detector de Field strenge

[Adrian Pop]

Magnetism

Magnetism is the force of attraction or repulsion resulting from the motion of electric charges. While the force lines associated with electric charges tend to be strait, magnetic force lines tend to be circular.

By Geek3 [GFDL or CC-BY-SA-3.0], via Wikimedia Commons
This is an illustration of the magnetic field around a cylindrical magnet Note that there are two poles in stead of one. The magnet force lines are depicted as going from north to south in a circular pattern.
By Geek3 [GFDL or CC-BY-SA-3.0], via Wikimedia Commons	By Geek3 [GFDL or CC-BY-SA-3.0], via Wikimedia Commons
This is an illustration of the magnetic field around antiparallel cylindrical magnets Note that each magnet has two poles in. The magnet force lines are depicted as going between the two magnets from a north pole to a south pole in a circular pattern As a result the two magnets are attracted to each other.	This is an illustration of the magnetic field around parallel cylindrical magnets. Note that each magnet has two poles in. The magnet force lines are depicted as going from the North Pole to South Pole of each magnet in a circular pattern. However they are repelling the force lines of the other magnet. As a result the two magnets are repelling each other.
By Geek3 [GFDL or CC-BY-SA-3.0], via Wikimedia Commons	By Geek3 [GFDL or CC-BY-SA-3.0], via Wikimedia Commons
This is an illustration of the magnetic field around two cylindrical magnets oriented end to end and North Pole to South Pole. Note that each magnet has two poles in it. The magnet force lines are depicted as going between the two magnets from a north pole to a south pole in a circular pattern. As a result the two magnets are attracted to each other.	This is an illustration of the magnetic field around two cylindrical magnets oriented end to end and North Pole to North Pole. Note that each magnet has two poles in it. The magnet force lines are depicted as going from the North Pole to South Pole of each magnet in a circular pattern However they are repelling the force lines of the other magnet resulting in the two magnets are repelling each other.

Magnetism is seen naturally is certain rare-earth minerals and ferromagnetic material such as iron can be artificially magnetized. The Earth has its own magnetic field as do the planets Mercury, Jupiter, Saturn, Uranus, and Neptune.
It was the tendency of natural magnets to point north when allowed to turn freely that helped lead to the discovery of Magnetism. The other key was their ability to pick up metal objects. However the fields of permanent magnets can not be controlled.

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Electrodynamics

Electrodynamics is the branch of physics dealing with the electromagnetic forces between electric charges. In its most basic form electrodynamics deals with the affect of charges in relative motion.

When an electric field is not in relative motion then you just the electric field but when this electric field is placed in relative motion the result is a magnetic field at right angles to both the electric field and relative motion. In addition a magnetic field in relative motion will in turn produce an electric field in the same directions as shown in the illustration.

[Adrian Pop]

A common way of determining field directions is called right hand rule. It show up several time in the field of electromagnetism To use it in this case hold you hand as shown here with the three fingers at right angles to each other.

The three vectors point as illustrated the velocity points in the direction of the thumb, the magnetic field points in the direction of the index finger and the electric field points in the direction of the middle finger.
It is this mutual production of electric and magnetic fields that forms the bases of the unification of eclectic and magnetic fields. Every thing else in electromagnetism extends from this starting principles.

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Electromagnets

An electromagnet is a magnet whose magnetic field is produced by way of an electric current. The magnetic field of an electromagnet exists only as long as the electric current is flowing. This magnetic field ceases to exist when the electric current is turned off.

An electromagnet starts with a wire.

Induce an electric current into the wire flowing in the direction of the arrow.

The flow of the electric current produces a magnetic field even though the wire remains electrically neutral.

[Adrian Pop]

This is where the right hand rule again come into play. Point you thumb in the direction of the current.

Rap your hand around the wire and the magnetic field points in the direction you fingers are pointing.

By Geek3 [GFDL or CC-BY-SA-3.0], via Wikimedia Commons
When the wire is bent into a loop it produces a dipole magnetic field.

By Geek3 [GFDL or CC-BY-SA-3.0], via Wikimedia Commons
When the loop is repeats several times the result is an electromagnet. Putting a peace of iron or other ferromagnetic material in the coil called the core it increases its strength by magnetizing the core material.

