Static Electric Field

1. Static Electric Field • where ε0 is the electric constant, a defined value: • in A2s4 kg-1m−3 or C2N−1m−2 or F m−1 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.Q1 and Q2: 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:

2. Gauss's lawGauss' 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:

3. Electrostatic potentialBecause 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 workper unit charge required to move a charge from infinity to the given point.

4. Poisson's equationThe 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.

5. 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.

6. 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.

7. 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.

8. 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

9. 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.)

10. 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 velocityvector 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.

11. Magnetism of Earth 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. While theinfluence 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).

12. 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 physicists in the late 1800s. The left-handed orientation is shown on the left, and the right-handed on the right

13. Right-hand rule

14. Right-hand rule Vector assigned to a rotation

15. Biot–Savart law The Biot–Savart law (pronounced is an equation in electromagnetism that describes the magnetic fieldB generated by an electric current. The vector fieldB 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]

16. 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), whereI is the current,dlis 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,μ0 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.

17. 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.

18. 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

19. 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 SIunit of magnetic flux is the weber (in derived units: volt-seconds), and the unit of magnetic field is the Weber per square meter, or Tesla. The flux through an element of areaperpendicular 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.

20. 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.

21. 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).

22. Maxwell's equations Gauss's law Gauss's law for magnetism Faraday's law Ampère-Maxwell law

23. Gauss's law may be expressed as: where ΦE is the electric flux through a closed surface S enclosing any volume V, Q is the total charge enclosed within S, and ε0 is the electric constant. The electric flux ΦE 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

24. 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.

25. Examples

26. » 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)

31. » 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).

32. » 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).

33. » 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).

34. Myocardial Function Improved byElectromagnetic Field Inductionof 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

36. Myocardial Function Improved byElectromagnetic Field Inductionof Stress Protein hsp70 Our dataindicate that pre-exposure withEMF prior to ischemia andreperfusion, in a mammalian model, induces up-regulation of theHSP70 gene, subsequently increased levels of hsp70 protein,and,most importantly, improved ventricular function afterischemia-reperfusion.

37. Myocardial Function Improved byElectromagnetic Field Inductionof 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.

38. 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.

44. EMREElectromagnetic 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

45. 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.