# Fundamental Laws in Physics

Physics | 13 July 2019

As I love physics, here is a single page reference for all those beautiful laws using which we could explore the universe around us. Kindly check out this before reading here.

#### Ampere’s Law

The line integral of the magnetic flux around a closed curve is proportional to the algebraic sum of electric currents flowing through that closed curve; or, in differential form curl $$B = J$$. This was later modified to add a second term when it was incorporated into Maxwell’s equations.

#### Archimedes’ Principle

A body that is submerged in a fluid is buoyed up by a force equal in magnitude to the weight of the fluid that is displaced, and directed upward along a line through the center of gravity of the displaced fluid.

Equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules. It is, in fact, only true for ideal gases.

#### Bernoulli’s Equation

In an irrotational fluid, the sum of the static pressure, the weight of the fluid per unit mass times the height, and half the density times the velocity squared is constant throughout the fluid.

#### Biot-Savart Law

A law which describes the contributions to a magnetic field by an electric current. It is analogous to Coulomb’s law.

#### Boyle’s Law; Mariotte’s Law

The produce of the pressure and the volume of an ideal gas at constant temperature is constant.

#### Bragg’s Law

When a beam of X-rays strikes a crystal surface in which the layers of atoms or ions are regularly separated, the maximum intensity of the reflected ray occurs when the complement of the angle of incidence $$\theta$$, the wavelength of the X-rays $$\lambda$$, and the distance between layers of atoms or ions $$d$$, are related by the equation $$2 d sin(\theta) = n \lambda$$.

#### Brownian Motion

The continuous random motion of solid microscopic particles when suspended in a fluid medium due to the consequence of ongoing bombardment by atoms and molecules.

#### Casimir Effect

A quantum mechanical effect, where two very large plates placed close to each other will experience an attractive force, in the absense of other two forces. The cause is virtual particle-antiparticle pair creation in the vicinity of the plates. Also, the speed of light will be increased in the region between the two plates, in the direction perpendicular to them.

#### Causality Principle

The principle that cause must always precede effect. More formally, if an event A (the cause) somehow influences an event B (the effect) which occurs later in time, then event B cannot in turn have an influence on event A. That is, event B must occur at later time than event A, and further, all frames must agree upon this ordering.

#### Centrifugal Pseudoforce

A pseudoforce on an object when it is moving in uniform circular motion. The force is directed outward from the center of motion.

#### Charles’ Law

The volume of an ideal gas at constant pressure is proportional to the thermodynamic temperature of that gas.

Radiation emitted by a massive particle which is moving faster than light in the medium through which it is traveling. No particle can travel faster than light in vacuum, but the speed of light in other media, such as water, glass, etc. are considerably slower. Cherenkov radiation is the electromagnetic analogue of the sonic boom, through Cherenkov radiation is a shockwave set up in the electromagnetic field.

#### Complementarity Principle

The principle that a given system cannot exhibit both wave-like behavior and particle-like behavior at the same time. That is, certain experiments will reveal the wave-like nature of a system, and certain experiments will reveal the particle-like nature of a system, but no experiment will reveal both simultaneously.

#### Compton Effect

An effect that demonstrates that photons (the quantum of electromagnetic radiation) have momentum. A photon fired at a stationary particle, such as an electron, will impart momentum to the electron and, since its energy has been decreased, will experience a corresponding decrease in frequency.

#### Conservation of mass-energy

The total mass-energy of a closed system remains constant.

#### Conservation of electric charge

The total electric charge of a closed system remains constant

#### Conservation of linear momentum

The total linear momentum of a closed system remains constant

#### Conservation of angular momentum

The total angular momentum of a closed system remains constant

#### Constancy Principle

One of the postulates of A. Einstein’s special theory of relativity, which puts forth that the speed of light in vacuum is measured as the same speed to all observers, regardless of their relative motion.

#### Continuity Equation

An equation which states that a fluid flowing through pipe flows at a rate which is inversely proportional to the cross-sectional area of the pipe. It is in essence a restatement of the conservation of mass during constant flow.

#### Copernican Principle

The idea, suggested by Copernicus, that the Sun, not the Earth, is at the center of the Universe. We now know that neither idea is correct.

