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I.6.2a
[ "f", "theta" ]
[ "Dimensionless", "Dimensionless" ]
[ "O", "V" ]
exp(-theta**2/2)/sqrt(2*pi)
[ null, [ 1, 3 ] ]
I.6.2
[ "f", "sigma", "theta" ]
[ "Dimensionless", "Dimensionless", "Dimensionless" ]
[ "O", "V", "V" ]
exp(-(theta/sigma)**2/2)/(sqrt(2*pi)*sigma)
[ null, [ 1, 3 ], [ 1, 3 ] ]
I.6.2b
[ "f", "sigma", "theta", "theta1" ]
[ "Dimensionless", "Dimensionless", "Dimensionless", "Dimensionless" ]
[ "O", "V", "V", "V" ]
exp(-((theta-theta1)/sigma)**2/2)/(sqrt(2*pi)*sigma)
[ null, [ 1, 3 ], [ 1, 3 ], [ 1, 3 ] ]
I.8.14
[ "d", "x1", "x2", "y1", "y2" ]
[ "Length", "Length", "Length", "Length", "Length" ]
[ "O", "V", "V", "V", "V" ]
sqrt((x2-x1)**2+(y2-y1)**2)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.9.18
[ "F", "m1", "m2", "G", "x1", "x2", "y1", "y2", "z1", "z2" ]
[ "Force", "Mass", "Mass", "Newton's constant", "Length", "Length", "Length", "Length", "Length", "Length" ]
[ "O", "V", "V", "V", "V", "V", "V", "V", "V", "V" ]
G*m1*m2/((x2-x1)**2+(y2-y1)**2+(z2-z1)**2)
[ null, [ 1, 2 ], [ 1, 2 ], [ 1, 2 ], [ 3, 4 ], [ 1, 2 ], [ 3, 4 ], [ 1, 2 ], [ 3, 4 ], [ 1, 2 ] ]
I.10.7
[ "m", "m_0", "v", "c" ]
[ "Mass", "Mass", "Velocity", "Velocity" ]
[ "O", "V", "V", "V" ]
m_0/sqrt(1-v**2/c**2)
[ null, [ 1, 5 ], [ 1, 2 ], [ 3, 10 ] ]
I.11.19
[ "A", "x1", "x2", "x3", "y1", "y2", "y3" ]
[ "Area", "Length", "Length", "Length", "Length", "Length", "Length" ]
[ "O", "V", "V", "V", "V", "V", "V" ]
x1*y1+x2*y2+x3*y3
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.12.1
[ "F", "mu", "Nn" ]
[ "Force", "Dimensionless", "Force" ]
[ "O", "V", "V" ]
mu*Nn
[ null, [ 1, 5 ], [ 1, 5 ] ]
I.12.2
[ "F", "q1", "q2", "epsilon", "r" ]
[ "Force", "Charge", "Charge", "Electric permitivity", "Length" ]
[ "O", "V", "V", "V", "V" ]
q1*q2*r/(4*pi*epsilon*r**3)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.12.4
[ "Ef", "q1", "epsilon", "r" ]
[ "Electric field", "Charge", "Electric permitivity", "Length" ]
[ "O", "V", "V", "V" ]
q1*r/(4*pi*epsilon*r**3)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.12.5
[ "F", "q2", "Ef" ]
[ "Force", "Charge", "Electric field" ]
[ "O", "V", "V" ]
q2*Ef
[ null, [ 1, 5 ], [ 1, 5 ] ]
I.12.11
[ "F", "q", "Ef", "B", "v", "theta" ]
[ "Force", "Charge", "Electric field", "Magnetic field", "Velocity", "Dimensionless" ]
[ "O", "V", "V", "V", "V", "V" ]
q*(Ef+B*v*sin(theta))
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.13.4
[ "K", "m", "v", "u", "w" ]
[ "Energy", "Mass", "Velocity", "Velocity", "Velocity" ]
[ "O", "V", "V", "V", "V" ]
1/2*m*(v**2+u**2+w**2)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.13.12
[ "U", "m1", "m2", "r1", "r2", "G" ]
[ "Energy", "Mass", "Mass", "Length", "Length", "Newton's constant" ]
[ "O", "V", "V", "V", "V", "V" ]
G*m1*m2*(1/r2-1/r1)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.14.3
[ "U", "m", "g", "z" ]
[ "Energy", "Mass", "Acceleration", "Length" ]
[ "O", "V", "V", "V" ]
m*g*z
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.14.4
[ "U", "k_spring", "x" ]
