This article was
prepared especially for "Crain's Petrophysical Handbook" by
E. R. (Ross) Crain, P.Eng. in 2005 based on numerous
This webpage version is the copyrighted intellectual
property of the author.
Do not copy or distribute in any form without explicit
LAWS OF PHYSICS
basic laws of physics fall into two categories: classical physics
that deals with the observable world (classical mechanics), and
atomic physics that deals with the interactions between elementary
and sub atomic particles (quantum mechanics). The basic laws of both
are listed here in alphabetical order. Some laws apply only to one
or the other category; some belong to both. A few of the laws listed
may have little impact on petrophysics and some may have been left
off the list for any number of reasons.
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.
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.
Avogadro's Hypothesis (1811)
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.
- 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.
- A law which describes the
contributions to a magnetic field by an electric current. It is
Boyle's Law (1662); Mariotte's law (1676)
- The product of the pressure
and the volume of an ideal gas at constant temperature is a
Bragg's Law (1912)
- 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
Brownian Motion (1827)
- The continuous random motion
of solid microscopic particles when suspended in a fluid medium
due to the consequence of ongoing bombardment by atoms and
- A quantum mechanical effect,
where two very large plates placed close to each other will
experience an attractive force, in the absence of other 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.
- The principle that cause must
always preceed 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 a later time t than event A, and
further, all frames must agree upon this ordering.
pseudoforce on an object when it is moving in uniform
circular motion. The "force" is directed outward from the center
Charles' Law (1787)
- 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
in vacuum, but the speed of light in other media, such as water,
glass, etc., are considerably lower. Cherenkov radiation is the
electromagnetic analogue of the sonic boom, though Cherenkov
radiation is a shockwave set up in the electromagnetic field.
- The principle that a given
system cannot exhibit both
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 (1923)
- 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.
There are several other laws
that deal with particle physics, such as conservation of baryon
number, of strangeness, etc., which are conserved in some
fundamental interactions (such as the electromagnetic
interaction) but not others (such as the weak interaction).
- 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
- An equation which states that
a fluid flowing through a 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
Copernican Principle (1624)
- 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 (1835)
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
- 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.
- 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.
- The susceptibility of an
isotropic paramagnetic substance is related to its thermodynamic
temperature T by the equation KHI =
- A more general form of
which states that the susceptibility of a paramagnetic substance
is related to its thermodynamic temperature T by the
W, where W is the Weiss constant.
Dalton's Law of partial
- 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.
- 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 (1819)
- 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 c2.
- The basic postulate of A.
Einstein's general theory of relativity, which posits that an
acceleration is fundamentally indistinguishable from a
- 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 = -dB/dt, where
here d/dt represents partial differentiation.
Faraday's first law of electrolysis
- The amount of chemical
change during electrolysis is proportional to the charge
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 =
F m z / M,
Faraday's first law of electromagnetic induction
- An electromotive force is
induced in a conductor when the magnetic field surrounding
Faraday's second law of electromagnetic induction
- The magnitude of the
electromotive force is proportional to the rate of change of
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.
- 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.
- The electric flux through a
closed surface is proportional to the algebraic sum of electric
charges contained within that closed surface; in differential
form div E =
rho, where rho
is the charge density.
Gauss' Law for magnetic
- The magnetic flux through a
closed surface is zero; no magnetic charges exist; in
div B = 0.
- 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.
- 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
- 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
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
= I2 R t .
- The sum of the
potential differences encountered in a round trip around
any closed loop in a circuit is zero.
- The sum of the
currents toward a branch point is equal to the sum of
the currents away from the same branch point.
- 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
- 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.
- If the rays meet the
surface at an angle, then the illuminance is
proportional to the cosine of the angle with the normal.
- The luminous
intensity of light decreases exponentially with distance
as it travels through an absorbing medium.
- 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 (1835)
- 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 (1870)
- 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 (1864)
- 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
div E = rho,
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
- 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
curl E = -dB/dt,..
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
curl H = J
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.
- If anything can go wrong, it
Newton's Law of universal
- 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;
e, where m and M 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 Laws of motion
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.
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.
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 (1340)
- 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.
- 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
- Pressure applied to an
enclosed incompressible static fluid is transmitted undiminished
to all parts of the fluid.
- In a hierarchy, every
employee tends to rise to his level of incompetence.
- The quantum mechanical
equation relating the energy of a photon E to its
- 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.
- 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 is
related to the angle of refraction phi by n1
sin theta = n2 sin phi.
- 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
- 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
Mathematically P = e
sigma A T4,.where the efficiency rating e
is called the emissivity of the object.
- 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
- 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.
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.
- For changes involving
only perfect crystalline solids at absolute zero, the change
of the total entropy is zero.
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 (1927)
- 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.
- 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
- 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.