# Electric And Magnetic Field Theory Pdf

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- Basic electromagnetic field theory
- Maxwell's equations
- Classical Theory of Electric and Magnetic Fields
- Electromagnetic field

*Bakshi, U. Bakshi — Co-ordinate Systems and Transformation : Cartesian co-ordinates, Circular cylindrical co-ordinates, Spherical co-ordinates.*

## Basic electromagnetic field theory

An electromagnetic field also EM field is a classical i. The electromagnetic field propagates at the speed of light in fact, this field can be identified as light and interacts with charges and currents. Its quantum counterpart is one of the four fundamental forces of nature the others are gravitation , weak interaction and strong interaction.

The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges currents ; these two are often described as the sources of the field.

The way in which charges and currents interact with the electromagnetic field is described by Maxwell's equations and the Lorentz force law.

From a classical perspective in the history of electromagnetism , the electromagnetic field can be regarded as a smooth, continuous field , propagated in a wavelike manner. By contrast, from the perspective of quantum field theory , this field is seen as quantized; meaning that the free quantum field i.

Note that the quantized field is still spatially continuous; its energy states however are discrete the field's energy states must not be confused with its energy values , which are continuous; the quantum field's creation operators create multiple discrete states of energy called photons. The electromagnetic field may be viewed in two distinct ways: a continuous structure or a discrete structure. Classically, electric and magnetic fields are thought of as being produced by smooth motions of charged objects.

For example, oscillating charges produce variations in electric and magnetic fields that may be viewed in a 'smooth', continuous, wavelike fashion. In this case, energy is viewed as being transferred continuously through the electromagnetic field between any two locations. For instance, the metal atoms in a radio transmitter appear to transfer energy continuously.

This view is useful to a certain extent radiation of low frequency , but problems are found at high frequencies see ultraviolet catastrophe. The electromagnetic field may be thought of in a more 'coarse' way. Experiments reveal that in some circumstances electromagnetic energy transfer is better described as being carried in the form of packets called quanta in this case, photons with a fixed frequency.

Planck's relation links the photon energy E of a photon to its frequency f through the equation: [5]. Although modern quantum optics tells us that there also is a semi-classical explanation of the photoelectric effect —the emission of electrons from metallic surfaces subjected to electromagnetic radiation —the photon was historically although not strictly necessarily used to explain certain observations. It is found that increasing the intensity of the incident radiation so long as one remains in the linear regime increases only the number of electrons ejected, and has almost no effect on the energy distribution of their ejection.

Only the frequency of the radiation is relevant to the energy of the ejected electrons. This quantum picture of the electromagnetic field which treats it as analogous to harmonic oscillators has proven very successful, giving rise to quantum electrodynamics , a quantum field theory describing the interaction of electromagnetic radiation with charged matter. It also gives rise to quantum optics , which is different from quantum electrodynamics in that the matter itself is modelled using quantum mechanics rather than quantum field theory.

In the past, electrically charged objects were thought to produce two different, unrelated types of field associated with their charge property. An electric field is produced when the charge is stationary with respect to an observer measuring the properties of the charge, and a magnetic field as well as an electric field is produced when the charge moves, creating an electric current with respect to this observer.

Over time, it was realized that the electric and magnetic fields are better thought of as two parts of a greater whole—the electromagnetic field. Until , when the Danish physicist H. Once this electromagnetic field has been produced from a given charge distribution, other charged or magnetised objects in this field may experience a force.

If these other charges and currents are comparable in size to the sources producing the above electromagnetic field, then a new net electromagnetic field will be produced. Thus, the electromagnetic field may be viewed as a dynamic entity that causes other charges and currents to move, and which is also affected by them. These interactions are described by Maxwell's equations and the Lorentz force law.

This discussion ignores the radiation reaction force. The behavior of the electromagnetic field can be divided into four different parts of a loop: [8]. A common misunderstanding is that a the quanta of the fields act in the same manner as b the charged particles, such as electrons, that generate the fields. The speed ratio between charged particles in a conductor and field quanta is on the order of one to a million. Maxwell's equations relate a the presence and movement of charged particles with b the generation of fields.

Those fields can then affect the force on, and can then move other slowly moving charged particles. Charged particles can move at relativistic speeds nearing field propagation speeds, but, as Albert Einstein showed [ citation needed ] , this requires enormous field energies, which are not present in our everyday experiences with electricity, magnetism, matter, and time and space. The feedback loop can be summarized in a list, including phenomena belonging to each part of the loop: [ citation needed ].