[ "Energy", "Spring constant", "Length" ]
[ "O", "V", "V" ]
1/2*k_spring*x**2
[ null, [ 1, 5 ], [ 1, 5 ] ]
I.15.3x
[ "x1", "x", "u", "c", "t" ]
[ "Length", "Length", "Velocity", "Velocity", "Τime" ]
[ "O", "V", "V", "V", "V" ]
(x-u*t)/sqrt(1-u**2/c**2)
[ null, [ 5, 10 ], [ 1, 2 ], [ 3, 20 ], [ 1, 2 ] ]
I.15.3t
[ "t1", "x", "c", "u", "t" ]
[ "Τime", "Length", "Velocity", "Velocity", "Τime" ]
[ "O", "V", "V", "V", "V" ]
(t-u*x/c**2)/sqrt(1-u**2/c**2)
[ null, [ 1, 5 ], [ 3, 10 ], [ 1, 2 ], [ 1, 5 ] ]
I.15.1
[ "p", "m_0", "v", "c" ]
[ "Momentum", "Mass", "Velocity", "Velocity" ]
[ "O", "V", "V", "V" ]
m_0*v/sqrt(1-v**2/c**2)
[ null, [ 1, 5 ], [ 1, 2 ], [ 3, 10 ] ]
I.16.6
[ "v1", "c", "v", "u" ]
[ "Velocity", "Velocity", "Velocity", "Velocity" ]
[ "O", "V", "V", "V" ]
(u+v)/(1+u*v/c**2)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.18.4
[ "r", "m1", "m2", "r1", "r2" ]
[ "Length", "Mass", "Mass", "Length", "Length" ]
[ "O", "V", "V", "V", "V" ]
(m1*r1+m2*r2)/(m1+m2)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.18.12
[ "tau", "r", "F", "theta" ]
[ "Torque", "Length", "Force", "Dimensionless" ]
[ "O", "V", "V", "V" ]
r*F*sin(theta)
[ null, [ 1, 5 ], [ 1, 5 ], [ 0, 5 ] ]
I.18.14
[ "L", "m", "r", "v", "theta" ]
[ "Angular momentum", "Mass", "Length", "Velocity", "Dimensionless" ]
[ "O", "V", "V", "V", "V" ]
m*r*v*sin(theta)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.24.6
[ "E_n", "m", "omega", "omega_0", "x" ]
[ "Energy", "Mass", "Frequency", "Frequency", "Length" ]
[ "O", "V", "V", "V", "V" ]
1/2*m*(omega**2+omega_0**2)*1/2*x**2
[ null, [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ] ]
I.25.13
[ "Volt", "q", "C" ]
[ "Voltage", "Charge", "Capacitance" ]
[ "O", "V", "V" ]
q/C
[ null, [ 1, 5 ], [ 1, 5 ] ]
I.26.2
[ "theta1", "n", "theta2" ]
[ "Dimensionless", "Dimensionless", "Dimensionless" ]
[ "O", "V", "V" ]
arcsin(n*sin(theta2))
[ null, [ 0, 1 ], [ 1, 5 ] ]
I.27.6
[ "foc", "d1", "d2", "n" ]
[ "Length", "Length", "Length", "Dimensionless" ]
[ "O", "V", "V", "V" ]
1/(1/d1+n/d2)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.29.4
[ "k", "omega", "c" ]
[ "Wave number", "Frequency", "Velocity" ]
[ "O", "V", "V" ]
omega/c
[ null, [ 1, 10 ], [ 1, 10 ] ]
I.29.16
[ "x", "x1", "x2", "theta1", "theta2" ]
[ "Length", "Length", "Length", "Dimensionless", "Dimensionless" ]
[ "O", "V", "V", "V", "V" ]
sqrt(x1**2+x2**2-2*x1*x2*cos(theta1-theta2))
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.30.3
[ "Int", "Int_0", "theta", "n" ]
[ "Light intensity", "Light intensity", "Dimensionless", "Dimensionless" ]
[ "O", "V", "V", "V" ]
Int_0*sin(n*theta/2)**2/sin(theta/2)**2
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.30.5
[ "theta", "lambd", "d", "n" ]
[ "Dimensionless", "Length", "Length", "Dimensionless" ]
[ "O", "V", "V", "V" ]
arcsin(lambd/(n*d))
[ null, [ 1, 2 ], [ 2, 5 ], [ 1, 5 ] ]
I.32.5
[ "Pwr", "q", "a", "epsilon", "c" ]
[ "Power", "Charge", "Acceleration", "Electric permitivity", "Velocity" ]
[ "O", "V", "V", "V", "V" ]
q**2*a**2/(6*pi*epsilon*c**3)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.32.17
