 |
SOPHIA OF WISDOM III - MAGNETIC FIELD
PICTURE BELOW
THE LIBRARY OF SOPHIA OF WISDOM III
THE SOPHIA OF ALL SOPHIA OF WISDOMS
AKA
CAROLINE E. KENNEDY, JR._______________________
JAN 27, 2007
****NOTES FROM SOPHIA OF WISDOM III-
- WITH A SNAP OF MY FINGERS I CAN PULL THE CHRIST GRID AND THE EARTH'S MAGNETIC GRID.......
MAGNETIC FIELD
In physics, a magnetic field is that part of the electromagnetic field that exerts a force on a moving charge. A magnetic field can be caused either by another moving charge (i.e., by an electric current) or by a changing electric field. The magnetic field is a vector quantity, and has SI units of tesla, 1 T= 1 kg·s−1·C−1.
There are two quantities that physicists may refer to as the magnetic field, notated and . Although the term "magnetic field" was historically reserved for , with being termed the "magnetic induction," is now understood to be the more fundamental entity, and most modern writers refer to as the magnetic field, except when context fails to make it clear whether the quantity being discussed is or . See [1]
Contents [hide]
1 Definition
2 The Difference between the field and the field
3 Magnetic field of current flow of charged particles
4 Lorentz force on wire segment
5 Symbols and terminology
6 Properties
6.1 Magnetic field lines
6.2 Pole labelling confusions
6.3 Field density
7 Historical Information
8 Rotating magnetic fields
9 Hall effect
10 Extension to the Theory of Relativity
11 See also
12 References
13 Notes
14 External links
[edit] Definition
The following term in Lorentz transformations of the electric field E of moving with the velocity v electric charge is called magnetic field B:
where
is velocity of the electric charge, measured in metres per second
indicates a vector cross product
c is the speed of light in a vacuum measured in metres per second
is the electric field measured in newtons per coulomb or volts per metre
As seen from the definition, the unit of magnetic field is newton-second per coulomb-metre (or newton per ampere-metre) and is called the tesla. Like the electric field, the magnetic field exerts force on electric charge — but unlike an electric field, only on moving charge:
where
is the force produced, measured in newtons
is electric charge that the magnetic field is acting on, measured in coulombs
is velocity of the electric charge , measured in metres per second
Because magnetic field is the relativistic product of Lorentz transformations, the force it produces is called the Lorentz force.
The force due to the magnetic field is different in different frames — moving magnetic field (as well as changing magnetic field) transforms partially or fully back into electric field under Lorentz transformations. This results in Faraday's law of induction.
[edit] The Difference between the field and the field
The difference between the vector and the vector can be traced back to Maxwell's 1855 paper entitled 'On Faraday's Lines of Force'. It is later clarified in his concept of a sea of molecular vortices that appears in his 1861 paper On Physical Lines of Force - 1861. Within that context, represented pure vorticity (spin), whereas was a weighted vorticity that was weighted for the density of the vortex sea. Maxwell considered magnetic permeability ì to be a measure of the density of the vortex sea. Hence the relationship,
(1) Magnetic Induction Current
was essentially a rotational analogy to the linear electric current relationship,
(2) Electric Convection Current
where ñ is electric charge density. was seen as a kind of magnetic current of vortices aligned in their axial planes, with being the circumferential velocity of the vortices.
The electric current equation can be viewed as a convective current of electric charge that involves linear motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the vector. The magnetic inductive current represents lines of force. In particular, it represents lines of inverse square law force.
The extension of the above considerations confirms that where is to , and where is to ñ, then it necessarily follows from Gauss's law and from the equation of continuity of charge that is to . Ie. parallels with , whereas parallels with .