There are different mathematical ways of representing the electromagnetic field. The first one views the electric and magnetic fields as three-dimensional vector fields. These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates.

As such, they are often written as E x, y, z, t electric field and B x, y, z, t magnetic field. If only the electric field E is non-zero, and is constant in time, the field is said to be an electrostatic field.

Similarly, if only the magnetic field B is non-zero and is constant in time, the field is said to be a magnetostatic field. However, if either the electric or magnetic field has a time-dependence, then both fields must be considered together as a coupled electromagnetic field using Maxwell's equations. With the advent of special relativity , physical laws became susceptible to the formalism of tensors.

Maxwell's equations can be written in tensor form, generally viewed by physicists as a more elegant means of expressing physical laws. The behavior of electric and magnetic fields, whether in cases of electrostatics, magnetostatics, or electrodynamics electromagnetic fields , is governed by Maxwell's equations.

In the vector field formalism, these are:. The units used above are the standard SI units. Inside a linear material, Maxwell's equations change by switching the permeability and permittivity of free space with the permeability and permittivity of the linear material in question. Inside other materials which possess more complex responses to electromagnetic fields, these terms are often represented by complex numbers, or tensors.

The Lorentz force law governs the interaction of the electromagnetic field with charged matter. When a field travels across to different media, the properties of the field change according to the various boundary conditions.

These equations are derived from Maxwell's equations. The tangential components of the electric and magnetic fields as they relate on the boundary of two media are as follows: [11]. Faraday's Law may be stated roughly as 'a changing magnetic field creates an electric field'. This is the principle behind the electric generator. Ampere's Law roughly states that 'a changing electric field creates a magnetic field'. Thus, this law can be applied to generate a magnetic field and run an electric motor.

Under these conditions, the electric and magnetic fields satisfy the electromagnetic wave equation : [12]. James Clerk Maxwell was the first to obtain this relationship by his completion of Maxwell's equations with the addition of a displacement current term to Ampere's circuital law.

Being one of the four fundamental forces of nature, it is useful to compare the electromagnetic field with the gravitational , strong and weak fields. The word 'force' is sometimes replaced by 'interaction' because modern particle physics models electromagnetism as an exchange of particles known as gauge bosons.

Sources of electromagnetic fields consist of two types of charge — positive and negative. This contrasts with the sources of the gravitational field, which are masses.

Masses are sometimes described as gravitational charges , the important feature of them being that there are only positive masses and no negative masses. Further, gravity differs from electromagnetism in that positive masses attract other positive masses whereas same charges in electromagnetism repel each other. The relative strengths and ranges of the four interactions and other information are tabulated below:.

When an EM field see electromagnetic tensor is not varying in time, it may be seen as a purely electrical field or a purely magnetic field, or a mixture of both. However the general case of a static EM field with both electric and magnetic components present, is the case that appears to most observers.

Observers who see only an electric or magnetic field component of a static EM field, have the other electric or magnetic component suppressed, due to the special case of the immobile state of the charges that produce the EM field in that case. In such cases the other component becomes manifest in other observer frames.

That is, a pure static electric field will show the familiar magnetic field associated with a current, in any frame of reference where the charge moves. Likewise, any new motion of a charge in a region that seemed previously to contain only a magnetic field, will show that the space now contains an electric field as well, which will be found to produces an additional Lorentz force upon the moving charge.

Thus, electrostatics , as well as magnetism and magnetostatics , are now seen as studies of the static EM field when a particular frame has been selected to suppress the other type of field, and since an EM field with both electric and magnetic will appear in any other frame, these "simpler" effects are merely the observer's.

The "applications" of all such non-time varying static fields are discussed in the main articles linked in this section. An electromagnetic field very far from currents and charges sources is called electromagnetic radiation EMR since it radiates from the charges and currents in the source, and has no "feedback" effect on them, and is also not affected directly by them in the present time rather, it is indirectly produced by a sequences of changes in fields radiating out from them in the past.

EMR consists of the radiations in the electromagnetic spectrum , including radio waves , microwave , infrared , visible light , ultraviolet light , X-rays , and gamma rays. The many commercial applications of these radiations are discussed in the named and linked articles. A notable application of visible light is that this type of energy from the Sun powers all life on Earth that either makes or uses oxygen. This type of dipole field near sources is called an electromagnetic near-field.