[ "Pwr", "epsilon", "c", "Ef", "r", "omega", "omega_0" ]
[ "Power", "Electric permitivity", "Velocity", "Electric field", "Length", "Frequency", "Frequency" ]
[ "O", "V", "V", "V", "V", "V", "V" ]
(1/2*epsilon*c*Ef**2)*(8*pi*r**2/3)*(omega**4/(omega**2-omega_0**2)**2)
[ null, [ 1, 2 ], [ 1, 2 ], [ 1, 2 ], [ 1, 2 ], [ 1, 2 ], [ 3, 5 ] ]
I.34.8
[ "omega", "q", "v", "B", "p" ]
[ "Frequency", "Charge", "Velocity", "Magnetic field", "Momentum" ]
[ "O", "V", "V", "V", "V" ]
q*v*B/p
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.34.1
[ "omega", "c", "v", "omega_0" ]
[ "Frequency", "Velocity", "Velocity", "Frequency" ]
[ "O", "V", "V", "V" ]
omega_0/(1-v/c)
[ null, [ 3, 10 ], [ 1, 2 ], [ 1, 5 ] ]
I.34.14
[ "omega", "c", "v", "omega_0" ]
[ "Frequency", "Velocity", "Velocity", "Frequency" ]
[ "O", "V", "V", "V" ]
(1+v/c)/sqrt(1-v**2/c**2)*omega_0
[ null, [ 3, 10 ], [ 1, 2 ], [ 1, 5 ] ]
I.34.27
[ "E_n", "omega", "h" ]
[ "Energy", "Frequency", "Angular momentum" ]
[ "O", "V", "V" ]
(h/(2*pi))*omega
[ null, [ 1, 5 ], [ 1, 5 ] ]
I.37.4
[ "Int", "I1", "I2", "delta" ]
[ "Light intensity", "Light intensity", "Light intensity", "Dimensionless" ]
[ "O", "V", "V", "V" ]
I1+I2+2*sqrt(I1*I2)*cos(delta)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.38.12
[ "r", "m", "q", "h", "epsilon" ]
[ "Length", "Mass", "Charge", "Angular momentum", "Electric permitivity" ]
[ "O", "V", "V", "V", "V" ]
4*pi*epsilon*(h/(2*pi))**2/(m*q**2)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.39.1
[ "E_n", "pr", "V" ]
[ "Energy", "Pressure", "volume" ]
[ "O", "V", "V" ]
3/2*pr*V
[ null, [ 1, 5 ], [ 1, 5 ] ]
I.39.11
[ "E_n", "gamma", "pr", "V" ]
[ "Energy", "Dimensionless", "Pressure", "volume" ]
[ "O", "V", "V", "V" ]
1/(gamma-1)*pr*V
[ null, [ 2, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.39.22
[ "pr", "n", "T", "V", "kb" ]
[ "Pressure", "Dimensionless", "Temperature", "volume", "Boltzmann constant" ]
[ "O", "V", "V", "V", "V" ]
n*kb*T/V
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.40.1
[ "n", "n_0", "m", "x", "T", "g", "kb" ]
[ "Dimensionless", "Dimensionless", "Mass", "Length", "Temperature", "Acceleration", "Boltzmann constant" ]
[ "O", "V", "V", "V", "V", "V", "V" ]
n_0*exp(-m*g*x/(kb*T))
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.41.16
[ "L_rad", "omega", "T", "h", "kb", "c" ]
[ "Spectral radiance", "Frequency", "Temperature", "Angular momentum", "Boltzmann constant", "Velocity" ]
[ "O", "V", "V", "V", "V", "V" ]
h/(2*pi)*omega**3/(pi**2*c**2*(exp((h/(2*pi))*omega/(kb*T))-1))
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.43.16
[ "v", "mu_drift", "q", "Volt", "d" ]
[ "Velocity", "Drift velocity constant", "Charge", "Voltage", "Length" ]
[ "O", "V", "V", "V", "V" ]
mu_drift*q*Volt/d
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.43.31
[ "D", "mob", "T", "kb" ]
[ "Diffusion coefficient", "Mobility", "Temperature", "Boltzmann constant" ]
[ "O", "V", "V", "V" ]
mob*kb*T
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.43.43