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Electromagnetic radiation

Electromagnetic radiation is the form of energy that charged particles absorb and emit and travels through space at the speed of light with a wave-like behavior.

By P.wormer (Own work) [CC-BY-SA-3.0 or GFDL], via Wikimedia Commons
Electromagnetic radiation contains both electric and magnetic field components. These field components osculate in a wave-like pattern at right angles to each other

By Inductiveload, NASA [GFDL or CC-BY-SA-3.0], via Wikimedia Commons
This results in the electromagnetic spectrum which includes radio waves, microwaves, infrared, visible light, ultraviolet, X – rays, gamma Rays and cosmic rays. Each type of electromagnetic radiation is distinguished by wavelength.

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Conclusion

Electromagnetism is one of the four fundamental forces of nature. It not only literally holds things together but it is light itself.

[Adrian Pop]

12.3.1 The Form of the Magnetic Lead Field

Plonsey extended the application of the reciprocity theorem to the time-varying conditions that arise in biomagnetic measurements (Plonsey, 1972). That development follows along lines similar to the proof of the reciprocity theorem for electric fields and therefore need not be repeated here. Only the equations for the reciprocity theorem for magnetic measurements are derived here. In this discussion subscript L denotes "lead," as in the previous chapter, but we add a subscript M to denote "magnetic leads" due to reciprocal current of unit time derivative.
The current induced in a conductor depends on the rate of change of the magnetic flux that links the current loop. In analogy to the electric field case (see Equations 11.30 and 11.52), the reciprocally energizing (time-varying) current I_r is normalized so that its time derivative is unityfor all values of ω. The necessary equations for the lead field theory for biomagnetic measurements can then be readily obtained from the corresponding equations in electric measurements.
An elementary bipolar lead in magnetic measurements is a solenoid (coil) with a core and disklike terminals of infinite permeability, as illustrated in Figure 12.2. If the coil is energized with a current, a magnetic field is set up, which can be considered to result from magnetic charges (equal and opposite) at the terminals of the core. These terminals are called magnodes (Baule and McFee, 1963). (The word "electrode" was introduced by Michael Faraday (1834).) This elementary bipolar magnetic lead is equivalent to the elementary bipolar electric lead illustrated in Figure 11.23.
When a reciprocal current I_r is fed to the elementary magnetic lead, it produces in an infinite space of uniform permeability a reciprocal magnetic scalar potential field Φ_LM of the same spatial behavior as the reciprocal scalar electric potential field Φ_LE in an infinite medium of uniform conductivity arising from a reciprocally energized electric lead, whose electrodes are located at sites corresponding to the magnodes. As noted in Section 11.6.6, if the electrodes or magnodes are parallel and their dimensions are large compared to their separation, both Φ_LE and Φ_LM are uniform in the central region..

• Fig. 12.2. Basic form of a bipolar magnetic lead, where

  where	Ir	= reciprocal current
  	ΦLM	= reciprocal magnetic scalar potential field
  	LM	= reciprocal magnetic field
  	LM	= reciprocal magnetic induction field
  	LM	= reciprocal electric field
  	LM	= lead field
  	VLM	= voltage in the lead due to the volume source i in the volume conductor
  	μ	= magnetic permeability of the medium
  	σ	= conductivity of the medium
  		= radius vector.

[Adrian Pop]

The relative directions of the magnetic field and the induced currents and detected signal are sketched in Figure 12.2. If the reciprocal magnetic field _LM of Equation 12.11 is uniform and in the negative coordinate direction, as in Figure 12.2, the form of the resulting lead field current density _LM is tangential and oriented in the positive direction of rotation. It should be remembered that harmonic conditions have been assumed so that since we are plotting the peak magnitude of _LM versus _LM, the sign chosen for each vector class is arbitrary. The instantaneous relationship can be found from Equation 12.11, if the explicit phasor notation is restored, including the 90-degree phase lag of _LM.

• Fig. 12.3. Lead field current density of a magnetic lead.
  (A) The lead field current density - that is, the sensitivity - is directed tangentially, and its magnitude is proportional to the distance from the symmetry axis. Note that in this figure the dashed line represents the symmetry axis where the lead field current density is zero.
  (B) Lead field current density shown on one plane with flow lines and
  (C) with current density vectors.
  (D) Lead field current density as a function of distance from the symmetry axis.
  (E) Isosensitivity lines of the lead.

