Static Electric Field
Coulomb's law
The fundamental
equation
of electrostatics is
Coulomb's law
, which
describes the force between two
point charges
.
The magnitude of the electrostatic force between two point electric
charges is directly proportional to the product of the magnitudes of
each charge and inversely proportional to the square of the distance
between the charges.
Q
1 and
Q
2:
where ε
0
is the
electric constant
, a defined value:
in
A
2
s
4
kg

1
m
−3
or
C
2
N
−1
m
−2
or
F
m
−1
The electric field (in units of
volts
per meter) at a point is defined as
the force (in) per unit charge (in
coulombs
) on a charge at that point:
From this definition and Coulomb's law, it
follows that the magnitude of the electric field
E
created by a single point charge
Q
is:
Gauss's law
Gauss' law
states that "the total electric flux through a
closed surface is proportional to the total
electric charge
enclosed within the surface". The constant of
proportionality is the
permittivity of free space
.
Mathematically, Gauss's law takes the form of an integral
equation:
Alternatively, in differential form, the equation becomes:
Electrostatic potential
Because the electric field is irrotational, it is possible to
express the electric field as the
gradient
of a scalar function,
called the
electrostatic potential
(also known as the
voltage
). An electric field,
E
, points from regions of high
potential, φ, to regions of low potential, expressed
mathematically as:
The electrostatic potential at a point can be defined as the
amount of
work
per unit charge required to move a charge
from infinity to the given point
.
Poisson's equation
The definition of electrostatic potential, combined with the
differential form of Gauss's law (above), provides a
relationship between the potential φ and the charge
density ρ:
Laplace's equation
In the absence of unpaired electric charge, the equation
becomes
which is
Laplace's equation
.
The electrostatic approximation
The validity of the electrostatic approximation rests on the
assumption that the electric field is
irrotational
:
From
Faraday's law
, this assumption implies the absence
or near

absence of time

varying magnetic fields:
In other words, electrostatics does not
require the absence of magnetic fields or
electric currents.
Rather, if magnetic fields or electric currents
do
exist, they must not
change with time, or in the worst

case, they must change with time
only
very slowly
. In some problems,
both electrostatics and
magnetostatics
may be required for accurate predictions,
but the coupling between the two can still be ignored
.
Triboelectric series
•
The
triboelectric effect
is a type of contact electrification in
which certain materials become electrically charged when
they are brought into contact with a different material and
then separated.
•
One of the materials acquires a positive charge, and the
other acquires an equal negative charge. The polarity and
strength of the charges produced differ according to the
materials, surface roughness, temperature, strain, and other
properties.
•
Amber, for example, can acquire an electric charge by
friction with a material like wool. This property, first recorded
by
Thales of Miletus
, was the first electrical phenomenon
investigated by man. Other examples of materials that can
acquire a significant charge when rubbed together include
glass rubbed with silk, and hard rubber rubbed with fur.
Charge induction
Charge induction occurs when a negatively charged
object repels electrons from the surface of a second
object. This creates a region in the second object that is
more positively charged. An attractive force is then
exerted between the objects.
For example, when a balloon is rubbed, the balloon will
stick to the wall as an attractive force is exerted by two
oppositely charged surfaces (the surface of the wall gains
an electric charge due to charge induction, as the free
electrons at the surface of the wall are repelled by the
negative balloon, creating a positive wall surface, which is
subsequently attracted to the surface of the balloon). You
can explore the effect with a simulation of the
balloon and
static electricity.
Magnetic Field
Compasses
reveal the
direction of the local
magnetic field. As seen
here, the magnetic field
points towards a
magnet's south pole
and away from its
north pole.
Various physical
phenomena have the
effect of displaying
magnetic field
Sources of magnetism
Magnetism, at its root, arises from two
sources:
•
Electric currents
, or more generally
moving
electric charges
, create magnetic
fields (see
Maxwell's Equations
).
•
Many
particles
have nonzero "intrinsic"
(or "
spin
") magnetic moments. (Just as
each particle, by its nature, has a certain
mass
and
charge
, each has a certain
magnetic moment, possibly zero.)
Magnetic fields and forces
•
When a charged particle moves through a magnetic field
B, it feels a force F given by the
cross product
:
–
•
where
–
q
is the electric charge of the particle,
–
v is the
velocity
vector
of the particle, and
–
B is the magnetic field.
–
Because this is a cross product, the force is
perpendicular
to both the motion of the particle and
the magnetic field. It follows that the magnetic force
does no
work
on the particle; it may change the
direction of the particle's movement, but it cannot
cause it to speed up or slow down. The magnitude of
the force is
•
–
where θ is the angle between v and B.
Magnetism of Earth
While the
influence of
the geomagnetic field
on organisms and the
biosphere as a whole
is well documented,
the underlying physical
mechanisms are not
well understood
(review:
Galland and
Pazur 2005
).
The magnetic flux density of the geomagnetic field is at the
equator 25 and at the poles about 75 µT. The van