[ "kappa", "gamma", "kb", "A", "v" ]
[ "Thermal conductivity", "Dimensionless", "Boltzmann constant", "Area", "Velocity" ]
[ "O", "V", "V", "V", "V" ]
1/(gamma-1)*kb*v/A
[ null, [ 2, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.44.4
[ "E_n", "n", "kb", "T", "V1", "V2" ]
[ "Energy", "Dimensionless", "Boltzmann constant", "Temperature", "volume", "volume" ]
[ "O", "V", "V", "V", "V", "V" ]
n*kb*T*ln(V2/V1)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.47.23
[ "c", "gamma", "pr", "rho" ]
[ "Velocity", "Dimensionless", "Pressure", "Density" ]
[ "O", "V", "V", "V" ]
sqrt(gamma*pr/rho)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
I.48.2
[ "E_n", "m", "v", "c" ]
[ "Energy", "Mass", "Velocity", "Velocity" ]
[ "O", "V", "V", "V" ]
m*c**2/sqrt(1-v**2/c**2)
[ null, [ 1, 5 ], [ 1, 2 ], [ 3, 10 ] ]
I.50.26
[ "x", "x1", "omega", "t", "alpha" ]
[ "Length", "Length", "Frequency", "Τime", "Dimensionless" ]
[ "O", "V", "V", "V", "V" ]
x1*(cos(omega*t)+alpha*cos(omega*t)**2)
[ null, [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ] ]
II.2.42
[ "Pwr", "kappa", "T1", "T2", "A", "d" ]
[ "Power", "Thermal conductivity", "Temperature", "Temperature", "Area", "Length" ]
[ "O", "V", "V", "V", "V", "V" ]
kappa*(T2-T1)*A/d
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.3.24
[ "flux", "Pwr", "r" ]
[ "Energy flux", "Power", "Length" ]
[ "O", "V", "V" ]
Pwr/(4*pi*r**2)
[ null, [ 1, 5 ], [ 1, 5 ] ]
II.4.23
[ "Volt", "q", "epsilon", "r" ]
[ "Voltage", "Charge", "Electric permitivity", "Length" ]
[ "O", "V", "V", "V" ]
q/(4*pi*epsilon*r)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.6.11
[ "Volt", "epsilon", "p_d", "theta", "r" ]
[ "Voltage", "Electric permitivity", "Electric dipole moment", "Dimensionless", "Length" ]
[ "O", "V", "V", "V", "V" ]
1/(4*pi*epsilon)*p_d*cos(theta)/r**2
[ null, [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ] ]
II.6.15a
[ "Ef", "epsilon", "p_d", "r", "x", "y", "z" ]
[ "Electric field", "Electric permitivity", "Electric dipole moment", "Length", "Length", "Length", "Length" ]
[ "O", "V", "V", "V", "V", "V", "V" ]
p_d/(4*pi*epsilon)*3*z/r**5*sqrt(x**2+y**2)
[ null, [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ] ]
II.6.15b
[ "Ef", "epsilon", "p_d", "theta", "r" ]
[ "Electric field", "Electric permitivity", "Electric dipole moment", "Dimensionless", "Length" ]
[ "O", "V", "V", "V", "V" ]
p_d/(4*pi*epsilon)*3*cos(theta)*sin(theta)/r**3
[ null, [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ] ]
II.8.7
[ "E_n", "q", "epsilon", "d" ]
[ "Energy", "Charge", "Electric permitivity", "Length" ]
[ "O", "V", "V", "V" ]
3/5*q**2/(4*pi*epsilon*d)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.8.31
[ "E_den", "epsilon", "Ef" ]
[ "Energy density", "Electric permitivity", "Electric field" ]
[ "O", "V", "V" ]
epsilon*Ef**2/2
[ null, [ 1, 5 ], [ 1, 5 ] ]
II.10.9
[ "Ef", "sigma_den", "epsilon", "chi" ]
[ "Electric field", "Surface Charge density", "Electric permitivity", "Dimensionless" ]
[ "O", "V", "V", "V" ]
sigma_den/epsilon*1/(1+chi)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.11.3