Changing electric dipole fields, as such, are used commercially as near-fields mainly as a source of dielectric heating. Otherwise, they appear parasitically around conductors which absorb EMR, and around antennas which have the purpose of generating EMR at greater distances. Changing magnetic dipole fields i. These include motors and electrical transformers at low frequencies, and devices such as metal detectors and MRI scanner coils at higher frequencies.

Sometimes these high-frequency magnetic fields change at radio frequencies without being far-field waves and thus radio waves; see RFID tags. See also near-field communication. Further uses of near-field EM effects commercially, may be found in the article on virtual photons , since at the quantum level, these fields are represented by these particles. Far-field effects EMR in the quantum picture of radiation, are represented by ordinary photons.

The potential effects of electromagnetic fields on human health vary widely depending on the frequency and intensity of the fields. The potential health effects of the very low frequency EMFs surrounding power lines and electrical devices are the subject of on-going research and a significant amount of public debate.

NIOSH has issued some cautionary advisories but stresses that the data are currently too limited to draw good conclusions. Employees working at electrical equipment and installations can always be assumed to be exposed to electromagnetic fields. The exposure of office workers to fields generated by computers, monitors, etc. However, industrial installations for induction hardening and melting or on welding equipment may produce considerably higher field strengths and require further examination.

If the exposure cannot be determined upon manufacturers' information, comparisons with similar systems or analytical calculations, measurements have to be accomplished.

The results of the evaluation help to assess possible hazards to the safety and health of workers and to define protective measures.

## Maxwell's equations

Electromagnetism is a branch of physics involving the study of the electromagnetic force , a type of physical interaction that occurs between electrically charged particles. The electromagnetic force is carried by electromagnetic fields composed of electric fields and magnetic fields , and it is responsible for electromagnetic radiation such as light. It is one of the four fundamental interactions commonly called forces in nature , together with the strong interaction , the weak interaction , and gravitation. Electromagnetic phenomena are defined in terms of the electromagnetic force, sometimes called the Lorentz force , which includes both electricity and magnetism as different manifestations of the same phenomenon. The electromagnetic force plays a major role in determining the internal properties of most objects encountered in daily life. The electromagnetic attraction between atomic nuclei and their orbital electrons holds atoms together.

Doug Tougaw , Valparaiso University. Download Chapter 7 - Potential Energy and Voltage 1. Download Chapter 10 - Electric Currents and Power 1. Download Chapter 11 - Magnetic Fields 1. Download Chapter 16 - Faraday's Law of Induction 1. Download Chapter 26 - Smith Charts 1. Download Chapter 31 - Antenna Parameters 1.

An electromagnetic field also EM field is a classical i. The electromagnetic field propagates at the speed of light in fact, this field can be identified as light and interacts with charges and currents. Its quantum counterpart is one of the four fundamental forces of nature the others are gravitation , weak interaction and strong interaction. The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges currents ; these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is described by Maxwell's equations and the Lorentz force law.

## Classical Theory of Electric and Magnetic Fields

Classical Theory of Electric and Magnetic Fields is a textbook on the principles of electricity and magnetism. This book discusses mathematical techniques, calculations, with examples of physical reasoning, that are generally applied in theoretical physics. This text reviews the classical theory of electric and magnetic fields, Maxwell's Equations, Lorentz Force, and Faraday's Law of Induction.

*Electric and magnetic fields are present around any electrical circuit, whether it carries alternating current AC or direct current DC electricity. In this chapter we intend to show that the study of electromagnetic field theory is vital to understanding many phenomena that take place in electrical engineering.*

### Electromagnetic field

Title page PDF. Dedication PDF. Preface PDF.

One of the side effects of each electrical device work is the electromagnetic field generated near its workplace. All organisms, including humans, are exposed daily to the influence of different types of this field, characterized by various physical parameters. Therefore, it is important to accurately determine the effects of an electromagnetic field on the physiological and pathological processes occurring in cells, tissues, and organs. Numerous epidemiological and experimental data suggest that the extremely low frequency magnetic field generated by electrical transmission lines and electrically powered devices and the high frequencies electromagnetic radiation emitted by electronic devices have a potentially negative impact on the circadian system.

TEXTBOOK CONTENTS, FILES. Front-End Matter. Title page (PDF). Dedication (PDF). Preface.

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The physicist James Clerk Maxwell in the 19th century based his description of electromagnetic fields on these four equations, which express experimental laws.

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