[edit] Magnetic field of current flow of charged particles
Charged particle drifts in a homogenous magnetic field. (A) No disturbing force (B) With an electric field, E (C) With an independent force, F (eg. gravity) (D) In an inhomgeneous magnetic field, grad HSubstituting into the definition of magnetic field
the proper electric field of point-like charge (see Coulomb's law)
results in the equation of magnetic field of moving charge, which is usually called the Biot-Savart law:
where
q is electric charge, whose motion creates the magnetic field, measured in coulombs
is velocity of the electric charge q that is generating , measured in metres per second
is the magnetic field (measured in teslas)
[edit] Lorentz force on wire segment
Integrating the Lorentz force on an individual charged particle over a flow (current) of charged particles results in the Lorentz force on a stationary wire carrying electric current:
where
F = forces, measured in newtons
I = current in wire, measured in amperes
B = magnetic field, measured in teslas
l = length of wire, measured in metres
In the equation above, the current vector I is a vector with magnitude equal to the scalar current, I, and direction pointing along the wire in which the current is flowing.
Alternatively, instead of current, the wire segment l can be considered a vector.
The Lorentz force on a macroscopic current carrier is often referred to as the Laplace force.
[edit] Symbols and terminology
Magnetic field is usually denoted by the symbol . Historically, was called the magnetic flux density or magnetic induction. A distinct quantity, , was called the magnetic field (strength), and this terminology is still often used to distinguish the two in the context of magnetic materials (non-trivial permeability ì). Otherwise, however, this distinction is often ignored, and both quantities are frequently referred to as "the magnetic field." (Some authors call the auxiliary field, instead.) In linear materials, such as air or free space, the two quantities are linearly related:
where
is the magnetic permeability of the medium, measured in henries per metre.
In SI units, and are measured in teslas (T) and amperes per metre (A/m), respectively; or, in cgs units, in gauss (G) and oersteds (Oe), respectively. Two parallel wires carrying an electric current in the same direction will generate a magnetic field that will cause a force of attraction between them. This fact is used to define the value of an ampere of electric current. While like charges repel and unlike ones attract, the opposite holds for currents: if the current in one of the two parallel wires is reversed, the two will repel.
[edit] Properties
Maxwell did much to unify static electricity and magnetism, producing a set of four equations relating the two fields. However, under Maxwell's formulation, there were still two distinct fields describing different phenomena. It was Albert Einstein who showed, using special relativity, that electric and magnetic fields are two aspects of the same thing (a rank-2 tensor), and that one stationary observer may perceive a magnetic force where a moving observer perceives only an electrostatic force. Thus, using special relativity, magnetic forces are a manifestation of electrostatic forces of charges in motion and may be predicted from knowledge of the electrostatic forces and the velocity of movement (relative to some observer) of the charges. Despite the fact that magnetic field can be replaced by the vector product of electric field and velocity of observer v (see the definition of B above), for practical purposes it is more convenient to keep symbol B (rather than v) in the equations of electromagnetism.
A thought experiment one can do to show this is with two identical infinite and parallel lines of charge having no motion relative to each other but moving together relative to an observer. Another observer is moving alongside the two lines of charge (at the same velocity) and observes only electrostatic repulsive force and acceleration. The first or "stationary" observer seeing the two lines (and second observer) moving past with some known velocity also observes that the "moving" observer's clock is ticking more slowly (due to time dilation) and thus observes the repulsive acceleration of the lines more slowly than that which the "moving" observer sees. The reduction of repulsive acceleration can be thought of as an attractive force, in a classical physics context, that reduces the electrostatic repulsive force and also that is increasing with increasing velocity. This pseudo-force is precisely the same as the electromagnetic force in a classical context.
A changing magnetic field is mathematically the same as a moving magnetic field (see relativity of motion). Thus, according to Einstein's field transformation equations (that is, the Lorentz transformation of the field from a proper reference frame to a non-moving reference frame), part of it is manifested as an electric field component. This is known as Faraday's law of induction and is the principle behind electric generators and electric motors.
[edit] Magnetic field lines
Magnetic field lines shown by iron filingsThe direction of the magnetic field vector follows from the definition above. It coincides with the direction of orientation of a magnetic dipole, such as a small magnet, a small loop of current in the magnetic field, or a cluster of small particles of ferromagnetic material (see figure).
[edit] Pole labelling confusions
See also Magnetic North Pole and Magnetic South Pole.