[ "x", "q", "Ef", "m", "omega_0", "omega" ]
[ "Length", "Charge", "Electric field", "Mass", "Frequency", "Frequency" ]
[ "O", "V", "V", "V", "V", "V" ]
q*Ef/(m*(omega_0**2-omega**2))
[ null, [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 3, 5 ], [ 1, 2 ] ]
II.11.17
[ "n", "n_0", "kb", "T", "theta", "p_d", "Ef" ]
[ "Dimensionless", "Dimensionless", "Boltzmann constant", "Temperature", "Dimensionless", "Electric dipole moment", "Electric field" ]
[ "O", "V", "V", "V", "V", "V", "V" ]
n_0*(1+p_d*Ef*cos(theta)/(kb*T))
[ null, [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ] ]
II.11.20
[ "Pol", "n_rho", "p_d", "Ef", "kb", "T" ]
[ "Polarization", "Inverse volume", "Electric dipole moment", "Electric field", "Boltzmann constant", "Temperature" ]
[ "O", "V", "V", "V", "V", "V" ]
n_rho*p_d**2*Ef/(3*kb*T)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.11.27
[ "Pol", "n", "alpha", "epsilon", "Ef" ]
[ "Polarization", "Dimensionless", "Dimensionless", "Electric permitivity", "Electric field" ]
[ "O", "V", "V", "V", "V" ]
n*alpha/(1-(n*alpha/3))*epsilon*Ef
[ null, [ 0, 1 ], [ 0, 1 ], [ 1, 2 ], [ 1, 2 ] ]
II.11.28
[ "theta", "n", "alpha" ]
[ "Dimensionless", "Dimensionless", "Dimensionless" ]
[ "O", "V", "V" ]
1+n*alpha/(1-(n*alpha/3))
[ null, [ 0, 1 ], [ 0, 1 ] ]
II.13.17
[ "B", "epsilon", "c", "I", "r" ]
[ "Magnetic field", "Electric permitivity", "Velocity", "Current Intensity", "Length" ]
[ "O", "V", "V", "V", "V" ]
1/(4*pi*epsilon*c**2)*2*I/r
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.13.23
[ "rho_c", "rho_c_0", "v", "c" ]
[ "Volume charge density", "Volume charge density", "Velocity", "Velocity" ]
[ "O", "V", "V", "V" ]
rho_c_0/sqrt(1-v**2/c**2)
[ null, [ 1, 5 ], [ 1, 2 ], [ 3, 10 ] ]
II.13.34
[ "j", "rho_c_0", "v", "c" ]
[ "Current density", "Volume charge density", "Velocity", "Velocity" ]
[ "O", "V", "V", "V" ]
rho_c_0*v/sqrt(1-v**2/c**2)
[ null, [ 1, 5 ], [ 1, 2 ], [ 3, 10 ] ]
II.15.4
[ "E_n", "mom", "B", "theta" ]
[ "Energy", "Magnetic moment", "Magnetic field", "Dimensionless" ]
[ "O", "V", "V", "V" ]
-mom*B*cos(theta)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.15.5
[ "E_n", "p_d", "Ef", "theta" ]
[ "Energy", "Electric dipole moment", "Electric field", "Dimensionless" ]
[ "O", "V", "V", "V" ]
-p_d*Ef*cos(theta)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.21.32
[ "Volt", "q", "epsilon", "r", "v", "c" ]
[ "Voltage", "Charge", "Electric permitivity", "Length", "Velocity", "Velocity" ]
[ "O", "V", "V", "V", "V", "V" ]
q/(4*pi*epsilon*r*(1-v/c))
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 2 ], [ 3, 10 ] ]
II.24.17
[ "k", "omega", "c", "d" ]
[ "Wave number", "Frequency", "Velocity", "Length" ]
[ "O", "V", "V", "V" ]
sqrt(omega**2/c**2-pi**2/d**2)
[ null, [ 4, 6 ], [ 1, 2 ], [ 2, 4 ] ]
II.27.16
[ "flux", "epsilon", "c", "Ef" ]
[ "Energy flux", "Electric permitivity", "Velocity", "Electric field" ]
[ "O", "V", "V", "V" ]
epsilon*c*Ef**2
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.27.18
[ "E_den", "epsilon", "Ef" ]
