Lists of physics equations

For the nomenclature used see Physical quantity and Defining equation (physics).

In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. The scope of the article is as follows:

1. General equations which are constructed from definitions or physical laws, or to the same status universal principles, but themselves not formulae of these types.
2. General equations which are or allow any of the following:

large applicability on a specific but important topic,

large applicability on a general topic,

reduce to a number of idealized special cases.

3. Formulae which frequently appear in physics literature, in a small addition some perhaps less common formulae.
4. Level of study is typically that of advanced school/ introductory degree level Physics, and beyond.
5. For generality, vector calculus and multivariable calculus is the main formalism; inline with complex numbers and some linear algebra (such as matrices and coordinate systems).

Only SI units and their corresponding dimensions are used; no natural/characteristic units or non-dimensional equations are included.

Nomenclature

The short-hand notation for the square of a vector, as the dot product of a vector with itself is used: $\mathbf {A} ^{2}\equiv \mathbf {A} \cdot \mathbf {A} \cos 0\equiv \left|\mathbf {A} \right|^{2}\equiv A^{2}.\,\!$ No confusion should arise by mistaking it for the cross product since the cross product of a vector with itself is always the null vector.

All symbols are matched as to standard closely as possible, but due to a variety of notations for any given variable, every table below has locally defined variables.

Electric circuits and electronics

Below N = number of conductors or circuit components. Subcript net refers to the equivalent and resultant property value.

Physical situation	Nomenclature	Series	Parallel
Resistors and conductors	Ri = resistance of resistor or conductor i Gi = conductance of conductor or conductor i	$R_{\mathrm {net} }=\sum _{i=1}^{N}R_{i}\,\!$ ${\frac {1}{G_{\mathrm {net} }}}=\sum _{i=1}^{N}{\frac {1}{G_{i}}}\,\!$	${\frac {1}{R_{\mathrm {net} }}}=\sum _{i=1}^{N}{\frac {1}{R_{i}}}\,\!$ $G_{\mathrm {net} }=\sum _{i}\sum _{i=1}^{N}\,\!$
Charge, capacitors, currents	qi = capacitance of capacitor i qi = charge of charge carrier i	$q_{\mathrm {net} }=\sum _{i=1}^{N}q_{i}\,\!$ $C_{\mathrm {net} }=\sum _{i=1}^{N}C_{i}\,\!$ $I_{\mathrm {net} }=\sum _{i=1}^{N}I_{i}\,\!$	$q_{\mathrm {net} }=\sum _{i=1}^{N}q_{i}\,\!$ $C_{\mathrm {net} }=\sum _{i=1}^{N}C_{i}\,\!$ $I_{\mathrm {net} }=\sum _{i=1}^{N}I_{i}\,\!$
Inductors	Li = self inductance of inductor i Lij = self inductance element ij of L matrix Mij = mutual inductance between inductors i and j	${\frac {1}{L_{\mathrm {net} }}}=\sum _{i}{\frac {1}{L_{i}}}\,\!$	$V_{i}=\sum _{j=1}^{N}L_{ij}{\frac {\mathrm {d} I_{j}}{\mathrm {d} t}}\,\!$