The end of a compass needle that points north was historically called the "north" magnetic pole of the needle. Since dipoles are vectors and align "head to tail" with each other, the magnetic pole located near the geographic North Pole is actually the "south" pole.
The "north" and "south" poles of a magnet or a magnetic dipole are labelled similarly to north and south poles of a compass needle. Near the north pole of a bar or a cylinder magnet, the magnetic field vector is directed out of the magnet; near the south pole, into the magnet. This magnetic field continues inside the magnet (so there are no actual "poles" anywhere inside or outside of a magnet where the field stops or starts). Breaking a magnet in half does not separate the poles but produces two magnets with two poles each.
Earth's magnetic field is probably produced by electric currents in its liquid core.
[edit] Field density
Magnetic field density, otherwise known as magnetic flux density, is essentially what the layman knows as a magnetic field — akin to a gravitational or electric field. It is a response of a medium to the presence of a magnetic field. The SI unit of magnetic flux density is the tesla. 1 tesla = 1 weber per square metre.
It can be more easily explained if one works backwards from the equation:
where
B is the magnitude of flux density, measured in teslas
F is the force experienced by a wire, measured in Newtons
I is the current, measured in amperes
L is the length of the wire, measured in metres
Demonstration of Fleming's left hand ruleFor a magnetic flux density to equal 1 tesla, a force of 1 newton must act on a wire of length 1 metre carrying 1 ampere of current.
1 newton of force is not easily accomplished. For example: the most powerful superconducting electromagnets in the world have flux densities of 'only' 20 T. This is true obviously for both electromagnets and natural magnets, but a magnetic field can only act on moving charge — hence the current, I, in the equation.
The equation can be adjusted to incorporate moving single charges, ie protons, electrons, and so on via
where
Q is the charge in coulombs, and
v is the velocity of that charge in metres per second.
Fleming's left hand rule for motion, current and polarity can be used to determine the direction of any one of those from the other two, as seen in the example. It can also be remembered in the following way. The digits from the thumb to second finger indicate 'Force', 'B-field', and 'I(Current)' respectively, or F-B-I in short. For professional use, the right hand grip rule is used instead which originated from the definition of cross product in the right hand system of coordinates.
Other units of magnetic flux density are
1 gauss = 10−4 teslas = 100 microteslas (µT)
1 gamma = 10−9 teslas = 1 nanotesla (nT)
[edit] Historical Information
The difference between the B field and the H field can be historically traced back to Maxwell's concept of a sea of molecular vortices. See his original 1861 paper 'On Physical Lines of Force'.
Within that context, H represented pure vorticity (spin), whereas B was a weighted vorticity that was weighted for the density of the vortex sea. Maxwell considered magnetic permeability to be a measure of the density of the vortex sea. Hence the relationship,
(1) Magnetic Induction Current
was essentially an angular analogy to the linear electric current relationship,
(2) Electric Convection Current
B was seen as a kind of magnetic current of vortices aligned in their axial planes, with H being the circumferential velocity of the vortices.
The electric current equation can be viewed as a convective current of electric charge that involves motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the B vector. The magnetic inductive current represents lines of force. In particular, it represents lines of inverse square law force.
The extension of the above considerations confirms that where B is to H, and where J is to ñ, then it necessary follows from Gauss's law and from the equation of continuity of charge that D is to E. Ie. B parallels with D, whereas H parallels with E.
[edit] Rotating magnetic fields
Main article: Alternator
The rotating magnetic field is a key principle in the operation of alternating-current motors. A permanent magnet in such a field will rotate so as to maintain its alignment with the external field. This effect was conceptualized by Nikola Tesla, and later utilised in his, and others, early AC (alternating-current) electric motors. A rotating magnetic field can be constructed using two orthogonal coils with 90 degrees phase differenc
LIBRARY OF SOPHIA OF WISDOM III
BACK UP INFO
Send E-Mail to: libraryofsophia3@webspawner.com
Copyright © 2007 SOPHIA OF WISDOM III - THE SOPHIA OF ALL SOPHIA OF WISDOMS. All Rights Reserved