[ "Energy density", "Electric permitivity", "Electric field" ]
[ "O", "V", "V" ]
epsilon*Ef**2
[ null, [ 1, 5 ], [ 1, 5 ] ]
II.34.2a
[ "I", "q", "v", "r" ]
[ "Current Intensity", "Charge", "Velocity", "Length" ]
[ "O", "V", "V", "V" ]
q*v/(2*pi*r)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.34.2
[ "mom", "q", "v", "r" ]
[ "Magnetic moment", "Charge", "Velocity", "Length" ]
[ "O", "V", "V", "V" ]
q*v*r/2
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.34.11
[ "omega", "g_", "q", "B", "m" ]
[ "Frequency", "Dimensionless", "Charge", "Magnetic field", "Mass" ]
[ "O", "V", "V", "V", "V" ]
g_*q*B/(2*m)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.34.29a
[ "mom", "q", "h", "m" ]
[ "Magnetic moment", "Charge", "Angular momentum", "Mass" ]
[ "O", "V", "V", "V" ]
q*h/(4*pi*m)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.34.29b
[ "E_n", "g_", "h", "Jz", "mom", "B" ]
[ "Energy", "Dimensionless", "Angular momentum", "Angular momentum", "Magnetic moment", "Magnetic field" ]
[ "O", "V", "V", "V", "V", "V" ]
g_*mom*B*Jz/(h/(2*pi))
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.35.18
[ "n", "n_0", "kb", "T", "mom", "B" ]
[ "Dimensionless", "Dimensionless", "Boltzmann constant", "Temperature", "Magnetic moment", "Magnetic field" ]
[ "O", "V", "V", "V", "V", "V" ]
n_0/(exp(mom*B/(kb*T))+exp(-mom*B/(kb*T)))
[ null, [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ] ]
II.35.21
[ "M", "n_rho", "mom", "B", "kb", "T" ]
[ "Magnetisation", "Inverse volume", "Magnetic moment", "Magnetic field", "Boltzmann constant", "Temperature" ]
[ "O", "V", "V", "V", "V", "V" ]
n_rho*mom*tanh(mom*B/(kb*T))
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.36.38
[ "f", "mom", "H", "kb", "T", "alpha", "epsilon", "c", "M" ]
[ "Dimensionless", "Magnetic moment", "Magnetic field", "Boltzmann constant", "Temperature", "Dimensionless", "Electric permitivity", "Velocity", "Magnetisation" ]
[ "O", "V", "V", "V", "V", "V", "V", "V", "V" ]
mom*H/(kb*T)+(mom*alpha)/(epsilon*c**2*kb*T)*M
[ null, [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ] ]
II.37.1
[ "E_n", "mom", "B", "chi" ]
[ "Energy", "Magnetic moment", "Magnetic field", "Dimensionless" ]
[ "O", "V", "V", "V" ]
mom*(1+chi)*B
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.38.3
[ "F", "Y", "A", "d", "x" ]
[ "Force", "Young modulus", "Area", "Length", "Length" ]
[ "O", "V", "V", "V", "V" ]
Y*A*x/d
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
II.38.14
[ "mu_S", "Y", "sigma" ]
[ "Shear modulus", "Young modulus", "Dimensionless" ]
[ "O", "V", "V" ]
Y/(2*(1+sigma))
[ null, [ 1, 5 ], [ 1, 5 ] ]
III.4.32
[ "n", "h", "omega", "kb", "T" ]
[ "Dimensionless", "Angular momentum", "Frequency", "Boltzmann constant", "Temperature" ]
[ "O", "V", "V", "V", "V" ]
1/(exp((h/(2*pi))*omega/(kb*T))-1)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
III.4.33
[ "E_n", "h", "omega", "kb", "T" ]
[ "Energy", "Angular momentum", "Frequency", "Boltzmann constant", "Temperature" ]
[ "O", "V", "V", "V", "V" ]