#### Coriolis Pseudoforce

A pseudoforce which arises because of motion relative to a frame of reference which is itself rotating relative to a second, inertial frame. The magnitude of the Coriolis “force” is dependent on the speed of the object relative to the noninertial frame, and the direction of the “force” is orthogonal to the object’s velocity.

#### Correspondence Principle

The principle that when a new, more general theory is put forth, it must reduce to the more specialized (and usually simpler) theory under normal circumstances. There are correspondence principles for general relativity to special relativity and special relativity to Newtonian mechanics, but the most widely known correspondence principle is that of quantum mechanics to classical mechanics.

#### Coulomb’s Law

The primary law for electrostatics, analogous to Newton’s law of universal gravitation. It states that the force between two point charges is proportional to the algebraic product of their respective charges as well as proportional to the inverse square of the distance between them.

#### Curie’s Law

The susceptibility of an isotropic paramagnetic substance $$\chi$$ is related to its thermodynamic temperature $$T$$ by the equation $$\chi = \frac{C}{T}$$ where $$C$$ is a material-specific Curie constant.

#### Curie-Weiss Law

A more general form of Curie’s Law, which states that the susceptibility of a paramagnetic substance $$\chi$$ is related to its thermodynamic temperature $$T$$ by the equation $$\chi = \frac{C}{T - T_c}$$ where $$C$$ is a material-specific Curie constant, $$T$$ is absolute temperature and $$T_c$$ is the Curie temperature, both measured in kelvin.

#### Dalton’s Law of partial pressures

The total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of its components; that is, the sum of the pressures that each component would exert if it were present alone and occupied the same volume as the mixture.

#### Doppler Effect

Waves emitted by a moving object as received by an observer will be blueshifted (compressed) if approaching, redshifted (elongated) if receding. It occurs both in sound as well as electromagnetic phenomena.

#### Dulong-Petit Law

The molar heat capacity is approximately equal to the three times the ideal gas constant.

#### Einstein Field Equation

The cornerstone of Einstein’s general theory of relativity, relating the gravitational tensor $$G$$ to the stress-energy tensor $$T$$ by the simple equation $$G = 8 \pi T$$.

#### Einstein’s Mass-Energy Equation

The energy $$E$$ of a particle is equal to its mass $$M$$ times the square of the speed of light $$c$$, giving rise to the best known physics equation in the Universe: $$E = M c^2$$

#### Equivalence Principle

The basic postulate of A. Einstein’s general theory of relativity, which posits that an acceleration is fundamentally indistinguishable from a gravitational field.

The line integral of the electric field around a closed curve is proportional to the instantaneous time rate of change of the magnetic flux through a surface bounded by that closed curve; in differential form curl $$E = -\frac{dB}{dt}$$, where $$\frac{d}{dt}$$ represents partial differentiation.

#### Faraday’s first law of electrolysis

The amount of chemical change during electrolysis is proportional to the charge passed.

#### Faraday’s second law of electrolysis

The charge $$Q$$ required to deposit or liberate a mass $$m$$ is proportional to the charge $$z$$ of the ion, the mass, and inversely proportional to the relative ionic mass $$M$$; mathematically $$Q = \frac{F m z}{M}$$

#### Faraday’s first law of electromagnetic induction

An electromotive force is induced in a conductor when the magnetic field surrounding it changes.

#### Faraday’s second law of electromagnetic induction

The magnitude of the electromotive force is proportional to the rate of change of the field.

#### Faraday’s third law of electromagnetic induction

The sense of the induced electromotive force depends on the direction of the rate of the change of the field.

#### Fermat’s Principle

The principle states that the path taken by a ray of light between any two points in a system is always the path that takes the least time.

#### Gauss Law

The electric flux through a closed surface is proportional to the algebraic sum of electric charges contained within that closed surface; in differential form $$\nabla . E = \frac{\rho}{\epsilon_0}$$, where $$\rho$$ is the charge density.

#### Gauss Law for magnetic fields

The magnetic flux through a closed surface is zero; no magnetic charges exist. In differential form $$\nabla . B = 0$$.