Allen

belts (green) protect the biosphere from charged cosmic
particles that move under the influence of the Lorentz

forces on helical trajectories (red) along the field lines.
Right

hand rule
In
mathematics
and
physics
, the right

hand rule is a
common
mnemonic
for understanding notation
conventions for
vectors
in 3 dimensions. It was invented
for use in electromagnetism by British physicist
s
in the
late 1800s.
The left

handed
orientation is
shown on the
left, and the
right

handed on
the right
Right

hand rule
Right

hand rule
Vector assigned to a rotation
Biot
–
Savart law
The
Biot
–
Savart law
(pronounced is an
equation in electromagnetism that describes
the
magnetic field
B
generated by an
electric
current
. The
vector field
B
depends on the
magnitude, direction, length, and proximity of
the electric current, and also on a
fundamental constant called the
magnetic
constant
. The law is valid in the
magnetostatic approximation
, and results in a
B
field consistent with both
Ampère's circuital
law
and
Gauss's law for magnetism
.
[2]
Biot
–
Savart law
The Biot
–
Savart law is used to compute the
magnetic
field
generated by a
steady
current
, i.e. a continual flow
of
charges
, for example through a wire, which is
constant in time and in which charge is neither building
up nor depleting at any point. The equation is as follows:
or (equivalently),
(in
SI
units), where
I
is the current,
dl
is a vector, whose magnitude is
the length of the
differential
element of the wire, and whose direction
is the direction of
conventional current
,
B
is the net magnetic field,
μ
0
is the
magnetic constant
,
is the displacement
unit vector
in the
direction pointing from the wire element towards the point at which
the field is being computed,
is the full
displacement vector
from the wire element to the point at which the field is being
computed,
the symbols in boldface denote
vector quantities
.
Gauss's law for magnetism
In
physics
, Gauss's law for magnetism is one of
Maxwell's equations
, the four equations that underlie
classical electrodynamics
. It states that the
magnetic
field
B has
divergence
equal to zero, in other words, that
it is a
solenoidal vector field
. It is equivalent to the
statement that
magnetic monopoles
do not exist. Rather
than "magnetic charges", the basic entity for magnetism
is the
magnetic dipole
.
The differential form for Gauss's
law for magnetism is the following:
where
denotes
divergence
,
B is the
magnetic field
.
Magnetic moment
The magnetic moment of a system is a measure of the
strength and the direction of its magnetism.
Planar loop
:
In the simplest case of a planar loop of
electric current
, its
magnetic moment is defined as:
is the magnetic
moment, a
vector
measured in
ampere
–
square meters
, or
equivalently in
joules
per
tesla
is the
vector area
of the
current loop, measured in
square meters
(
x
,
y
, and
z
coordinates of this vector
are the areas of
projections of the loop
onto the
yz
,
zx
, and
xy
planes)
is the current in the loop
(assumed to be
constant), a
scalar
measured in
amperes
Magnetic flux
Magnetic flux
, represented by the Greek letter Φ (
phi
), is a
measure of quantity of
magnetism
, taking into account the
strength and the extent of a
magnetic field
. The
SI
unit
of
magnetic flux is the
weber
(in derived units: volt

seconds),
and the unit of magnetic field is the Weber per square meter,
or
T
esla
.
The
flux
through an element of
area
perpendicular
to the direction of
magnetic field is given by the product of the
magnetic field
and the
area
element.
More generally, the magnetic flux at any angle to a surface is defined by a
scalar product
of the magnetic field and the area element vector.
The direction of the magnetic field vector
B
is, by definition, from the south
to the north pole of a magnet (within the magnet). Outside of the magnet,
the field lines will go from north to south.
The magnetic flux through a surface is proportional to the number of
magnetic field lines
that pass through the surface. This is the
net
number,
i.e. the number passing through in one direction, minus the number passing
through in the other direction.
Magnetic flux
In the special case where the surface
S
is a planar surface
with area
A
, and the magnetic field is constant with
magnitude
B
, the formula simplifies to:
where θ is the angle between
B
and the surface normal to
S
.
ELECTROMAGNETIC FIELDS
•
The electromagnetic field
extends indefinitely
throughout space and
describes the
electromagnetic interaction
.
It is one of the four
fundamental forces
of
nature (the others are
gravitation
, the
weak
interaction
, and the
strong
interaction
).
Maxwell's equations
Gauss's law
Gauss's law for magnetism
Faraday's law
Ampère

Maxwell law
Gauss's law may be expressed as:
where Φ
E
is the
electric flux
through a closed surface
S
enclosing any
volume
V
,
Q
is the total
charge
enclosed within
S
, and
ε
0
is the
electric
constant
. The electric flux Φ
E
is defined as a
surface integral
of the
electric field
:
where E is the electric field, dA is a vector representing an
infinitesimal
element of
area
,
[note 1]
and ∙ represents the
dot product
of two vectors.
Since the flux is defined as an
integral
of the electric field,
this expression of Gauss's law is called the
integral form
Living things
Some
organisms
can detect magnetic
fields, a phenomenon known as
magnetoception
.
Magnetobiology
studies magnetic fields as a
medical
treatment; fields naturally produced by
an organism are known as
biomagnetism
.
»
University
»
Biologie
»
Fachgebiete
»
Pflanzenphysiologie und Photobiologie
»
AG Galland
»
Research
»
Magnetoreception
»
Magnetotropism: oriented growth of roots in some wheat cultivars
•
The roots of some Canadian wheat cultivars grow preferentially
(73.4%) in North