(h/(2*pi))*omega/(exp((h/(2*pi))*omega/(kb*T))-1)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
III.7.38
[ "omega", "mom", "B", "h" ]
[ "Frequency", "Magnetic moment", "Magnetic field", "Angular momentum" ]
[ "O", "V", "V", "V" ]
2*mom*B/(h/(2*pi))
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
III.8.54
[ "prob", "E_n", "t", "h" ]
[ "Dimensionless", "Energy", "Τime", "Angular momentum" ]
[ "O", "V", "V", "V" ]
sin(E_n*t/(h/(2*pi)))**2
[ null, [ 1, 2 ], [ 1, 2 ], [ 1, 4 ] ]
III.9.52
[ "prob", "p_d", "Ef", "t", "h", "omega", "omega_0" ]
[ "Dimensionless", "Electric dipole moment", "Electric field", "Τime", "Angular momentum", "Frequency", "Frequency" ]
[ "O", "V", "V", "V", "V", "V", "V" ]
(p_d*Ef*t/(h/(2*pi)))*sin((omega-omega_0)*t/2)**2/((omega-omega_0)*t/2)**2
[ null, [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 3 ], [ 1, 5 ], [ 1, 5 ] ]
III.10.19
[ "E_n", "mom", "Bx", "By", "Bz" ]
[ "Energy", "Magnetic moment", "Magnetic field", "Magnetic field", "Magnetic field" ]
[ "O", "V", "V", "V", "V" ]
mom*sqrt(Bx**2+By**2+Bz**2)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
III.12.43
[ "L", "n", "h" ]
[ "Angular momentum", "Dimensionless", "Angular momentum" ]
[ "O", "V", "V" ]
n*(h/(2*pi))
[ null, [ 1, 5 ], [ 1, 5 ] ]
III.13.18
[ "v", "E_n", "d", "k", "h" ]
[ "Velocity", "Energy", "Length", "Wave number", "Angular momentum" ]
[ "O", "V", "V", "V", "V" ]
2*E_n*d**2*k/(h/(2*pi))
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
III.14.14
[ "I", "I_0", "q", "Volt", "kb", "T" ]
[ "Current Intensity", "Current Intensity", "Charge", "Voltage", "Boltzmann constant", "Temperature" ]
[ "O", "V", "V", "V", "V", "V" ]
I_0*(exp(q*Volt/(kb*T))-1)
[ null, [ 1, 5 ], [ 1, 2 ], [ 1, 2 ], [ 1, 2 ], [ 1, 2 ] ]
III.15.12
[ "E_n", "U", "k", "d" ]
[ "Energy", "Energy", "Wave number", "Length" ]
[ "O", "V", "V", "V" ]
2*U*(1-cos(k*d))
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
III.15.14
[ "m", "h", "E_n", "d" ]
[ "Mass", "Angular momentum", "Energy", "Length" ]
[ "O", "V", "V", "V" ]
(h/(2*pi))**2/(2*E_n*d**2)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
III.15.27
[ "k", "alpha", "n", "d" ]
[ "Wave number", "Dimensionless", "Dimensionless", "Length" ]
[ "O", "V", "V", "V" ]
2*pi*alpha/(n*d)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
III.17.37
[ "f", "beta", "alpha", "theta" ]
[ "Dimensionless", "Dimensionless", "Dimensionless", "Dimensionless" ]
[ "O", "V", "V", "V" ]
beta*(1+alpha*cos(theta))
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
III.19.51
[ "E_n", "m", "q", "h", "n", "epsilon" ]
[ "Energy", "Mass", "Charge", "Angular momentum", "Dimensionless", "Electric permitivity" ]
[ "O", "V", "V", "V", "V", "V" ]
-m*q**4/(2*(4*pi*epsilon)**2*(h/(2*pi))**2)*(1/n**2)
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
III.21.20
[ "j", "rho_c_0", "q", "A_vec", "m" ]
[ "Current density", "Volume charge density", "Charge", "Vector potential", "Mass" ]
[ "O", "V", "V", "V", "V" ]
-rho_c_0*q*A_vec/m
[ null, [ 1, 5 ], [ 1, 5 ], [ 1, 5 ], [ 1, 5 ] ]
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