Series circuit equations

Circuit	DC Circuit equations	AC Circuit equations
RC circuits	Circuit equation $R{\frac {\mathrm {d} q}{\mathrm {d} t}}+{\frac {q}{C}}={\mathcal {E}}\,\!$ Capacitor charge $q=C{\mathcal {E}}\left(1-e^{-t/RC}\right)\,\!$ Capacitor discharge $q=C{\mathcal {E}}e^{-t/RC}\,\!$
RL circuits	Circuit equation $L{\frac {\mathrm {d} I}{\mathrm {d} t}}+RI={\mathcal {E}}\,\!$ Inductor current rise $I={\frac {\mathcal {E}}{R}}\left(1-e^{-Rt/L}\right)\,\!$ Inductor current fall $I={\frac {\mathcal {E}}{R}}e^{-t/\tau _{L}}=I_{0}e^{-Rt/L}\,\!$
LC circuits	Circuit equation $L{\frac {\mathrm {d} ^{2}q}{\mathrm {d} t^{2}}}+q/C={\mathcal {E}}\,\!$	Circuit equation $L{\frac {\mathrm {d} ^{2}q}{\mathrm {d} t^{2}}}+q/C={\mathcal {E}}\sin \left(\omega _{0}t+\phi \right)\,\!$ Circuit resonant frequency $\omega _{\mathrm {res} }=1/{\sqrt {LC}}\,\!$ Circuit charge $q=q_{0}\cos(\omega t+\phi )\,\!$ Circuit current $I=-\omega q_{0}\sin(\omega t+\phi )\,\!$ Circuit electrical potential energy $U_{E}=q^{2}/2C=Q^{2}\cos ^{2}(\omega t+\phi )/2C\,\!$ Circuit magnetic potential energy $U_{B}=Q^{2}\sin ^{2}(\omega t+\phi )/2C\,\!$
RLC Circuits	Circuit equation $L{\frac {\mathrm {d} ^{2}q}{\mathrm {d} t^{2}}}+R{\frac {\mathrm {d} q}{\mathrm {d} t}}+{\frac {q}{C}}={\mathcal {E}}\,\!$	Circuit equation $L{\frac {\mathrm {d} ^{2}q}{\mathrm {d} t^{2}}}+R{\frac {\mathrm {d} q}{\mathrm {d} t}}+{\frac {q}{C}}={\mathcal {E}}\sin \left(\omega _{0}t+\phi \right)\,\!$ Circuit charge $q=q_{0}eT^{-Rt/2L}\cos(\omega 't+\phi )\,\!$

See also

• Variables commonly used in physics
• Continuity equation
• Constitutive equation
• Operator (physics)
• Defining equation (physical chemistry)
• Physical constant

References

• David Halliday; Robert Resnick; Jearl Walker (15 March 2010). Fundamentals of Physics. John Wiley and Sons. ISBN 978-0-470-46911-8. Retrieved 31 March 2011.
• Nouredine Zettili (2009). Quantum mechanics: concepts and applications. John Wiley and Sons. ISBN 978-0-470-02678-6. Retrieved 31 March 2011.

Sources

• The Cambridge Handbook of Physics Formulas, G. Woan, Cambridge University Press, 2010, ISBN 978-0-521-57507-2.
• Essential Principles of Physics, P.M. Whelan, M.J. Hodgeson, 2nd Edition, 1978, John Murray, ISBN 0-7195-3382-1
• Encyclopaedia of Physics (2nd Edition), R.G. Lerner, G.L. Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3
• McGraw Hill Encyclopaedia of Physics (2nd Edition), C.B. Parker, 1994, ISBN 0-07-051400-3
• Physics with Modern Applications, L.H. Greenberg, Holt-Saunders International W.B. Saunders and Co, 1978, ISBN 0-7216-4247-0
• Principles of Physics, J.B. Marion, W.F. Hornyak, Holt-Saunders International Saunders College, 1984, ISBN 4-8337-0195-2
• Physics for Scientists and Engineers: With Modern Physics (6th Edition), P.A. Tipler, G. Mosca, W.H. Freeman and Co, 2008, 9-781429-202657
• 3000 Solved Problems in Physics, Schaum Series, A. Halpern, Mc Graw Hill, 1988, ISBN 978-0-07-025734-4
• Dynamics and Relativity, J.R. Forshaw, A.G. Smith, Wiley, 2009, ISBN 978-0-470-01460-8
• The Physics of Vibrations and Waves (3rd edition), H.J. Pain, John Wiley & Sons, 1983, ISBN 0-471-90182-2
• Electromagnetism (2nd edition), I.S. Grant, W.R. Phillips, Manchester Physics Series, 2008 ISBN 0-471-92712-0

External links

• Physics formulae at xs4all.nl

• Alternative version on wikiversity Tables of Physics Formulae Wikiversity
• http://mathworld.wolfram.com/SphericalCoordinates.html