South direction; only 5.1% orient in the East

West plane (Pitman, 1962). Magnetotropism was also reported
for the secondary roots of pea (Maharramov, 2005)
»
University
»
Biologie
»
Fachgebiete
»
Pflanzenphysiologie und Photobiologie
»
AG Galland
»
Research
»
Magnetoreception
»
Magnetotaxis: Aquaspirillum magnetotacticum
•
Magnetotactic bacteria possess a chain of magnetosomes
(magnetite Fe3O4) that align themselves
–
and as a
consequence also the bacterium
–
parallel to the geomagnetic
field lines (Blakemore 1982).
»
University
»
Biologie
»
Fachgebiete
»
Pflanzenphysiologie und
Photobiologie
»
AG Galland
»
Research
»
Magnetoreception
»
Dependence of the phototropic balance on the magnetic flux density
•
Sporangiophores of the fungus
Phycomyces blakesleeanus
are placed
between two monochro

matic light sources and the phototropic balance
point is determined after eight hours. The ratio of the photon

fluence rates of
green (532 nm) and blue (470 nm) light depends on the magnetic flux
density (Galland unpublished).
•
»
University
»
Biologie
»
Fachgebiete
»
Pflanzenphysiologie und Photobiologie
»
AG Galland
»
Research
»
Magnetoreception
»
Hypocotyl growth in seedlings of Arabidopsis thaliana
•
Cryptochromes 1 und 2 mediate the blue

light induced shortening of
hypocotyls and the accumulation of anthocyanins in seedlings of
dicotyledonous plants. Elevated magnetic flux densities of 500 µT that
can be generated in an Helmholtz

coil enhance the effectiveness of the
blue

light irradiation. The radical

pair mechanism provides an
explanation for this magnetoresponse (
Ahmad et al. 2007
).
Myocardial Function Improved by
Electromagnetic Field Induction
of Stress Protein hsp70
•
(1)
ISAAC GEORGE, MEHMET C. OZ, ZACHARY LILL
;
Department of
Surgery, Division of Cardiothoracic Surgery, Columbia University
College of Physicians and Surgeons, New York
•
(2)
MATTHEW S. GEDDIS, TEODORO GOMEZ
;
Department of Surgery,
Division of Surgical Sciences, Columbia University College of
Physicians and Surgeons, New York, New York
•
(3)
HANA LIN AND REBA GOODMAN
;
Department of Anatomy and
Pathology, Columbia University College of Physicians and Surgeons,
New York, New York
•
(4)
MARTIN BLANK
;
Department of Physiology and Cellular
Biophysics, Columbia University College of Physicians and Surgeons,
New York, New York
Myocardial Function Improved by
Electromagnetic Field Induction
of Stress Protein hsp70
Our data
indicate that pre

exposure with
EMF prior to ischemia and
reperfusion, in a
mammalian model, induces up

regulation of
the
HSP70 gene, subsequently increased
levels of hsp70 protein,
and,
most
importantly, improved ventricular function
after
ischemia

reperfusion.
Myocardial Function Improved by
Electromagnetic Field Induction
of Stress Protein hsp70
Studies on myocardial function have shown
that hsp70, stimulated by an increase in
temperature, leads to improved survival
following ischemia

reperfusion (I

R). Low
frequency electromagnetic fields (EMFs)
also induce the stress protein hsp70, but
without elevating temperature.
EMF exposure
system:
Animals
were exposed to
60 Hz/8 mT
EMFs by
Helmholtz coils
(19G copper wire,
164 turns, 1.5
inches thick
covered with
electrical tape;
part A) that was
contained within a
plastic exposure
cage (part B). The
EMF was
perpendicular
to the exposure
device.
EMRE
Electromagnetic Response Element
•
Electromagnetic fields stress living
cells
•
(a) Martin Blank
,
(b) Reba Goodman
•
(a)
Department of Physiology, Columbia
University, New York, NY, USA
•
(b)
Department of Pathology, Columbia University,
New York, NY, USA
•
Received 30 January 2009; accepted 30 January
2009;
Pathophysiology xxx (2009) xxx
–
xxx
Diagram of the HSP70 promoter showing the two
different DNA sequences that have been identified
as activated by EMF (non

thermal) and by thermal
stimuli, respectively. The EMF domain contains
three nCTCTn consensus sequences
(electromagnetic response elements; EMRE), and
differs from the consensus sequence (nGAAn) in
the temperature or thermal domain.
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