The 30 Most Important Equations in Physics - ChatGPT

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Concepts

id creditedTo country fieldOfPhysics equation yearAppeared applications complexity
Newton's Second Law Isaac Newton England Mechanics F = ma 1687 100 2
Einstein's Mass-Energy Equivalence Albert Einstein Switzerland Relativity E = mc^2 1905 50 5
Schrödinger Equation Erwin Schrödinger Austria Quantum Mechanics i\hbar\frac{\partial}{\partial t}\psi = \hat{H}\psi 1926 100 7
Maxwell's Equations James Clerk Maxwell Scotland Electromagnetism \begin{align*} \nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0} \\ \nabla \cdot \mathbf{B} &= 0 \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \end{align*} 1865 50 6
Boltzmann Equation Ludwig Boltzmann Austria Statistical Mechanics \frac{\partial f}{\partial t} + \mathbf{v} \cdot \nabla f + \mathbf{a} \cdot \frac{\partial f}{\partial \mathbf{v}} = \left( \frac{\partial f}{\partial t} \right)_\text{collision} 1872 30 8
Planck's Equation Max Planck Germany Quantum Mechanics E = h\nu 1900 40 6
Heisenberg Uncertainty Principle Werner Heisenberg Germany Quantum Mechanics \Delta x \Delta p \geq \frac{\hbar}{2} 1927 20 5
Hubble's Law Edwin Hubble USA Cosmology v = H_0 d 1929 25 4
Fourier Transform Joseph Fourier France Mathematical Physics \hat{f}(\xi) = \int_{-\infty}^{\infty} f(x) e^{-2\pi i x \xi} \, dx 1822 70 6
Lorentz Transformation Hendrik Lorentz Netherlands Relativity \begin{align*} t' &= \gamma \left( t - \frac{vx}{c^2} \right) \\ x' &= \gamma (x - vt) \end{align*} 1904 20 6
Dirac Equation Paul Dirac UK Quantum Mechanics \left( i\gamma^\mu \partial_\mu - m \right) \psi = 0 1928 30 9
Navier-Stokes Equation Claude-Louis Navier, George Gabriel Stokes France, UK Fluid Mechanics \rho \left( \frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla) \mathbf{u} \right) = -\nabla p + \mu \nabla^2 \mathbf{u} + \mathbf{f} 1822 50 9
Ohm's Law Georg Ohm Germany Electromagnetism V = IR 1827 100 2
Hooke's Law Robert Hooke England Mechanics F = -kx 1678 60 2
Kepler's Third Law Johannes Kepler Germany Astronomy T^2 \propto r^3 1619 30 3
Bernoulli's Principle Daniel Bernoulli Switzerland Fluid Mechanics p + \frac{1}{2}\rho v^2 + \rho gh = \text{constant} 1738 50 4
Faraday's Law of Induction Michael Faraday England Electromagnetism \mathcal{E} = -\frac{d\Phi_B}{dt} 1831 40 5
Stefan-Boltzmann Law Josef Stefan, Ludwig Boltzmann Austria Thermodynamics j^* = \sigma T^4 1879 30 5
Lenz's Law Heinrich Lenz Russia Electromagnetism \mathcal{E} = -\frac{d\Phi_B}{dt} 1834 30 4
Coulomb's Law Charles-Augustin de Coulomb France Electrostatics F = k_e \frac{q_1 q_2}{r^2} 1785 50 3
Fermi-Dirac Statistics Enrico Fermi, Paul Dirac Italy, UK Quantum Mechanics f(E) = \frac{1}{e^{(E - \mu)/kT} + 1} 1926 40 7
Bose-Einstein Statistics Satyendra Nath Bose, Albert Einstein India, Germany Quantum Mechanics f(E) = \frac{1}{e^{(E - \mu)/kT} - 1} 1924 30 7
Wien's Displacement Law Wilhelm Wien Germany Thermodynamics \lambda_\text{peak} T = b 1893 25 5
Poisson's Equation Siméon Denis Poisson France Mathematical Physics \nabla^2 \phi = -\frac{\rho}{\epsilon_0} 1813 30 6
AmpÚre's Law André-Marie AmpÚre France Electromagnetism \nabla \times \mathbf{B} = \mu_0 \mathbf{J} 1826 40 4
Biot-Savart Law Jean-Baptiste Biot, FĂ©lix Savart France Electromagnetism d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \mathbf{\hat{r}}}{r^2} 1820 30 5
Kirchhoff's Circuit Laws Gustav Kirchhoff Germany Electrical Circuits \begin{align*} \sum I = 0 \\ \sum V = 0 \end{align*} 1845 50 3
Gibbs Free Energy Josiah Willard Gibbs USA Thermodynamics G = H - TS 1873 30 6
Avogadro's Law Amedeo Avogadro Italy Chemistry V \propto n 1811 30 3
de Broglie Hypothesis Louis de Broglie France Quantum Mechanics \lambda = \frac{h}{p} 1924 25 6

Measures

Name Values Coverage Question Example Type Source SortIndex IsComputed IsRequired IsConceptDelimiter Crux
id 30 100% What is the ID of this concept? Newton's Second Law string 1 false true true
creditedTo 30 100% The person or persons credited with the formulation of the equation Isaac Newton string 1.9 false
country 30 100% The country associated with the credited person(s) at the time of the formulation England string 1.9 false
fieldOfPhysics 30 100% The field of physics where the equation is primarily used Mechanics string 1.9 false
equation 30 100% The equation written in KaTeX (LaTeX) F = ma string 1.9 false
yearAppeared 30 100% The year the equation first appeared or was formulated 1687 number 1.9 false
applications 30 100% The number of major applications or uses of the equation 100 number 1.9 false
complexity 30 100% The relative complexity of the equation (scale 1 to 10) 2 number 1.9 false
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