[Adrian Pop]

• The region where the coils produce linear reciprocal magnetic fields is rather small and therefore Figures 12.4A and 12.4B are not to scale.

• Fig. 12.5. The three components of the lead field _LM of an ideal lead system detecting the magnetic dipole moment of a volume source.

[Adrian Pop]

MAGNETOMETER CONFIGURATION	LEAD FIELD OF ONE COMPONENT
A	UNIPOLAR LEADS, SMALL COILS

B	BIPOLAR LEADS, SMALL COILS

C	BIPOLAR LEADS, LARGE COILS

• Fig. 12.6. Properties of unipolar and bipolar leads in detecting the equivalent magnetic dipole moment of a volume source. The dashed lines illustrate the isosensitivity lines. The thin solid circular lines represent the lead field flow lines.

[Adrian Pop]

The arrangement of bipolar lead must not be confused with the differential magnetometer or gradiometer system, which consists of two coaxial coils on the same side of the source wound in opposite directions. The purpose of such an arrangement is to null out the background noise, not to improve the quality of the lead field. The realization of the bipolar lead system with gradiometers is illustrated in Figure 12.8. Later Figure 12.20 illustrates the effect of the second coil on the gradiometer sensitivity distribution for several baselines..

• Fig. 12.7. Flux tubes of the reciprocal magnetic field of
  (A) the Helmholtz coils having a coil separation of r
  (B) bipolar lead with a coil separation of 5r.
  The isosensitivity lines for
  (C) the Helmholtz coils having a coil separation of r
  (D) bipolar lead with a coil separation of 5r.
  (Note, that the isosensitivity lines are not the same as the flux tubes of the reciprocal magnetic field.).

• Fig. 12.8. Bipolar lead system for detecting the magnetic dipole moment of a volume source realized with gradiometers.

[Adrian Pop]

We note from Equations 12.26 and 12.27 that the total sensitivity of these two components of the electric lead to radial and tangential current source elements ⁱ is equal and independent of their location. The same conclusion also holds in all three dimensions..

• Fig. 12.9. Relative sensitivity of the electric lead system to radial and tangential current dipoles ⁱ_r and ⁱ_t.

12.8.2 Sensitivity of the Magnetic Lead

From Equation 12.13 and from the definition of the magnetic dipole moment of a volume source (see Equation 12.22), it may be seen that the magnetic lead system and its components are sensitive only to tangential source-elements. The magnitude of the sensitivity is, as noted before, proportional to the distance from the symmetry axis.

[Adrian Pop]

1. The reciprocity theorem also applies to the reciprocal situation. This means that in a tank model it is possible to feed a "reciprocally reciprocal" current to the dipole in the conductor and to measure the signal from the lead. However, the result may be interpreted as having been obtained by feeding the reciprocal current to the lead with the signal measured from the dipole. The benefit of this "reciprocally reciprocal" arrangement is that for technical reasons the signal-to-noise ratio may be improved while we still have the benefit of interpreting the result as the distribution of the lead field current in the volume conductor (Malmivuo, 1976)..

• Fig. 12.10. The poorly conducting skull does not affect the magnetic detection of the electric activity of the brain.

• Fig. 12.11. Magnetic lead fields in volume conductors exhibiting spherical symmetry are always directed tangentially. The figure illustrates also the approximate form of the zero sensitivity line in the volume conductor. (The zero sensitivity line may be imagined to continue hypothetically through the magnetometer coil.).

• Fig. 12.12. If the electrodes of a symmetric bipolar electric lead are located on the symmetry axis of the bipolar magnetic field detector arranged for a spherical volume conductor, these lead fields of the electric and magnetic leads are normal to each other throughout the volume conductor.

• Fig. 12.13. Zero sensitivity lines in volume conductors of various forms. The dimensions are given in millimeters (Eskola, 1979, 1983; Eskola and Malmivuo, 1983). As in Figure 12.11, the zero sensitivity lines are illustrated to continue hypothetically through the magnetometer coils.