho_c_0/sqrt(1-v**2/c**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.13.23"}
|
| 80 |
+
{"symbols": ["j", "rho_c_0", "v", "c"], "symbol_descs": ["the current density of a charged object", "the object's rest charge density", "the object's velocity", "the speed of light"], "symbol_properties": ["O", "V", "V", "V"], "expression": "rho_c_0*v/sqrt(1-v**2/c**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.13.34"}
|
| 81 |
+
{"symbols": ["E_n", "mom", "B", "theta"], "symbol_descs": ["the normal component of the electric field", "the magnetic moment of a magnet", "the magnetic field strength", "the angle between the magnetic moment and the magnetic field"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-mom*B*cos(theta)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.15.4"}
|
| 82 |
+
{"symbols": ["E_n", "p_d", "Ef", "theta"], "symbol_descs": ["the normal component of the electric field at the surface", "the dipole moment per unit area", "the external electric field", "the angle between the dipole moment and the external electric field"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-p_d*Ef*cos(theta)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.15.5"}
|
| 83 |
+
{"symbols": ["k", "omega", "c", "d"], "symbol_descs": ["the wave number", "the angular frequency", "the speed of the wave", "the diameter or thickness of the waveguide or medium"], "symbol_properties": ["O", "V", "V", "V"], "expression": "sqrt(omega**2/c**2-pi**2/d**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.24.17"}
|
| 84 |
+
{"symbols": ["flux", "epsilon", "c", "Ef"], "symbol_descs": ["the energy flux density", "the electric constant or permittivity of free space", "the speed of light", "the magnitude of the electric field"], "symbol_properties": ["O", "V", "V", "V"], "expression": "epsilon*c*Ef**2", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.27.16"}
|
| 85 |
+
{"symbols": ["E_den", "epsilon", "Ef"], "symbol_descs": ["the energy density", "the electric permittivity", "the electric field strength"], "symbol_properties": ["O", "V", "V"], "expression": "epsilon*Ef**2", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.27.18"}
|
| 86 |
+
{"symbols": ["I", "q", "v", "r"], "symbol_descs": ["the current in a circular path", "the charge of the object", "the velocity of the charge", "the radius of the circular path"], "symbol_properties": ["O", "V", "V", "V"], "expression": "q*v/(2*pi*r)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.34.2a"}
|
| 87 |
+
{"symbols": ["mom", "q", "v", "r"], "symbol_descs": ["the momentum of an object", "a factor or quantity, possibly a charge or a proportionality constant, though more context is needed for precise definition", "the velocity of an object", "possibly the radius of a circular path or a distance, more context is needed for precise definition"], "symbol_properties": ["O", "V", "V", "V"], "expression": "q*v*r/2", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.34.2"}
|
| 88 |
+
{"symbols": ["omega", "g_", "q", "B", "m"], "symbol_descs": ["the cyclotron frequency", "the gyromagnetic ratio", "the charge of the particle", "the magnetic field strength", "the mass of the particle"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "g_*q*B/(2*m)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.34.11"}
|
| 89 |
+
{"symbols": ["mom", "q", "h", "m"], "symbol_descs": ["the momentum of a particle", "the charge of a particle", "the Planck constant", "the mass of a particle"], "symbol_properties": ["O", "V", "V", "V"], "expression": "q*h/(4*pi*m)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.34.29a"}
|
| 90 |
+
{"symbols": ["E_n", "mom", "B", "chi"], "symbol_descs": ["the nth energy level", "the magnetic moment", "the magnetic field strength", "the magnetic susceptibility"], "symbol_properties": ["O", "V", "V", "V"], "expression": "mom*(1+chi)*B", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.37.1"}
|
| 91 |
+
{"symbols": ["F", "Y", "A", "d", "x"], "symbol_descs": ["the force exerted on an object", "the Young's modulus of the material", "the cross-sectional area of the object", "the original length of the object", "the displacement or extension of the object"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "Y*A*x/d", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.38.3"}
|
| 92 |
+
{"symbols": ["mu_S", "Y", "sigma"], "symbol_descs": ["the shear modulus of the solid", "the Young's modulus of the solid", "the Poisson's ratio of the solid"], "symbol_properties": ["O", "V", "V"], "expression": "Y/(2*(1+sigma))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "II.38.14"}
|
| 93 |
+
{"symbols": ["n", "h", "omega", "kb", "T"], "symbol_descs": ["the number of phonons in a mode", "the Planck constant", "the angular frequency of the mode", "the Boltzmann constant", "the temperature in Kelvin"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "1/(exp((h/(2*pi))*omega/(kb*T))-1)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.4.32"}
|
| 94 |
+
{"symbols": ["omega", "mom", "B", "h"], "symbol_descs": ["the Larmor frequency", "the magnetic moment of a particle", "the magnetic field strength", "the Planck constant"], "symbol_properties": ["O", "V", "V", "V"], "expression": "2*mom*B/(h/(2*pi))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.7.38"}
|
| 95 |
+
{"symbols": ["E_n", "mom", "Bx", "By", "Bz"], "symbol_descs": ["the energy of a particle in a magnetic field", "the magnetic moment of the particle", "the x-component of the magnetic field", "the y-component of the magnetic field", "the z-component of the magnetic field"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "mom*sqrt(Bx**2+By**2+Bz**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.10.19"}
|
| 96 |
+
{"symbols": ["L", "n", "h"], "symbol_descs": ["the angular momentum of an object", "a quantum number representing the energy level", "the Planck constant"], "symbol_properties": ["O", "V", "V"], "expression": "n*(h/(2*pi))", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.12.43"}
|
| 97 |
+
{"symbols": ["I", "I_0", "q", "Volt", "kb", "T"], "symbol_descs": ["the current flowing through a device", "the reverse saturation current of the device", "the elementary charge", "the voltage applied across the device", "the Boltzmann constant", "the temperature of the device in Kelvin"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "I_0*(exp(q*Volt/(kb*T))-1)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.14.14"}
|
| 98 |
+
{"symbols": ["m", "h", "E_n", "d"], "symbol_descs": ["the mass of a particle in a quantum mechanical system", "the Planck constant", "the nth energy level of the system", "the width or distance between the boundaries of the quantum well"], "symbol_properties": ["O", "V", "V", "V"], "expression": "(h/(2*pi))**2/(2*E_n*d**2)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.15.14"}
|
| 99 |
+
{"symbols": ["k", "alpha", "n", "d"], "symbol_descs": ["the spring constant or a proportionality constant", "a material-dependent constant or a dimensionless parameter", "the number of turns or a dimensionless quantity", "the diameter or a characteristic length"], "symbol_properties": ["O", "V", "V", "V"], "expression": "2*pi*alpha/(n*d)", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.15.27"}
|
| 100 |
+
{"symbols": ["j", "rho_c_0", "q", "A_vec", "m"], "symbol_descs": ["the current density", "the charge carrier density", "the elementary charge", "the vector potential", "the mass of a charge carrier"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "-rho_c_0*q*A_vec/m", "desc": null, "sympy_format": null, "lambda_format": null, "program_format": null, "name": "III.21.20"}
|