Electric and Magnetic Fields

In this chapter, we study the effects of uniform static electric and magnetic fields on the thermodynamic properties of material. The source of the fields may be in the surroundings or included in the system of interest. In either case, the properties of the material affect the value of the effective field at any point in the material. It is for this reason that the study of electric and magnetic fields is more complicated than the study of gravitational and centrifugal fields presented in the next chapter. 

In Sec. 14-1, we discuss the thermodynamic properties of uniform, homogeneous dielectric material in an electrostatic field. In Sec. 14-2, a brief resume of the properties of material in a magnetic field is presented. 

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The central equations of electromagnetic theory are elegantly written in the fonn of four coupled equations for the electric and magnetic fields. These are known as Maxwell s equations. In free space, these equations take the fonn ... 

To this point, we have considered only the radiation field. We now turn to the interaction between the matter and the field. According to classical electromagnetic theory, the force on a particle with charge e due to the electric and magnetic fields is... 

Another powerftil class of instmnientation used to study ion-molecule reactivity is trapping devices. Traps use electric and magnetic fields to store ions for an appreciable length of time, ranging from milliseconds to thousands of seconds. Generally, these devices mn at low pressure and thus can be used to obtain data at pressures well below the range in which flow tubes operate. 

Probing electric and magnetic fields, and the effects induced by them, is of obvious mterest in many areas of science and technology. We considered earlier the influence of such perturbations in a general fashion in section Bl.5.2.2. Here we describe some related experimental measurements and applications. Electric fields act to break hrversion and thus... 

Using the above relationship between the electric and magnetic field amplitudes from equation (Bl.26.15)) ... 

The transport of particles in the plasma is diffusive or convective for the neutrals, whereas the charge carriers move under the influence of the external and internal electric and magnetic fields. The drift velocityv of the charged particles is proportional to the electric field E ... 

Scanning for metastable ions requires adjustment of electric and magnetic fields which can be adjusted individually or in conjunction with each other. If two fields are automatically adjusted at the same time, it is known as linked scanning. It is important to remember that metastable ions are not the product ions m2 but are the ions undergoing fragmentation (precursor ions mj). 

As with a light beam and glass lenses, an ion beam can be directed and focused using electric and magnetic fields, often called lenses by analogy with their optical counterparts. 

The system of electric and magnetic fields or lenses is called the ion optics of the mass spectrometer. Electric lenses correct aberrations in the shape of the ion beam. 

Electric and magnetic fields can be used sequentially to focus the beam of ions. The use of crossed electromagnetic fields is described in the discussion of quadrupoles (Chapter 25). 

Another important property of electric and magnetic fields is their ability to separate ions according to their individual masses (m, mj,. .., m ) or, more strictly, their mass-to-charge ratio (mj/z, raji,. mjz). 

By changing the strengths of the electric and magnetic fields, ions of different m/z values can be focused at just one spot (the collector). 

From the strengths of the electric and magnetic fields, m/z values are obtained. 

Wien analyzer. A velocity filter with crossed homogeneous electric and magnetic fields for transmitting only ions of a fixed velocity. 

In this discussion we define the x direction to be the direction of propagation of the light waves. This means that the yz plane contains the oscillating electrical and magnetic fields which carry the energy of the radiation. Only the electric field concerns us in scattering. Since the oscillation is periodic in both time t and location x, the electric field can be represented by the equation... 

The transverse modes are labelled TEM , where TEM stands for transverse electric and magnetic (field) m and I are integers that refer to the number of vertical and horizontal... 

Once the primary electron beam is created, it must be demagnified with condenser lenses and then focused onto the sample with objective lenses. These electron lenses are electromagnetic in nature and use electric and magnetic fields to steer the electrons. Such lenses are subject to severe spherical and chromatic aberrations. Therefore, a point primary beam source is blurred into a primary beam disk to an extent dependent on the energy and energy spread of the primary electrons. In addition, these lenses are also subject to astigmatism. AH three of these effects ultimately limit the primary beam spot size and hence, the lateral resolution achievable with sem. 

One of the benefits of an OMC is its immunity against static electricity and magnetic fields. Its capacity is 4.11 MByte in the version mentioned when used as a ROM, 2.6 MByte for the WORM version. 

The selective redection of chiral nematic Hquid crystals has also been used to develop sensors for pressure, radiation (especially infrared), wind shear over surfaces, stmctural fatigue, and foreign chemical vapor (48). Other types of Hquid crystals have been used to make sensors to measure both electric and magnetic fields. 

Now the effective conductivity ia the direction of the electric field is <7/(1 + /5 ), ie, the scalar conductivity reduced by a factor of (1 + /5 ) by the magnetic field. Also, the electric current no longer flows in the direction of the electric field a component j exists which is perpendicular to both the electric and magnetic fields. This is the Hall current. The conductivity in the direction of the Hall current is greater by a factor of P than the conductivity in the direction of the electric field. The calculation of the scalar conductivity starts from its definition ... 

In order to calculate the distribution function must be obtained in terms of local gas properties, electric and magnetic fields, etc, by direct solution of the Boltzmann equation. One such Boltzmann equation exists for each species in the gas, resulting in the need to solve many Boltzmann equations with as many unknowns. This is not possible in practice. Instead, a number of expressions are derived, using different simplifying assumptions and with varying degrees of vaUdity. A more complete discussion can be found in Reference 34. 

Oak Ridge Associated Universities Panel for the Committee on Interagency Radiation Research and PoHcy Coordination, Health Effects ofEow Frequemy Electric and Magnetic Fields, Washington, D.C., June 1992. 

The more penetrating P-rays were easily studied. In 1899 their direction of deflection in a magnetic field was observed, indicating the negative charge. Then Becquerel was able to deflect P-rays in electric and magnetic fields and thereby deterrnined the charge-to-mass ratio. This ratio showed that the mass was much smaller than that of any atom and corresponded to that of electrons. 

In 1903, Rutherford and associates were finally able to deflect the a-rays by electric and magnetic fields, showing that these are positively charged. Measurement of the charge-to-mass ratio indicated that a-rays were of atomic dimensions. In 1908 definitive experiments showed a-rays to be doubly chaiged helium atoms, ie, helium nuclei. 

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