#### Hall Effect

When charged particles flow through a tube which has both an electric field and a magnetic field (perpendicular to the electric field) present in it, only certain velocities of the charged particles are preferred, and will make it un-deviated through the tube; the rest will be deflected into the sides.

#### Hooke’s Law

The stress applied to any solid is proportional to the strain it produces within the elastic limit for that solid. The constant of that proportionality is the Young modulus of elasticity for that substance.

#### Huygens’ Principle

The mechanical propagation of a wave (specifically, of light) is equivalent to assuming that every point on the wavefront acts as point source of wave emission

#### Ideal Gas Law

An equation which sums up the ideal gas laws in one simple equation $$P V = n R T$$

#### Joule-Thomson Effect; Joule-Kelvin Effect

The change in temperature that occurs when a gas expands into a region of lower pressure.

#### Joule’s first law

The heat $$Q$$ produced when a current $$I$$ flows through a resistance $$R$$ for a specified time $$t$$ is given by $$Q = I^2 R t$$.

#### Kepler’s First Law

The orbit of a planet is an ellipse with the Sun at one of the two foci.

#### Kepler’s Second Law

A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

#### Kepler’s Third Law

The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

#### Kirchhoff’s Loop Rule

The sum of the potential differences encountered in a round trip around any closed loop in a circuit is zero.

#### Kirchhoff’s Point Rule

The sum of the currents toward a branch point is equal to the sum of the currents away from the same branch point.

#### Kohlrausch’s Law

If a salt is dissolved in water, the conductivity of the solution is the sum of two values – one depending on the positive ions and the other on the negative ions

#### Lambert’s first law

The illuminance on a surface illuminated by light falling on it perpendicularly from a point source is proportional to the inverse square of the distance between the surface and the source.

#### Lambert’s second law

If the rays meet the surface at an angle, then the illuminance is proportional to the cosine of the angle with the normal. Lambert’s third law The luminous intensity of light decreases exponentially with distance as it travels through an absorbing medium.

#### Laplace Equation

For steady-state heat conduction in one dimension, the temperature distribution is the solution to Laplace’s equation, which states that the second derivative of temperature with respect to displacement is zero.

#### Lenz’s Law

An induced electric current always flows in such a direction that it opposes the change producing it.

#### Mach Number

The ratio of the speed of an object in a given medium to the speed of sound in that medium.

#### Mach’s Principle

The inertia of any particular particle or particles of matter is attributable to the interaction between that piece of matter and the rest of the Universe. Thus, a body in isolation would have no inertia.

### Maxwell’s Equations

#### Gauss law

The electric flux through a closed surface is proportional to the algebraic sum of electric charges contained within that closed surface; in differential form $$\nabla . E = \frac{\rho}{\epsilon_0}$$, where $$\rho$$ is the charge density.

#### Gauss law for magnetic fields

The magnetic flux through a closed surface is zero; no magnetic charges exist. In differential form $$\nabla . B = 0$$.

The line integral of the electric field around a closed curve is proportional to the instantaneous time rate of change of the magnetic flux through a surface bounded by that closed curve; in differential form $$\nabla X E = -\frac{\partial B}{\partial t}$$

#### Ampere’s law, modified form

The line integral of the magnetic field around a closed curve is proportional to the sum of two terms: first, the algebraic sum of electric currents flowing through that closed curve; and second, the instantaneous time rate of change of the electric flux through a surface bounded by that closed curve; in differential form $$\nabla X B = \mu_0 ( J + \epsilon_0 \frac{\partial D}{\partial t} )$$. In addition to describing electromagnetism, his equations also predict that waves can propagate through the electromagnetic field, and would always propagate at the the speed of light in vacuum.

#### Murphy’s Law

If anything can go wrong, it will.

#### Newton’s Law of universal gravitation

Two bodies attract each other with equal and opposite forces; the magnitude of this force is proportional to the product of the two masses and is also proportional to the inverse square of the distance between the centers of mass of the two bodies; $$F = (\frac{G m_1 m_2}{r^2}) e$$, where $$m_1$$ and $$m_2$$ are the masses of the two bodies, $$r$$ is the distance between the two, and $$e$$ is a unit vector directed from the test mass to the second.

#### Newton’s first law of motion

A body continues in its state of constant velocity (which may be zero) unless it is acted upon by an external force.

#### Newton’s second law of motion

For an unbalanced force acting on a body, the acceleration produced is proportional to the force impressed; the constant of proportionality is the inertial mass of the body.

#### Newton’s third law of motion

In a system where no external forces are present, every action force is always opposed by an equal and opposite reaction force.

#### Occam’s Razor

If two theories predict phenomena to the same accuracy, then the one which is simpler is the better one. Moreover, additional aspects of a theory which do not lend it more powerful predicting ability are unnecessary and should be stripped away.

#### Ohm’s Law

The ratio of the potential difference between the ends of a conductor to the current flowing through it is constant; the constant of proportionality is called the resistance, and is different for different materials.

#### Pascal’s Principle

Pressure applied to an enclosed incompressible static fluid is transmitted undiminished to all parts of the fluid.

#### Peter Principle

In a hierarchy, every employee tends to rise to his level of incompetence.

#### Planck Equation

The quantum mechanical equation relating the energy of a photon $$E$$ to its frequency $$f$$: $$E = h f$$.

#### Reflection Law, Snell’s Law

For a wavefront intersecting a reflecting surface, the angle of incidence is equal to the angle of reflection, in the same plane defined by the ray of incidence and the normal.

#### Refraction Law

For a wavefront traveling through a boundary between two media, the first with a refractive index of $$n1$$, and the other with one of $$n2$$, the angle of incidence $$\theta_1$$ is related to the angle of refraction $$\theta_2$$ by $$n1 sin(\theta_1) = n2 sin(\theta_2)$$.

#### Relativity Principle

The principle, employed by Einstein’s relativity theories, that the laws of physics are the same, at least qualitatively, in all frames. That is, there is no frame that is better (or qualitatively any different) from any other. This principle, along with the constancy principle, constitute the founding principles of special relativity.

#### Stefan-Boltzmann Law

The radiated power $$P$$ (rate of emission of electromagnetic energy) of a hot body is proportional to the radiating surface area $$A$$, and the fourth power of the thermodynamic temperature $$T$$. The constant of proportionality is the Stefan-Boltzmann constant. Mathematically $$P = A \epsilon \sigma T^4$$, where the efficiency rating $$\epsilon$$ is called the emissivity of the object.

#### Superposition Principle

The general idea that, when a number of influences are acting on a system, the total influence on that system is merely the sum of the individual influences; that is, influences governed by the superposition principle add linearly.

#### First law of thermodynamics

The change in internal energy of a system is the sum of the heat transferred to or from the system and the work done on or by the system.

#### Second law of thermodynamics

The entropy – a measure of the unavailability of a system’s energy to do useful work – of a closed system tends to increase with time.

#### Third law of thermodynamics

For changes involving only perfect crystalline solids at absolute zero, the change of the total entropy is zero.

#### Zeroth law of thermodynamics

If two bodies are each in thermal equilibrium with a third body, then all three bodies are in thermal equilibrium with each other.

#### Uncertainty Principle

A principle, central to quantum mechanics, which states that two complementary parameters (such as position and momentum, energy and time, or angular momentum and angular displacement) cannot both be known to infinite accuracy; the more you know about one, the less you know about the other.

#### van der Waals force

Forces responsible for the non-ideal behavior of gases, and for the lattice energy of molecular crystals. There are three causes: dipole-dipole interaction; dipole-induced dipole moments; and dispersion forces arising because of small instantaneous dipoles in atoms.

#### Wave-Particle Duality

The principle of quantum mechanics which implies that light (and, indeed, all other subatomic particles) sometimes act like a wave, and sometime act like a particle, depending on the experiment you are performing. For instance, low frequency electromagnetic radiation tends to act more like a wave than a particle; high frequency electromagnetic radiation tends to act more like a particle than a wave.

#### Wiedemann-Franz Law

The ratio of the thermal conductivity of any pure metal to its electrical conductivity is approximately constant for any given temperature. This law holds fairly well except at low temperatures.

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